Solution of the discrete-time stochastic optimal control problem in the 2-domain

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Abstract
The design of discrete-time optimal multivariate systems is considered in the z-domain. The constant plant can be non-square, unstable and/or non-minimum phase and feedback system dynamics can be modelled. The stationary coloured noise processes are assumed to be represented by discrete rational spectral densities. The system can contain transport delay elements and the effects of plant saturation can be limited by the choice of performance criterion. The system inputs are assumed to contain both stochastic and deterministic components. The two-stage design procedure is original and it enables the stochastic and deterministic control functions to be separated, A performance criterion is first defined which is insensitive to the deterministic signals and this defines the closed-loop optimal controller. The resulting closed-loop system acts as an optimum regulator to minimize the effects of stochastic disturbances. A second tracking error performance criterion is then specified which determines the optimal reference input to the closed-loop system. This reference signal is generated by two further discrete-time controllers. The first controller ensures that the plant is following a desired trajectory and the second acts as a feedforward controller to counteract measurable disturbances. The minimum variance regulators of Astrom (1970) and Peterka (1972) are also derived from these results.

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