Abstract
The paper deals with the problem of the stabilizing optimal control for the multivariable discrete-time stochastic systems in the case of the quadratic optimality criterion. The stability of the closed control loop is ensured by the proper choice of the terminal state penalization matrix in the optimality criterion, i.e. the initial condition for the considered computational algorithm based on the dynamic programming. In addition, the choice of this matrix presented in the paper is also suitable in the cases when the nonminimal realization of the system is of interest. Then the reduction of the calculated matrix dimension is possible when using the square root algorithm of the computation. All the results obtained for the state-space system model are applied to the analogical problem for the system described by the single-input, single-output (SISO) regression model.
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