Generalized Minimum Variance Control of Constrained Multi- Variable Systems

We propose a control scheme for a discrete-time linear stochastic multi-input multi-output (MIMO) system, with imperfectly known or slowly time-varying parameters. The selected approach is generalized minimum variance control, but the method can easily be extended to generalized predictive control. The quadratic criterion to be minimized penalizes the variance of the difference between the output of a reference model and the predicted variable to be regulated. It also penalizes the difference between two successive control vectors. We have also included, in the model, quadratic constraints on control variables. In application to production planning problems, these correspond to minimal and maximal production capacities. The predicted auxiliary output is determined by an extended least-squares algorithm, and the optimality conditions evolve by periodical resetting of the criterion weights. This resetting is achieved from the Lagrangean problem formulation, since the role of Lagrange multipliers is similar to that of control weights. Weighting parameters can therefore be periodically adjusted by a Robbins-Monro type algorithm to solve the system of equations obtained from Kuhn·Tucker necessary conditions.