Research & Publications by L. Gerard van Willigenburg
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Introduction / Subjects / Publications / Submitted publications / Software
Personal profile:

Assistant professor (b. 1958) at Wageningen University, received his M.Sc. in Electrical Engineering from Delft University of Technology (1983) and a Ph.D. degree from Delft University of Technology (1991) for his thesis entitled "Digital optimal control of rigid manipulators".
Professional and private interests:
 My professional research interests include digital optimal control, reducedorder control, adaptive control and model predictive control (receding horizon control). The application areas are indoor climate control (greenhouses, stables, buildings, stadiums), robot control, automatic guidance of agricultural field machines and the control of processes in the food industry (bioreactors, sterilization, drying). My private research interests also include fundamentals of physics (thermodynamics, relativity and quantummechanics)
Appropriate control system design methodologies
Control is an applied science. Control theorists have developed an impressive amount of sophisticated control methodologies under all kinds of different assumptions. These assumptions are hardly ever all satisfied in practice. Therefore control practitioners face the problem of selecting an appropriate control system design methodology which is not an entirely scientific or mathematical issue. An interesting line of research is to investigate to what extend science and mathematics can help and how to bridge the remaining gap. A first attempt in this direction has been published [L.G. Van Willigenburg et al. Preprints IFAC World Congres, Prague, 38 July, 2005, 04926.pdf ]. For a visualisation of this result see appropriate poster.pdf .
Introduction / Subjects /
Publications / Submitted publications
/ Software
Digital optimal control: Short introduction
For nonlinear systems digital optimal controllers are synthesized that explicitly take into account the intersample (continuoustime) behaviour of the controlled system, the digital nature of the controller, and the way in which the system is sampled. Synchronous (conventional), asynchronous and random sampling schemes are considered [R.E. Kalman and J.E. Bertram, 1959, "A unified approach to the theory of sampling systems", Journal of the Franklin Institute, 67, 405436 ]. Based on an accurate mathematical model of the system and a mathematical criterion describing the control objectives, a digital optimal control sequence and a digital optimal LQG compensator are computed offline. Both the digital optimal control sequence and the digital optimal LQG compensator are stored in the controller memory. The only online computations that need to be performed by the controller are a small number of matrix vector multiplications to compute control corrections from the online measured data. This type of control of nonlinear systems is approximately optimal if the model structure and its parameter values are well established and if the remaining uncertainty is small [M. Athans, 1971, "The role and use of the stochastic LinearQuadraticGaussian problem in control system design", IEEE Trans. Aut. Contr., AC16(6), 529552 ]. If the model structure is well established but some of the parameter values are not, and the online data contain information regarding these parameter values, actively adaptive controllers are required. As opposed to other (passively) adaptive controllers, actively adaptive controllers take into account the need to identify the parameters in selecting the control [Y. BarShalom, 1981, "Stochastic dynamic programming: Caution and probing", IEEE Trans. Aut. Contr., AC26(5), 11841195 ]. Since most of our research regarding digital optimal control and LQG compensation of nonlinear systems has been completed actively (dual) adaptive controllers have become a new subject of our research [L.G. Van Willigenburg et al. Preprints IFAC World Congres, Prague, 38 July, 04926.pdf ].
The application areas are indoor climate control (greenhouses, stables, storage buildings), the control of mechanical systems (agricultural field machines, a tomato picking robot), processes in the food industry (sterilization, drying) and economics.
Introduction / Subjects / Publications / Submitted publications / Software
Digital optimal control: Subjects
Introduction / Subjects
/ Publications / Submitted publications
/ Software
Systems theory & physics: Short introduction
Systems theory lies at the heart of any type of mathematical
modeling. Therefore modeling the fundamentals of physics may largely benefit from
systems theory. In building models physicists often presume systems to be in equilibrium.
Although generally for very good reasons the equilibrium assumptions and their justification
may sometimes lead to erroneous models or unprovable mathematical requirements.
A good example is the equilibrium assumptions that underly statistical mechanics
and thermodynamics. In our opinion statistical mechanics, and in fact any type of
statistical modeling, is a "last resort" if no apriori knowledge or insight is
available. Starting from very simple linear dynamics at the microscale of physical
systems we showed how the second law of thermodynamics emerges from them. No statistical
mechanics or equilibrium conditions are needed to obtain this result [48].
Motivated by this insight we are currently investigating the further consequences
of this result for thermodynamics. In addition we are investigating the modeling
and understanding of possible energy transfer mechanisms at the level of fundamental
physical particles, particularly electrons and photons. This issue appears to be
connected to the question why the speed of light is always observed to be constant.
This constant velocity, independent of observer motion, is a widely accepted postulate
of special relativity but not all well understood.
