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, reduced-order 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, 3-8 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 non-linear systems digital optimal controllers are synthesized that explicitly take into account the inter-sample (continuous-time) 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, 405-436 ]. 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 off-line. Both the digital optimal control sequence and the digital optimal LQG compensator are stored in the controller memory. The only on-line computations that need to be performed by the controller are a small number of matrix vector multiplications to compute control corrections from the on-line measured data. This type of control of non-linear 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 Linear-Quadratic-Gaussian problem in control system design", IEEE Trans. Aut. Contr., AC-16(6), 529-552 ]. If the model structure is well established but some of the parameter values are not, and the on-line 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. Bar-Shalom, 1981, "Stochastic dynamic programming: Caution and probing", IEEE Trans. Aut. Contr., AC-26(5), 1184-1195 ]. Since most of our research regarding digital optimal control and LQG compensation of non-linear 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, 3-8 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 a-priori knowledge or insight is available. Starting from very simple linear dynamics at the micro-scale 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

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 time-shared 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 non-linear 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 time-shared 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 reduced-order 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 (full-order) 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 non-linear 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 full-order LQG design becomes optimal reduced-order LQG design. For this more difficult problem strengthened discrete-time optimal projection equations have been developed, which in contrast to the conventional version, are equivalent to first-order necessary optimality conditions and the minimality of the compensator. Based on these equations numerical algorithms have been developed to compute optimal reduced-order LQG compensators for time-invariant and time-varying discrete-time 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 full-order 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., AC-37(5), 579-588 ]. 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 non-conservative robust control systems.

Introduction / Subjects / Publications / Submitted publications / Software

Robust control, systems with white parameters (mutiplicative white noise), compensatability & optimal compensation, delta operator and U-D 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 continuous-time 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 full-order 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., AC-37(5), 579-588 ]. 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 non-conservative robust control systems. Formulation of the full and reduced-order control and compensation problems in the delta domain offers the possibility to unify continuous and discrete-time results. It also enables transferring discrete-time results to continuous-time. 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].

U-D factorization has the potential to improve computational efficiency and accuracy. A formulation of the full and reduced-order LQG problem by means of Lyapunov equations offers alternative ways for U-D factorization [39]. For discrete-time systems with white stochastic parameters (multiplicative white noise) U-D factorization of the algorithm for full-order and reduced-order 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 non-linear systems are often based on the linearised dynamics about optimal control and state trajectories. These linearised dynamics constitute a time-varying 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 continuous-time and to N-step controllability is discrete-time. The description and detection of temporal uncontrollability and temporal unreconstructability in both continuous and discrete time requires the introduction of systems with time-varying (state) dimensions. These type of systems moreover enable a well rounded realization theory for time-varying linear systems as already suggested by Kalman in 1969. The description of systems with time-varying 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.

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 time-varying 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 non-linear 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 non-linear 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 on-line 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. Bar-Shalom, 1981, "Stochastic dynamic programming: Caution and probing", IEEE Trans. Aut. Contr., AC-26(5), 1184-1195 ]

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 real-time and in simulation. In real-time 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 inter-sample 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 time-varying systems with time-varying dimensions

The minimality of discrete-time linear time-varying systems is fundamental to optimal digital reduced-order LQG controller synthesis. From the associated LQG theory minimal realizations with time-varying dimensions emerge "automatically". The associated realization theory however does not consider the influence of non-zero initial conditions, while the initial condition of the optimal LQG controller is usually non-zero. In [25], [30] the minimality property is generalized for systems with non-zero 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 non-linear 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 time-varying continuous-time systems piecewise constant rank systems are introduced. They constitute continuous-time systems with time-varying 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 time-optimal control of mechanical systems

Algorithms for the digital time-optimal 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 n-dimensional non-linear systems, linear in the control variables, it has been shown that non-singular solutions to time-optimal control problems with bounded control and fixed initial and final states generally have no more than a total of n-1 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. 499-506 ] used to solve continuous-time 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 reduced-order 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 discrete-time 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 non-linear systems [10] has been successfully implemented, as a receding horizon optimal controller, in a greenhouse optimal control experiment [12]. Difficulties concerning different time-scales 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 tomato-picking robot is under investigation. An end-effector to pick all the fruits on a single truss has been designed is currently being manufactured. Currently the tomato picking robot is the MK-II of Eshed Robotec. Software to control both the end-effector 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 IMAG-DLO (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 set-ups

Digital LQG tracking controllers have been successfully implemented on the "ball and plate" laboratory set-up which constitutes an almost linear two-input system. A "helicopter type" laboratory set-up has been manufactured, which constitutes a non- linear multivariable two-input system. The laboratory set-ups 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 non-linear 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 micro-scale. 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 Einstein’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 wave-particle 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

