Robust adaptive control of discrete nominally stabilizable plants

摘要

This paper presents an indirect pole-placement based adaptive control scheme for discrete linear time-invariant non-necessarily inversely stable and stabilizable systems. The scheme is a pole-placement type without requiring the plant inverse stability assumption. The control objective is that the plant output should asymptotically track in the absence of unmodeled dynamics and bounded disturbances a reference signal, given by an arbitrary stable filter, under a bounded tracking error while ensuring robust closed-loop stability. The adaptive stabilizability and the robustness of this system under the presence of unmodeled dynamics and, possibly, bounded disturbances, are proved without assuming the controllability of the modeled plant. A normalized least-squares algorithm with a relative adaptation dead-zone and ‘a posteriori’ modification of the parameter estimates is used to ensure the controllability of the modified estimation plant model at all sampling instants and at the limit. Such a property is crucial to solve the stable pole-placement problem. On the other hand, the relative adaptation dead-zone is included for robustness purposes under unmodeled dynamics and, possibly, bounded disturbances.