Systems theory & physics: Subjects
 Equipartition and the second law of thermodynamics
 Connecting and unmasking relativity and quantum theory
Introduction / Subjects / Publications / Submitted publications / Software
Asynchronous and aperiodically sampled digital control systems, multirate control systems
Asynchronous and aperiodic sampling very often occur in digital control systems. This may be due to the fact that the computer is timeshared or part of a computer network or due to technical imperfections of the instrumentation. Asynchronous and aperiodic sampling is preferred over synchronous sampling if some measurements are cheap and some are expensive. Asynchronous and aperiodic sampling may be applied intentionally to eliminate hidden oscillations, to reduce the influence of intelligent disturbances, or to increase stabilizability. Asynchronous and aperiodic sampling occurs in economic and biological systems. The theory and several related algorithms concerning the digital optimal control and LQG compensation of nonlinear systems have been generalized from synchronous to asynchronous and aperiodic sampling. Publications: [9], [10], [11], [23], [41].
Introduction / Subjects / Publications / Submitted publications / Software
Randomly sampled digital control systems, randomized digital optimal control
Random sampling occurs in computer controlled systems if the computer is timeshared or is part of a computer network. Random sampling is also caused by technical imperfections in the instrumentation. Random sampling occurs in economic and biological systems and when a stochastic process like a radar or sonar echo governs the sampling . Random sampling may be applied intentionally to eliminate hidden oscillations, to reduce the influence of intelligent disturbances, or to increase stabilizability. Theory and algorithms to synthesize digital optimal full and reducedorder LQG controllers for randomly sampled linear systems have been developed. Publication: [24].
Introduction / Subjects / Publications / Submitted publications / Software
Reduced order LQG control, fixed order dynamic compensation, optimal projection equations
The conventional optimal (fullorder) LQG
compensator (controller) for systems with deterministic parameters is very well
known and very well established computationally and is a very powerful tool to control
both linear and nonlinear systems. Especially
if the dimension of the system model is large and the sampling intervals are small
reducing the order of the LQG compensator (controller) becomes vital. Then optimal
fullorder LQG design becomes optimal reducedorder LQG design. For this more difficult
problem strengthened discretetime optimal projection equations have been developed,
which in contrast to the conventional version, are equivalent to firstorder necessary
optimality conditions and the minimality of the compensator. Based on these equations
numerical algorithms have been developed to compute optimal reducedorder LQG compensators
for timeinvariant and timevarying discretetime systems, with either deterministic
or white parameters. The algorithms need further investigation, optimization and
proof. Publications: [13], [15],
[18], [19], [23],
[25], [39].
The optimal fullorder
compensator for systems with white parameters (multiplicative white noise) generalises
the LQG compensator result and therefore is more powerful while it is also well
established computationally [W.L. De Koning, 1992, "Compensatability and optimal
compensation of systems with white parameters",
IEEE Trans.
Aut. Contr., AC37(5), 579588 ]. Nevertheless it is not very well known despite
the fact that systems with white parameters arise in the design of digital control
systems if some of the parameters are white, such as the parameters of the plant
or the sampling period. Furthermore parameters may be assumed to be white to design
nonconservative robust control systems.
Introduction / Subjects / Publications / Submitted publications / Software
Robust control, systems with white parameters (mutiplicative white noise), compensatability & optimal compensation, delta operator and UD factored algorithm formulations
White system parameters (multiplicative white noise) may destabilize
a system, as opposed to additive white noise. White parameters may therefore be
used to design robust controllers. Also they may result from stochastic sampling
of a continuoustime system
[24]. LQG like controllers may be
designed for these systems. The optimal LQG like output feedback controller is called
an optimal compensator computed from an LQG like optimal compensation problem.
Compensatability and the optimal fullorder
compensator for systems with white parameters generalises the LQG result and therefore
is more powerful while it is also well established computationally [W.L. De Koning,
1992, "Compensatability and optimal compensation of systems with white parameters",
IEEE Trans.
Aut. Contr., AC37(5), 579588 ]. Nevertheless it is not very well known despite
the fact that systems with white parameters arise in the design of digital control
systems if some of the parameters are white, such as the parameters of the plant
or the sampling period. Furthermore parameters may be assumed to be white to design
nonconservative robust control systems. Formulation of the full and
reducedorder control and compensation problems in the delta domain offers the possibility
to unify continuous and discretetime results. It also enables transferring discretetime
results to continuoustime. Finally it allows for more efficient and accurate control
designs, especially if the sampling interval becomes very small. These opportunities
have been exploited by us in the papers [19], [51],
[52], [54].
UD factorization has the potential to improve computational efficiency and accuracy.
A formulation of the full and reducedorder LQG problem by means of Lyapunov equations
offers alternative ways for UD factorization [39].
For discretetime systems with white stochastic parameters (multiplicative white
noise) UD factorization of the algorithm for fullorder and reducedorder compensation
is new and associated with the minimal realization of matrix valued white stochastic
processes [55],[60].