Publications

[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, "First-order controllability and the time optimal control problem for rigid articulated arm robots with friction", Int. J. Contr., Vol. 51, no 6, pp. 1159-1171.
[2] L.G. Van Willigenburg, 1991, "Computation of time-optimal controls applied to rigid manipulators with friction", Int. J. Contr., Vol. 54, no 5, pp. 1097-1117.
[3] L.G. Van Willigenburg, W.L. De Koning, 1992, "The digital optimal regulator and tracker for stochastic time-varying systems", Int. J. Syst. Sci., Vol 23, no 12, pp. 2309-2322.
[4] L.G. Van Willigenburg, 1992, "Computation of the digital LQG regulator and tracker for time-varying systems", Opt. Contr. Appl. Meth., Vol. 13, pp. 289-299 , request associated Matlab software: ml4.tar
[5] L.G. Van Willigenburg, 1993, "Computation and implementation of digital time-optimal feedback controllers for an industrial X-Y robot subjected to path, torque and velocity constraints", Int. J. Rob. Res., Vol. 12, no 5, pp. 420-433.
[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 28-July 4, 1993, pp. 1348-1352.
[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, 18-23 July 1993.
[8] J.C. Engwerda, L.G. Van Willigenburg, 1995, "Optimal Sampling-Rates 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. 107-125, 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", C-TAT, Vol. 10, no 4, part 5, pp. 2083-2098, request associated Matlab software: ml9.tar
[10] L.G. Van Willigenburg, 1995, Digital optimal control and LQG compensation of asynchronous and aperiodically sampled non-linear systems", Proceedings 3rd European Control Conference, Rome, Italy, September 1995, Vol. 1, pp. 496-500.
[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 June-5 July, 1996, paper 4a-01 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. 229-238.(Proceedings of the Second IFAC/ISHS Workshop on Mathematical and Control Applications in Agriculture and Horticulture, Silsoe UK, 12-15 sept. 1994).
[13] W.L. De Koning, L.G. van Willigenburg, 1998, "Numerical algorithms and issues concerning the discrete-time optimal projection equations for systems with white parameters", Proceedings UKACC International Conference on Control '98, 1-4 Sept. 1998, University of Swansea, UK, Vol. 2, pp.1605-1610. , request associated Matlab software: ml13.tar
[14] H.L. Dijksterhuis, L.G. Van Willigenburg, R.P. Van Zuydam, 1998, "Centimetre-precision guidance of moving implements in the open field: a simulation based on GPS measurements", Computers and Electronics in agriculture, 20, pp. 185-197.
[15] L.G. van Willigenburg, W.L. De Koning, 1999, "Optimal reduced-order compensators for time-varying discrete-time systems with deterministic and white parameters", Automatica, 35, 129-138 , 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. 207-218.
[16a] G. Van Straten, R.F. Tap, L.G. Van Willigenburg, 1999, "Sensitivity of on-line RHOC of greenhouse climate to adjoint variables for the crop", Proceedings 14th IFAC World Congres, Beiing, China, July 5-9, 1999, Paper no. K-4a-01-1.
[17] L.G. van Willigenburg, W.L. De Koning, 2000, "The equivalent discrete-time optimal control problem for time-varying continuous-time systems with white stochastic parameters", International Journal of System Science, 31, 4, pp. 479-487., request associated Matlab software: ml17.tar
[18] L.G. Van Willigenburg, W.L. De Koning, 2000, "Numerical algorithms and issues concerning the discrete-time optimal projection equations", European Journal of Control, 6, 1, pp. 93-110, request associated Matlab software: ml18.tar
[19] L.G. van Willigenburg, W.L. De Koning, 2000, "Finite and infinite horizon fixed-order LQG compensation using the delta operator", Proceedings UKACC International Conference on Control 2000, 4-7 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. 437-442, 14-16 June, Pisa,Italy
[21] L.G. van Willigenburg, E.J. Van Henten, W.Th.M. Van Meurs, "Three time-scale receding horizon optimal control in a greenhouse with a heat storage tank", Proceedings of the Agricontrol 2000 conference, 12-14 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 2000-11, Proceedings of the Agricontrol 2000 conference, 12-14 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, 12-14 July 2000, Wageningen, The Netherlands, pp. 39-44.
[23] L.G. van Willigenburg, W.L. De Koning, 2001, "Synthesis of digital optimal reduced-order compensators for asynchronously sampled systems", International Journal of System Science, 32, 7, pp. 825-835 , 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 0-306-46445-4, Edited by Farokh Marvasti, request associated Matlab software: ml24.tar
[25] L.G. Van Willigenburg, W.L. De Koning, 2002, "Minimal and non-minimal optimal fixed-order compensators for time-varying discrete-time systems", Automatica, 38, 1, pp. 157-165.
[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 24-27, Cancun Mexico, pp. 155-161.
[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 21-24, Cancun, Mexico, pp. 211-216.
[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, 6-8 June, pp. 123-128.
