Adaptive control of linear stochastic systems

  • Authors:

  • J. G. Deshpande;T. N. Upadhyay;D. G. Lainiotis

  • Affiliations:

  • The authors are with the Department of Electrical Engineering and Electronics Research Center, University of Texas at Austin, Austin, Texas USA;The authors are with the Department of Electrical Engineering and Electronics Research Center, University of Texas at Austin, Austin, Texas USA;The authors are with the Department of Electrical Engineering and Electronics Research Center, University of Texas at Austin, Austin, Texas USA

  • Venue:
  • Automatica (Journal of IFAC)
  • Year:
  • 1973

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Abstract

An adaptive control algorithm for linear systems with unknown constant parameters and quadratic performance criterion has been obtained. The control is nonlinear in the estimate of the state of the plant and is given as the weighted integral of the model conditional optimal controls with the a-posteriori probabilities as weights. The control scheme is separated into a bank of model-conditional deterministic control gains, and a corresponding bank of known nonlinear functions of the model conditional, causal, mean-square state-vector estimate. The separation here can be viewed as a decomposition of the control into a bank of model conditional optimal non-adaptive linear controls, one for each admissible value of the unknown parameter, and the bank of a-posteriori model probabilities which incorporate the learning nature of the adaptive control. The computational requirements are reduced by a great extent for the special case when the uncertainity is only in the measurement matrix.