Introduction / Subjects / Publications / Submitted publications / Software
Temporal linear system structure
LQG perturbation feedback controllers for nonlinear systems are often based on the linearised dynamics about optimal control and state trajectories. These linearised dynamics constitute a timevarying linear system that may be temporarily uncontrollable or temporarily unreconstructable. This highly relevant information for the LQG feedback controller design is not detected by any of the four conventional Kalman decompositions. Temporal uncontrollability is associated to differential controllability in continuoustime and to Nstep controllability is discretetime. The description and detection of temporal uncontrollability and temporal unreconstructability in both continuous and discrete time requires the introduction of systems with timevarying (state) dimensions. These type of systems moreover enable a well rounded realization theory for timevarying linear systems as already suggested by Kalman in 1969. The description of systems with timevarying dimensions in combination with suitable Kalman decompositions does enable the description and detection of temporal uncontrollability and temporal unreconstructability [43], [45], [47]. Associated to temporal uncontrollability and temporal unreconstructability are the properties temporal and differential stabilizability and detectability [52], [57], [58]. They determine whether temporal uncontrollability and temporal unreconstructability cause temporal instability of the closed loop system. In case of perturbation feedback control of nonlinear systems about trajectories causes and fixes of temporal uncontrollability of the linerized dynamics about the trajectory have been determined. These are linked to the structure of the nonlinear system dynamics as well as properties of the trajectory to be tracked [S20161].Introduction / Subjects / Publications / Submitted publications / Software
Optimal sampling rates and LQG control
The existence of optimal sampling rates and a way to compute them have been established for digital timevarying LQG tracking problems with an exogenous component and costs associated to taking measurements. They have been published in an economic context. Currently the extension to unconventional sampling schemes and the digital optimal control of nonlinear systems is under investigation. Publications: [3], [4], [8], [15], [18], [23].Introduction / Subjects / Publications / Submitted publications / Software
Actively (dual) adaptive receding horizon controllers
Digital optimal control and LQG compensation of nonlinear systems is approximately optimal only if the model structure and its parameter values are well established and if the remaining uncertainty is small and may be represented by small additive white noise. If the model structure is well established but some of the parameter values are not, while the online data contain information regarding these parameter values, actively adaptive controllers are required. As opposed to other (passively) adaptive controllers, actively adaptive controllers take into account the need to identify the parameters in selecting the control [Y. BarShalom, 1981, "Stochastic dynamic programming: Caution and probing", IEEE Trans. Aut. Contr., AC26(5), 11841195 ]Based on an extensive literature search an actively adaptive digital controller structure has been developed which involves a least squares parameter estimator and a receding horizon optimal controller. Besides being actively adaptive the advantage of this structure is that it consists of two well established parts in the control literature being the least squares parameter estimator and the receding horizon optimal controller. Due to the receding horizon optimal controller this structure computes a reasonably accurate "cost to go" and due to the least squares parameter estimator it exploits fully all the currently collected data to estimate the uncertain parameters. A disadvantage is that this controller structure is computationally expensive, both in realtime and in simulation. In realtime this problem can be relaxed by selecting larger sampling periods which does not pose a problem since our digital controller design procedure explicitly considers the intersample behaviour. The current application areas are greenhouse climate control and the control of drying and sterilization processes where initially some of the model parameters are not very well known. Related publication: [40]
Introduction / Subjects / Publications / Submitted publications / Software
Minimal realization of timevarying systems with timevarying dimensions
The minimality of discretetime linear timevarying systems is fundamental to optimal digital reducedorder LQG controller synthesis. From the associated LQG theory minimal realizations with timevarying dimensions emerge "automatically". The associated realization theory however does not consider the influence of nonzero initial conditions, while the initial condition of the optimal LQG controller is usually nonzero. In [25], [30] the minimality property is generalized for systems with nonzero initial conditions. After this generalization minimality is no longer equivalent with reachability together with observability but with weak (modified) reachability together with observability. Weak reachability is a weaker property than reachability and both properties rely partly on an empty matrix concept. For empty initial conditions weak reachability and reachability become identical [44], [46].When designing perturbation feedback controllers for nonlinear systems based on linearized dynamics the linearized dynamics may be temporarily uncontrollable/unreconstructable [1]. To detect this as well as to obtain a satisfactory realization theory for timevarying continuoustime systems piecewise constant rank systems are introduced. They constitute continuoustime systems with timevarying dimensions. In combination with a Kalman decomposition based on differential controllability and differential reconstructability they enable the description and detection of temporal system structure as well as temporal uncontrollability and/or unreconstructability [43], [45], [47].
Introduction / Subjects / Publications / Submitted publications / Software
Applications of receding horizon controllers
Receding horizon controllers are especially appropriate for control problems where the data provide accurate state information but poor or no information concerning possible model improvements, such as the values of certain parameters. The current applications areas are greenhouse climate control and the control of sterilization and drying processes. Publications: [11], [12], [16], [21], [22].
Introduction / Subjects / Publications / Submitted publications / Software
Digital timeoptimal control of mechanical systems
Algorithms for the digital timeoptimal control of mechanical systems, subjected to actuator constraints, have been developed. It concerns either systems that travel a path in space or systems that travel from a specified initial to a specified final configuration. For ndimensional nonlinear systems, linear in the control variables, it has been shown that nonsingular solutions to timeoptimal control problems with bounded control and fixed initial and final states generally have no more than a total of n1 switch times. Publications: [1], [2], [5], [29] .
