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IMA Journal of Mathematical Control and Information 1985 2(4):319-334; doi:10.1093/imamci/2.4.319
© 1985 by Institute of Mathematics and its Applications
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Adaptive Linear-Quadratic Control for Stochastic Discrete-Time Systems

H. F. CHEN and P. E. CAINES

Institute of Systems Science, Academia Sinica, and Department of Electrical Engineering, McGill University Montreal P. Q., Canada
Department of Electrical Engineering, McGill University Montreal P. Q., Canada Canadian Institute for Advanced Research

The optimality of certain adaptive control laws for partially observed linear stochastic systems with unknown parameters and with averaged quadratic-loss functions of the state and control values is demonstrated. First, an explicit formula for the loss function


in terms of system parameters, control actions, and the solution of the Riccati equation is given; then the optimal value for this loss function and an associated set of optimal controls are derived using certain stability, observability, and controllability conditions on the system. Second, assuming strongly consistent parameter estimates are available and that the noise part of the system is minimum-phase, an adaptive control law is presented that with arbitrarily high probability achieves a loss arbitrarily close to the optimum.


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