[29] C.W.J. Hol, L.G, van Willigenburg, E.J. van Henten, G. van Straten, 2001, "A new optimization algorithm for singular and non-singular digital time-optimal control of robots", Proceedings IEEE International Conference on Robotics and Automation (ICRA), May 21-26, Seoul, Korea, vol. 2, pp. 1136 -1141.
[30] L.G. van Willigenburg, W.L. De Koning, 2002, "Minimality, canonical forms and storage of finite-horizon discrete-time compensators", Preprints IFAC World Congress, Barcelona, 21-26 July, 2002, paper 984.
[31] G. van Straten, L.G. van Willigenburg, R.F. Tap, 2002, "The significance of crop co-states for receding horizon optimal control of greenhouse climate", Control Engineering Practice, 10, 625-632.
[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): 97-122.
[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 (1-3): 179-197.
[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 1-4, 2003.
[35] L.G. van Willigenburg, J. Bontsema, W.L. De Koning, L. Valenzuela, C. Martinez, "Digital optimal reduced-order control of a solar power plant", Proceedings of the UKACC Control 2004, Paper 205, Bath, UK, 6-9 September 2004.
[36] L.G. van Willigenburg, C.W.J. Hol, E.J. van Henten, 2004, "On-line near minimum time path planning and control of an industrial robot picking fruits", Computers and Electronics in Agriculture, 44, 3, 223-237.
[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 12-16, In: GreenSys2004 Sustainable Greenhouse Systems : Greensys2004, Leuven, 12-16 September 2004.
[38] L.G. van Willigenburg, J. Bontsema, W.L. De Koning, L. Valenzuela, C. Martinez, 2004, "Direct reduced-order 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. 9-16, ISBN 84-7834-474-8.
[39] L.G. van Willigenburg, W.L. De Koning, 2004, "UDU factored discrete-time Lyapunov recursions solve optimal reduced-order LQG problems", European Journal of Control, 10, pp. 588-601., 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. 602-613.
[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, 3-8 July, 04926.pdf.
[41] L.G. van Willigenburg, W.L. De Koning, 2006, "On the synthesis of time-varying LQG weights and noises along optimal control and state trajectories", Optimal Control Applications and Methods, 27, 137-160. , 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, 3-7 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 2-7, 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 6-11.
[44] L.G. van Willigenburg, W.L. De Koning, 2008, "Linear systems theory revisited, Automatica, 44, 1669-1683, 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, 1318-1323, request associated Matlab software: ml45.tar
[46] L.G. van Willigenburg, W.L. De Koning, 2008, "How non-zero initial conditions affect the minimality of linear discrete-time systems", International Journal of System Science, 39, 10, 969-983, request associated Matlab software: ml46.tar
[47] L.G. van Willigenburg, W.L. De Koning, "Temporal linear system structure: The discrete-time case", Proceedings of the ECC 2009, 23-26 August, 2009, Budapest, pp. 225-230, 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, 1217-1239, 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. 247-258.
[50] E.J. Van Henten, E.J. Schenk, L.G. van Willigenburg, J. Meuleman and P. Barreiro, 2010, "Collision-free inverse kinematics of the redundant seven-link manipulator used in a cucumber picking robot", Biosystems Engineering, 106, 2, 112-124.
[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, 2546-2563, 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, 302-317, 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 978-1-4200-5961-8, 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, 509-522, 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 U-D factorization of algorithms for optimal control", International Journal of Control, 86, 2, 309-321, request associated Matlab software: ml55.tar
[56] L.G. Van Willigenburg, W.L. De Koning, 2013, "Temporal and one-step stabilisability and detectability of discrete time linear systems", IET Control Theory & Applications, 7, 1, 151-159, request associated Matlab software: ml56.tar
[57] L.G. Van Willigenburg, W.L. De Koning, 2013,
"Temporal and one-step stabilizability and detectability of time-varying discrete-time linear systems", System Modeling and Optimization, IFIP Advances in Information and Communication Technology, Volume 391, 306-317, 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, 13-15 March, paper 117, 368-375, 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,121,186-199.
[60] L.G. Van Willigenburg, W.L. De Koning, 2014, "U-D factorization of the strengthened discrete-time 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 time-varying linear discrete-time 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, 392-398.,
[64] L.G. Van Willigenburg, W.L. De Koning, 2016, "Improvements and corrections concerning UD factorisations of algorithms for optimal full and reduced-order output feedback" Journal of Control Engineering and Technology, 6, 2, 14-18, request associated Matlab software:ml64.tar

Submitted publications
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Introduction / 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 e-mail to Gerard van Willigenburg

Part 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
 

 

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