Introduction / Subjects / Publications / Submitted publications / Software
Solution of optimal control problems with state constraints using Chebyshev polynomials
A known numerical algorithm based on Chebyshev polynomials [J. Vlassenbroeck, "A Chebyshev polynomial method for optimal control with state constraints", 1988, Automatica , vol. 24 (4), pp. 499506 ] used to solve continuoustime optimal control problems, including state and control constraints, has been investigated and programmed in Matlab to be applicable to general problems.
Introduction / Subjects / Publications / Submitted publications / Software
Application of digital controllers in economics
The application of digital optimal fixed and reducedorder LQG controllers, especially those for systems with white parameters, has large potentials in economics. Therefore the transformation of digital control problems, involving systems with stochastic parameters, into discretetime equivalents, in the case of unconventional sampling, is under investigation. Publications: [8], [17].
Introduction / Subjects / Publications / Submitted publications / Software
Greenhouse climate control
The digital optimal control algorithm for nonlinear systems [10] has been successfully implemented, as a receding horizon optimal controller, in a greenhouse optimal control experiment [12]. Difficulties concerning different timescales of the system have been partially solved but remain under investigation. Publications: [6], [7], [11], [12], [16a], [34], [37].
Introduction / Subjects / Publications / Submitted publications / Software
Mechanical design and digital optimal control of a tomato harvester
Sponsored by DISC (Dutch Institute of Systems and Control) the mechanical design and digital control of a tomatopicking robot is under investigation. An endeffector to pick all the fruits on a single truss has been designed is currently being manufactured. Currently the tomato picking robot is the MKII of Eshed Robotec. Software to control both the endeffector and the robot is being developed and will be implemented using MATLAB and dSPACE control equipment. Publications: [22a], [29], [36], [42].
Introduction / Subjects / Publications / Submitted publications / Software
Automatic guidance and high precision control of agricultural field machines
The automatic guidance and high precision control of agricultural field machines is under investigation. The research is performed in corporation with IMAGDLO (Van Zuydam). Among the sensors used is GPS. Also the design of a digital control system to control the movement of a plow is under investigation. This research is conducted in corporation with Rumpstadt, an agricultural field machine manufacturer. Publication: [14] .
Introduction / Subjects / Publications / Submitted publications / Software
Control of laboratory setups
Digital LQG tracking controllers have been successfully implemented on the "ball and plate" laboratory setup which constitutes an almost linear twoinput system. A "helicopter type" laboratory setup has been manufactured, which constitutes a non linear multivariable twoinput system. The laboratory setups are used for education and for evaluating digital optimal control algorithms designed for different sampling strategies. Software, based on MATLAB and dSPACE control equipment, has been developed, that allows for the implementation of arbitrary sampling strategies (asynchronous, random).
Introduction / Subjects / Publications / Submitted publications / Software
Evolutionary algorithms for optimal control
Several nonlinear optimal control problems
in the chemical and food industry as well as in the area of climate control, have
local solutions. The majority of optimal control algorithms are gradient based and
are therefore inclined to find local solutions. Evolutionary algorithms have the
potential of locating global solutions but there efficiency is generally poor. The
work of Lopez Cruz [26], [27],
[28], [32], [33]
has (finally) convinced me that differential evolution algorithms, an efficient
type of evolutionary algorithm, can compete and outperform existing optimal control
algorithms developed to find global solutions.
Introduction / Subjects / Publications / Submitted publications / Software
Equipartition and the second law of thermodynamics
Having to teach a small course on thermodynamics raised our interest
in the foundations of the second law of thermodynamics that are still debated among
scientists. In a recent paper [48]
we investigated these foundations starting from the hypothesis that the second law
should have a "Darwanian explanation" that entirely follows from the simple reversible
Hamiltonian dynamics of particles at the microscale. This work was also inspired
by a recent book that takes a dynamical systems approach to thermodynamics (Haddad,
Chellaboina, Nersesov, 2005, Thermodynamics A dynamical systems approach, Princeton
University Press) and by some recent publications on equipartition of energy (Bernstein
& Bhat, Rapisarda & Willems) also from a dynamical systems perspective.
Introduction / Subjects / Publications / Submitted publications / Software
Connecting and unmasking relativity and quantum theory
Many people tell you not to even try to understand physics, especially Einsteinâ€™s relativity and most of all quantum theory. Even among physicists themselves the advice not to try to understand quantum theory is heard. The good news is that it is actually quite simple to understand both! To see this it is necessary to cut of the mask of both relativity and quantum theory. Both are not entirely without error and these errors have obscured what can now be simply understood. From an appropriate inspection of the history of relativity and quantum theory modifications of both are proposed. Also by inspection of the literature part of these modifications can be found, but only separately. When combined these provide a conceptually very simple model of physics that is largely equivalent to acoustic waves moving in air. Particles do not exist, they are local manifestations of wave structures so matter has a wave structure (WSM: wave structure of matter) immediately explaining waveparticle duality. At the very bottom of this simple model describing wave propagation lies a computational difficulty. That probably explains why all kinds of approximate models have been proposed leading to many paradoxes as it comes to understanding fundamental physics. Although the understanding of fundamental physics through our proposed model becomes easy the challenge shifts towards explaining how all known physics emerges from this simple model. Wave interference, wave modulation, and the Doppler effect will be prominent parts of these explanations. A paper describing these ideas and results has been published [63].
