A globally stable APCS in the presence of bounded unmeasured noises and disturbances

This paper presents a globally stable adaptive, predictive control system for discrete time multivariable linear processes with pure time-delays under the effect of measurement and process noise plus unmeasured disturbances. This solution, which extends a previous result by the author et al. [1], is based on a different approach compared to recent results in stochastic adaptive control literature. The proof of stability relies on convergence properties of the a posteriori error and the estimated parameters, which are derived from an adaptive algorithm that includes a criterion for stopping or continuing parameter adaptation. The main features of the present result are: i) the only restriction on noise and disturbances acting on the system is that they be bounded; ii) the estimated parameters converge towards the actual process parameters as much as necessary to obtain the stability results and no persistent excitation is required, and iii) the global stability results guarantee boundedness of the process input and output and minimization of the control or tracking error in terms of the absolute value.