Cybernetics and Computer Engineering, 2020, 1(199)
MISHCHENKO M.D., Student
National Technical University of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute” 37, Peremohy av., 03056, Kyiv, Ukraine
GUBAREV V.F., DSc. (Engineering), Corresponding Member of NAS of Ukraine,
Head of the Dynamic Systems Control Department
Space Research Institute of the National Academy of Sciences of Ukraine and the State Space Agency of Ukraine
40, Acad. Glushkova, 03187, Kyiv, Ukraine
METHODS OF MODEL PREDICTIVE CONTROL FOR DISCRETE MULTI-VARIABLE SYSTEMS WITH INPUT
Introduction. There are a lot of systems which can be conveniently modelled as a discrete linear multi-input multi-variable system. When a control problem for such systems arises, it is usually done with methods derived from the control theory. But these methods have several known drawback. For example, for non-deterministic systems, they are based on assumption about certain convenient statistical properties of noises.
The purpose of the paper is to develop synthesis algorithms based on ideas and approaches of the Model Predictive Control (MPC).
Methods. In contrast to the common approach, in this work we aim to synthesize the best control sequence in terms of some criterion. We use results derived from the Kuhn-Tucker theorem for control synthesis.
Results. A new class of methods capable of leading linear system’s state to zero (or, in case of noisy environment, to its neighbourhood) and stabilization of cognitive map’s functioning was developed. This new methods are capable of controlling not only stable systems, but also unstable and semi-stable ones, even in presence of random perturbations and with constrained control resource. These methods differ in efficiency of control resource utilization and required computational resources. More efficient methods require more computations. That’s why it is necessary to choose an appropriate method in each particular case.
Conclusions. The developed methods can be used to control both technical and any other kinds of systems represented either as controllable linear systems with multiple inputs and outputs or as controllable cognitive maps.
Keywords: variational method, cognitive map, control synthesis, discrete controllable system, moving horizon, linear system, MPC
1. Garcia C. E., Prett D.M., Morari M. Model predictive control: Theory and Practice – a survey. Automatica. 1989, no. 25, pp. 335-347.
2. Rawlings, J. B., Muske K.R. The stability of constrained receding horizon control. IEEE Trans. Automat. Control. 1993, AC-38(10), pp. 1512-1516.
3. Mayne D. Q. Optimization in model based control. In Proc. IFAC Symposium Dynamics and Control of Chemical Reactors, Distillation Columns and Batch Proacesses. Helsingor. 1995. pp. 229-242.
4. Den Boom V. T. J. J. Model based predictive control: Status and perspective. In Symposium on Control, Optimization and Supervision, CESA’96 IMACS Multiconference. Lille, 1996. pp. 1-12.
5. Rawlings J.B., Mayne D.Q. Model Predictive Control: Theory and Design. Nob Hill Publishing, Madison, WI, 2009, ISBN 978-0-9759377-0-9. 576 p.
6. Richalet, J., Rault A., Testud J.L., Papon J. Model predictive heuristic control: Application to industrial processes. Automatica. 1978, no. 14, pp. 413-428.
7. Qin S.J., Badgwell T.A. An overview of industrial model predictive control technology. In Kantor Y.C., Garcia C.E. Carnahan (Eds) Chemical Process Control-Assessment and New Directions for Research AIChE Symposium series. Vol. 93, no. 316, pp. 232-256.
8. Gubarev V.F., Mishchenko M.D., Snizhko B.M. (Kondratenko Y., Chikrii A., Gubarev V., Kacprzyk J. (eds)). Model Predictive Control for Discrete MIMO Linear Systems. Advanced Control Techniques in Complex Engineering Systems: Theory and Applications. Studies in Systems, Decision and Control. 2019, Vol. 203.
9. Gubarev V.F., Shevchenko V.M., Zhykov A.O., Gummel A.V. State estimation for Systems Subjected to Bounded Uncertainty using Mooing Horizon Approach. In Preprints of the 15th IFAC Symposium on System Identification, Saint-Malo, France, July 6-8, 2009, pp. 910-915.