Mail comments, suggestions or questions to: Gerard van Willigenburg
[0] L.G.
Van Willigenburg, 1989, "True digital tracking for an orthogonal robot
manipulator",
Proceedings. ICCON '89. IEEE International Conference on Control and
Applications.
[1] L.G.
Van Willigenburg, 1990, "Firstorder controllability and the time optimal control
problem for rigid articulated arm robots with friction",
Int.
J. Contr., Vol. 51, no 6, pp. 11591171.
[2] L.G. Van Willigenburg, 1991, "Computation of timeoptimal
controls applied to rigid manipulators with friction",
Int.
J. Contr., Vol. 54, no 5, pp. 10971117.
[3] L.G. Van Willigenburg, W.L. De Koning, 1992, "The digital
optimal regulator and tracker for stochastic timevarying systems",
Int.
J. Syst. Sci., Vol 23, no 12, pp. 23092322.
[4] L.G. Van Willigenburg, 1992, "Computation of the digital
LQG regulator and tracker for timevarying systems",
Opt.
Contr. Appl. Meth., Vol. 13, pp. 289299 , request associated Matlab software:
ml4.tar
[5] L.G. Van Willigenburg, 1993, "Computation and implementation
of digital timeoptimal feedback controllers for an industrial XY robot subjected
to path, torque and velocity constraints",
Int. J.
Rob. Res., Vol. 12, no 5, pp. 420433.
[6] M. Tchamitchian, L.G. Van Willigenburg, G. Van Straten, 1993,
"Optimal control applied to tomato crop production in a greenhouse",
Proceedings
of the 2nd European Control Conference, Groningen, The Netherlands, June 28July
4, 1993, pp. 13481352.
[7] R.F. Tap, L.G. Van Willigenburg, G. Van Straten, 1993, "Optimal
control of greenhouse climate: computation of the influence of fast and slow dynamics",
Proceedings 12th IFAC World Congress, Sydney Australia, 1823 July 1993.
[8] J.C. Engwerda, L.G. Van Willigenburg, 1995, "Optimal SamplingRates
and Tracking Properties of Digital LQ and LQG Tracking Controllers for Systems with
an exogenous component and Costs Associated to Sampling".
Computational
Economics 8, pp. 107125, 1995., request associated Matlab software:
ml8.tar
[9] L.G. Van Willigenburg, W.L. De Koning, 1995, "Derivation
and computation of the digital LQG regulator and tracker in the case of asynchronous
and aperiodic sampling",
CTAT,
Vol. 10, no 4, part 5, pp. 20832098, request associated Matlab software:
ml9.tar
[10] L.G. Van Willigenburg, 1995, Digital optimal control and
LQG compensation of asynchronous and aperiodically sampled nonlinear systems",
Proceedings
3rd European Control Conference, Rome, Italy, September 1995, Vol. 1, pp. 496500.
[11] R.F. Tap, L.G. Van Willigenburg, G. Van Straten, 1996, "Receding
horizon optimal control of greenhouse climate using the lazy man weather prediction",
Proceedings of the 13th IFAC World Congress, San Francisco, USA, 30 June5 July,
1996, paper 4a01 3.
[12] R.F. Tap, L.G. Van Willigenburg, G. Van Straten, 1996,
"Experimental results of receding horizon optimal control of greenhouse climate",
Acta
Horticulturae, 406, pp. 229238.(Proceedings of the Second IFAC/ISHS Workshop
on Mathematical and Control Applications in Agriculture and Horticulture, Silsoe
UK, 1215 sept. 1994).
[13] W.L. De Koning, L.G. van Willigenburg, 1998, "Numerical
algorithms and issues concerning the discretetime optimal projection equations
for systems with white parameters",
Proceedings
UKACC International Conference on Control '98, 14 Sept. 1998, University of Swansea,
UK, Vol. 2, pp.16051610. , request associated Matlab software:
ml13.tar
[14] H.L. Dijksterhuis, L.G. Van Willigenburg, R.P. Van Zuydam,
1998, "Centimetreprecision guidance of moving implements in the open field: a simulation
based on GPS measurements", Computers and Electronics in agriculture, 20, pp. 185197.
[15] L.G. van Willigenburg, W.L. De Koning, 1999, "Optimal
reducedorder compensators for timevarying discretetime systems with deterministic
and white parameters",
Automatica,
35, 129138 , request associated Matlab software: ml15.tar
[16] Z.S. Chalabi, L.G. van Willigenburg, G. van Straten, 1999, "Robust optimal
receding horizon control of the thermal sterilization of canned food",
Journal
of Food Engineering, 40, pp. 207218.
[16a] G. Van Straten, R.F. Tap, L.G. Van Willigenburg, 1999,
"Sensitivity of online RHOC of greenhouse climate to adjoint variables for the
crop",
Proceedings
14th IFAC World Congres, Beiing, China, July 59, 1999, Paper no. K4a011.
