Adaptive predictive control with mean-square input constraint

Convergence properties of a self-tuning regulator incorporating an input mean-square constraint are studied. An algorithm, derived from the long-range controller MUSMAR, is considered. For this algorithm, using the ODE method for analysing stochastic recursive algorithms and singularly perturbed ODE theory, a local convergence result is proved. This result characterizes possible convergence points of the algorithm as the constrained minima of the underlying steady-state quadratic cost. The actual convergence of the algorithm to the possible equilibrium points predicted by theory is verified by means of simulation examples including unmodelled plant dynamics.