Design of stochastic optimal feedback control systems

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Abstract
The design of stochastic, linear, multivaribale feedback systems is considered where the plant is constant and the noise processes are stationary. The plant can be unstable and nonminimum-phase and feedback-system dynamics can be modelled. Approximate methods are described for limiting the effects of plant saturation and for modelling transport delays. The closed-loop system is assumed, to have a coloured process, disturbance and measurement noise inputs and a coloured reference input. The plant disturbance and the closed-loop-system reference inputs are also assumed to contain deterministic components, e.g. step or ramp signals. The design procedure is original and involves two stages. A performance criterion is defined first that is not sensitive to the deterministic signals, and this defines the closed-loop controller. The resulting closed-loop system acts as an optimum regulator to minimise the effects of stochastic disturbances. A second tracking-error performance criterion is then specified that determines the optimal reference input to the closed-loop system. This reference signal is generated by two optimal open-loop controllers. One controller ensures the plant output is following a desired trajectory, and the second acts as a feedforward controller to offset plant disturbances.

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