[17] L.G. van Willigenburg, W.L. De Koning, 2000, "The equivalent
discretetime optimal control problem for timevarying continuoustime systems with
white stochastic parameters",
International
Journal of System Science, 31, 4, pp. 479487., request associated Matlab software:
ml17.tar
[18] L.G. Van Willigenburg, W.L. De Koning, 2000, "Numerical
algorithms and issues concerning the discretetime optimal projection equations",
European
Journal of Control, 6, 1, pp. 93110, request associated Matlab software:
ml18.tar
[19] L.G. van Willigenburg, W.L. De Koning, 2000, "Finite
and infinite horizon fixedorder LQG compensation using the delta operator",
Proceedings
UKACC International Conference on Control 2000, 47 September, Cambridge, UK, (paper002.pdf)
[20] E.J. Quirijns, L.G. Van Willigenburg, A.J.B. van
Boxtel, 2000, "New perspectives for optimal control of drying processes",
Proceedings
ADCHEM 2000 International Symposium on Advanced Control of Chemical Processes, pp.
437442, 1416 June, Pisa,Italy
[21] L.G. van Willigenburg, E.J. Van Henten, W.Th.M.
Van Meurs, "Three timescale receding horizon optimal control in a greenhouse with
a heat storage tank",
Proceedings
of the Agricontrol 2000 conference, 1214 July 2000 , Wageningen, The Netherlands
[22] M. Timmerman, L.G. van Willigenburg, A. Van 't
Ooster, "Automatic receding horizon optimal control of the natural ventilation in
cattle barns", MRS report 200011,
Proceedings
of the Agricontrol 2000 conference, 1214 July 2000., Wageningen, The Netherlands
[22a] E.J. van Henten, G. van Dijk, M.C. Kuypers, B.A.J.
van Tuijl, L.G. van Willigenburg, 2000, "Motion planning for a cucumber picking
robot",
Proceedings
of the Agricontrol 2000 conference, 1214 July 2000, Wageningen, The Netherlands,
pp. 3944.
[23] L.G. van Willigenburg, W.L. De Koning, 2001, "Synthesis
of digital optimal reducedorder compensators for asynchronously sampled systems",
International Journal of System Science, 32, 7, pp. 825835 , request associated
Matlab software: ml23.tar
[24] W.L. De Koning, L.G. van Willigenburg, 2001, Randomized
digital optimal control,
Chapter
12 in Non Uniform Sampling Theory and Practice , Kluwer Acadamic/Plenum Publishers,
ISBN 0306464454, Edited by Farokh Marvasti, request associated Matlab software:
ml24.tar
[25] L.G. Van Willigenburg, W.L. De Koning, 2002, "Minimal
and nonminimal optimal fixedorder compensators for timevarying discretetime
systems",
Automatica,
38, 1, pp. 157165.
[26] I.L. Lopez Cruz, L.G. van Willigenburg, G. van Straten,
2000, "Evolutionary algorithms for optimal control of chemical processes", Proceedings
of the IASTED International Conference on Control Applications, May 2427, Cancun
Mexico, pp. 155161.
[27] I.L. Lopez Cruz, L.G. van Willigenburg, G. van
Straten, 2001, "A parameter control strategy inside differential evolution algorithms
for optimal control", Proceedings of the IASTED International Conference on Artificial
Intelligence and Soft Computing, May 2124, Cancun, Mexico, pp. 211216.
[28] I.L. Lopez Cruz, L.G. van Willigenburg, G. van
Straten, 2001, "Optimal control of nitrate in lettuce by gradient and differential
evolution algorithms", Proceedings 4th IFAC workshop on Artificial Intelligence
in Agriculture, Budapest, Hungary, 68 June, pp. 123128.
[29] C.W.J. Hol, L.G, van Willigenburg, E.J. van Henten,
G. van Straten, 2001, "A new optimization algorithm for singular and nonsingular
digital timeoptimal control of robots",
Proceedings IEEE International Conference
on Robotics and Automation (ICRA), May 2126, Seoul, Korea, vol. 2, pp. 1136 1141.
[30] L.G. van Willigenburg, W.L. De Koning, 2002, "Minimality,
canonical forms and storage of finitehorizon discretetime compensators",
Preprints
IFAC World Congress, Barcelona, 2126 July, 2002, paper 984.
[31] G. van Straten, L.G. van Willigenburg, R.F. Tap,
2002, "The significance of crop costates for receding horizon optimal control of
greenhouse climate",
Control
Engineering Practice, 10, 625632.
[32] I.L. Lopez Cruz, L.G. van Willigenburg, G. van Straten,
2003. Efficient evolutionary algorithms for multimodal optimal control problems,
Journal of Applied Soft Computing 3 (2): 97122.
[33] I.L. Lopez Cruz, L.G. van Willigenburg, G. van Straten,
2003. Optimal control of nitrate in lettuce by a hybrid approach: differential evolution
and adjustable control weight gradient algorithms,
Computers and Electronics in Agriculture 40 (13): 179197.
