Robust model predictive control of multivariable systems using input-output models with stochastic parameters

Model predictive control (MPC) algorithms that minimize the expectation of a multi-step quadratic loss function are formulated for systems described through an input-output model with stochastic parameters. The parameter matrix is modelled as a constant matrix plus a random perturbation matrix parameterized through a white noise vector. In open-loop optimal feedback control, the future inputs are optimized as deterministic variables. In closed-loop optimal receding horizon control, they are optimized as stochastic variables that depend on the future feedback measurements. In the absence of inequality constraints, optimal control policies for both cases are shown to be constant state feedback laws. Online implementation of these algorithms in the presence of inequality constraints is also discussed. The implications of the results for robust control and MPC are given and examples are shown to support their significance