Design of stochastic optimal feedback control systems

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.