Adaptive pole-placement control of MIMO stochastic systems

Abstract

An adaptive pole-placement control algorithm using delayed normalized least mean squares (DNLMS) estimation with inverse logarithm step size is proposed for controlling the multi-input multi-output (MIMO) stochastic systems. The DNLMS estimation is used to identify the plant parameters and then a pole-placement controller is designed and adaptively adjusted using the estimates. Based on the assumptions of a mixing input condition and the satisfaction of a certain law of large numbers, the estimation with inverse logarithm step size has almost sure convergence. Further, by using the perturbation scheme, the control algorithm facilitates the establishment of the adaptive pole-placement control and prevents the closed-loop control system from incurring unstable pole-zero cancellation. An analysis shows that the proposed control algorithm guarantees parameter estimation convergence and system stability in the mean squares sense, with the output of the system approaching zero if there are no uncertainties and disturbances and converging to a neighborhood of zero if they exist. A series of simulations for controlling a mobile robot system are given to illustrate the effectiveness of the proposed scheme. The results show that the proposed control scheme is fairly robust for systems with uncertainties as well as has satisfactory performance characteristics.