[34] R.J.C. van Ooteghem, J.D. Stigter, L.G. Van Willigenburg,
G. Van Straten, 2004. "Optimal control of a solar greenhouse",
European Control
Conference 2003, University of Cambridge, Cambridge, United Kingdom, September 14,
2003.
[35] L.G. van Willigenburg, J. Bontsema, W.L. De Koning,
L. Valenzuela, C. Martinez, "Digital optimal reducedorder control of a solar power
plant",
Proceedings
of the UKACC Control 2004, Paper 205, Bath, UK, 69 September 2004.
[36] L.G. van Willigenburg, C.W.J. Hol, E.J. van Henten,
2004, "Online near minimum time path planning and control of an industrial robot
picking fruits",
Computers
and Electronics in Agriculture, 44, 3, 223237.
[37] Ooteghem, R.J.C. van; Stigter,
J.D.; Willigenburg, L.G. van; Straten, G. van (2004 )
Receding Horizon Optimal Control of a Solar Greenhouse.
GreenSys2004, Leuven, 2004 september 1216, In: GreenSys2004
Sustainable Greenhouse Systems : Greensys2004, Leuven, 1216 September 2004.
[38] L.G. van Willigenburg, J. Bontsema, W.L. De Koning,
L. Valenzuela, C. Martinez, 2004, "Direct reducedorder digital control of a solar
power plant", In: The improving human potential programme: access to research infrastructure
activities. research results at Plata Forma Solar de Almeria within the year 2003
access campaign, pp. 916, ISBN 8478344748.
[39] L.G. van Willigenburg, W.L. De Koning, 2004, "UDU
factored discretetime Lyapunov recursions solve optimal reducedorder LQG problems",
European
Journal of Control, 10, pp. 588601., request associated Matlab software:
ml39.tar. Discussions on this paper (one of them by D.C.
Hyland who discovered the optimal projection equations) and final comments from
us,
European
Journal of Control, 10, pp. 602613.
[40] L.G. van Willigenburg, W.L. De Koning, Z.S. Chalabi,
M. Tchamitchian, 2005, "On the selection of appropriate control system design methodologies",
Preprints IFAC World Congres, Prague, 38 July,
04926.pdf.
[41] L.G. van Willigenburg, W.L. De Koning, 2006, "On
the synthesis of timevarying LQG weights and noises along optimal control and state
trajectories",
Optimal
Control Applications and Methods, 27, 137160. , request associated Matlab software:
ml41.tar
[42] Henten, E.J. van, Slot, D.A. van 't, Hol, C.W.J.,
Willigenburg, L.G. van, 2006, "Optimal design of a cucumber harvesting robot", Proceedings
of AgEng 2006, Bonn, Germany, 37 september 2006,
Paper
nr. 802, 6 pp.
[43] L.G. van Willigenburg, W.L. De Koning, "A Kalman
decomposition to detect temporal linear system structure", Proceedings European
Control Conference 2007, Kos, Greece, July 27,
Paper
no. 78, 6 pp, request associated Matlab software:
ml43.tar
[43a] G van Straten, L.G. van Willigenburg, 2008, "On Evaluating Optimality
Losses of Greenhouse Climate Controllers",
Proceedings of the 17th World
Congress, The International Federation of Automatic Control, Seoul, Korea,
July 611.
[44] L.G. van Willigenburg, W.L. De Koning, 2008, "Linear
systems theory revisited,
Automatica,
44, 16691683, request associated Matlab software:
ml44.tar
[45] L.G. van Willigenburg, W.L. De Koning, 2008, "Temporal
linear system structure",
IEEE
Transactions on Automatic Control, 53, 5, 13181323, request associated Matlab
software: ml45.tar
[46] L.G. van Willigenburg, W.L. De Koning, 2008, "How
nonzero initial conditions affect the minimality of linear discretetime systems",
International Journal of System Science, 39, 10, 969983, request associated
Matlab software: ml46.tar
[47] L.G. van Willigenburg, W.L. De Koning, "Temporal
linear system structure: The discretetime case",
Proceedings of the ECC 2009, 2326 August, 2009, Budapest, pp. 225230,
request associated Matlab software: ml47.tar
[48] L.G. van Willigenburg, W.L. De Koning, 2009, "Emergence
of the second law out of reversible dynamics",
Foundations of Physics, 39, 12171239,
Open
Access , request associated Matlab software: ml48.tar
[49] E.J. Van Henten, D.A. van 't Slot, C.W.J. Hol,
L.G. van Willigenburg, 2009, Optimal manipulator design for a cucumber harvesting
robot,
Computers
and Electronics in Agriculture 65 (2), pp. 247258.
[50] E.J. Van Henten, E.J. Schenk, L.G. van Willigenburg,
J. Meuleman and P. Barreiro, 2010, "Collisionfree inverse kinematics of the redundant
sevenlink manipulator used in a cucumber picking robot",
Biosystems Engineering, 106, 2, 112124.
