“Multivariable controller for discrete stochastic amplitude-constrained systems”

Authors: Hannu T. Toivonen,
Affiliation: Åbo Akademi, Finland
Reference: 1983, Vol 4, No 2, pp. 83-93.

Keywords: Control non-linearities, discrete-time systems, non-linear systems, optimal control, saturation, stochastic control

Abstract: A sub-optimal multivariable controller for discrete stochastic amplitude-constrained systems is presented. In the approach the regulator structure is restricted to the class of linear saturated feedback laws. The stationary covariances of the controlled system are evaluated by approximating the stationary probability distribution of the state by a gaussian distribution. An algorithm for minimizing a quadratic loss function is given, and examples are presented to illustrate the performance of the sub-optimal controller.

PDF PDF (1951 Kb)        DOI: 10.4173/mic.1983.2.2

DOI forward links to this article:
[1] P.M. Mäkilä, T. Westerlund and H.T. Toivonen (1984), doi:10.1016/0005-1098(84)90061-X
[2] A. Królikowski (1995), doi:10.1002/acs.4480090306
[3] P. Makila and H. Toivonen (1987), doi:10.1109/TAC.1987.1104686
[1] FLETCHER, R. (1980). Practical Methods of Optimization, Vol. 1, New York: Wiley.
[2] FULLER, A.T. (1970). Nonlinear Stochastic Control Systems, London: Taylor and Francis.
[3] GOLDSTEIN, A.A. (1965). On steepest descent, SIAM J. Cont., 3, 147-151.
[4] GUTMAN, P.-O. (1982). Controllers for bilinear and constrained linear systems, CODEN: LUTFD2/(TFRT-1022)/1-133/(1982), Dep. Aut. Contr., Lund Univ., Sweden.
[5] GUTMAN, P.-O., HAGANDER, P. (1982). A new design of constrained controller for linear systems, Proceedings of the 21st IEEE Conference on Decision and Control, Florida.
[6] MÄKILÄ, P.M. (1982). Self-tuning control with linear input constraints, Optimal Control Appl. and Methods, 3, 337-353.
[7] MÄKILÄ, P. M. (1982). Constrained linear quadratic gaussian control for process application, Ph.D. Thesis, Åbo Akademi, Turku, Finland.
[8] MÄKILÄ, P.M., WESTERLUND, T., TOIVONEN, H.T. (1982). Constrained linear quadratic gaussian control, Proceedings of the 21st IEEE Conference on Decision and Control, Florida.
[9] O´REILLY, J. (1980). Optimal low-order feedback controllers for linear discrete-time systems, In Control and Dynamic Systems, edited by C.T. Leondes, New York: Academic Press, Vol. 16, pp. 335-367.
[10] POLAK, E. (1971). Computational Methods in Optimization, New York: Academic Press.
[11] TOIVONEN, H.T. (1981). Minimum variance control of first-order systems with a constraint on the input amplitude, IEEE Trans. Autom. Control, AC-26, 556-558 doi:10.1109/TAC.1981.1102627
[12] TOIVONEN, H.T. (1983). Suboptimal control of linear discrete stochastic systems with linear input constraints, IEEE Trans. Autom. Control, AC-28, 246-248 doi:10.1109/TAC.1983.1103205
[13] TOIVONEN, H.T. (1983). Suboptimal control of discrete stochastic amplitude-constrained systems, Int. J. Control, 37, 493-502 doi:10.1080/00207178308932988
[14] WESTERLUND, T. (1981). A digital quality control system for an industrial dry process rotary cement kiln, IEEE. Trans. Autom. Control, AC-26, 885-890 doi:10.1109/TAC.1981.1102738
[15] WONHAM, W.M., CASHMAN, W.F. (1969). A computational approach to optimal control of stochastic saturating systems, Int. J. Control, 10, 77-98 doi:10.1080/00207176908905801

  title={{Multivariable controller for discrete stochastic amplitude-constrained systems}},
  author={Toivonen, Hannu T.},
  journal={Modeling, Identification and Control},
  publisher={Norwegian Society of Automatic Control}