[51] L.G. van Willigenburg, W.L. De Koning, 2010, "Compensatability
and optimal compensation of systems with white parameters in the delta domain",
International
Journal of Control, 83, 12, 25462563, request associated Matlab software:
ml51.tar
[52] L.G. van Willigenburg, W.L. De Koning, 2012, "Temporal
and differential stabilizability and detectability of piecewise constant rank systems",
Optimal Control Applications & Methods, 33, 302317, request associated Matlab
software: ml52.tar
[53] G. van Straten, L.G. van Willigenburg, R.J.C. van
Ooteghem, E.J. van Henten, 2011, Optimal Control of Greenhouse Cultivation, CRC
Press, ISBN 9781420059618, request associated Matlab
software: ml53.tar
[54] L.G. Van Willigenburg, W.L. De Koning, 2014, "Equivalent
optimal control problem in the delta domain for systems with white stochastic parameters",
International Journal of System Science, 45, 3, 509522, request associated Matlab
software: ml54.tar
[55] L.G. Van Willigenburg, W.L. De Koning, 2013, "Minimal
representation of matrix valued white stochastic processes and UD factorization
of algorithms for optimal control",
International Journal of Control, 86, 2, 309321, request associated Matlab
software: ml55.tar
[56] L.G. Van Willigenburg, W.L. De Koning, 2013, "Temporal and onestep stabilisability and detectability of discrete time linear systems",
IET Control Theory & Applications, 7, 1, 151159, request associated Matlab
software: ml56.tar
[57] L.G. Van Willigenburg, W.L. De Koning, 2013,
"Temporal and onestep stabilizability and detectability
of timevarying discretetime linear systems",
System Modeling and Optimization, IFIP Advances in Information and Communication Technology,
Volume 391, 306317, request associated Matlab software: ml57.tar
[58] L.G. Van Willigenburg, W.L. De Koning, 2014,
"Theoretical and numerical issues concerning temporal stabilisability and detectability",
Preprints ACODS 2014 Conference, Kanpur, India, 1315 March,
paper 117, 368375, request associated Matlab software: ml58.tar
[59] B.A. Vroegindeweij, L.G. van Willigenburg, P.W.G. Grootkoerkamp, E.J. van Henten, 2014,
"Pathplanning for the autonomous collection of eggs on floors",
Biosystems Engineering,121,186199.
[60] L.G. Van Willigenburg, W.L. De Koning, 2014, "UD factorization of the strengthened discretetime optimal projection equations",
International Journal of System Science, http://dx.doi.org/10.1080/00207721.2014.911388.
[61] L.G. Van Willigenburg, H.M. Vollebregt, R.G.M. van der Sman, 2015, "Optimal adaptive scheduling and control of beer membrane filtration",
Control Engineering Practice, http://dx.doi.org/10.1016/j.conengprac.2014.10.004.
[62] L.G. Van Willigenburg, W.L. De Koning, 2015, "Temporal stabilizability and compensatability of timevarying linear discretetime sytems with white stochastic parameters",
European Journal of Control, http://dx.doi.org/10.1016/j.ejcon.2015.01.005.
[63] W.L. De Koning, L.G. Van Willigenburg, 2015, "Connecting and unmasking relativity and quantum theory",
Physics Essays, 28, 3, 392398.
[64] L.G. Van Willigenburg, W.L. De Koning, 2016, "Improvements and corrections concerning UD factorisations of algorithms for optimal full and reducedorder output feedback"
Journal of Control Engineering and Technology, 6, 2, 1418, request associated Matlab software:ml64.tar
Submitted publications
[S20161] L.G. Van Willigenburg, "Causes and fixes of temporal and conventional uncontrollability about control and state trajectories of nonlinear systems".
[S20171] L.G. Van Willigenburg, W.L. De Koning, "Wave structure of matter explaining time dilation and length contraction in classical physics".
IntroductionIntroduction / Subjects / Publications / Submitted publications / Software
Software associated to the publications available upon request
To keep track of the users the following software is freely available upon request. Send an email to Gerard van WilligenburgPart of the software is also available through Matlab Central: http://www.mathworks.nl/matlabcentral/fileexchange/authors/31018
[04] Associated Matlab software ml4.tar
[08] Associated Matlab software ml8.tar
[09] Associated Matlab software ml9.tar
[13] Associated Matlab software ml13.tar
[15] Associated Matlab software ml15.tar
[17] Associated Matlab software ml17.tar
[18] Associated Matlab software ml18.tar
[23] Associated Matlab software ml23.tar
[24] Associated Matlab software ml24.tar
[39] Associated Matlab software ml39.tar
[41] Associated Matlab software ml41.tar
[43] Associated Matlab software ml43.tar
[44] Associated Matlab software ml44.tar
[45] Associated Matlab software ml45.tar
[46] Associated Matlab software ml46.tar
[47] Associated Matlab software ml47.tar
[48] Associated Matlab software ml48.tar
[51] Associated Matlab software ml51.tar
[52] Associated Matlab software ml52.tar
[53] Associated Matlab software ml53.tar
[54] Associated Matlab software ml54.tar
[55] Associated Matlab software ml55.tar
[56] Associated Matlab software ml56.tar
[57] Associated Matlab software ml57.tar
[58] Associated Matlab software ml58.tar
[64] Associated Matlab software ml64.tar