Stable multi-estimation model for single-input single-output discrete adaptive control systems

A pole-placement-based adaptive controller synthesized from a multi-estimation scheme is designed for linear single-input single-output time-invariant plants. A higher level switching structure between the various estimation schemes is used to supervise the reparameterization of the adaptive controller in real time. The basic usefulness of the proposed scheme is to improve the transient behaviour while guaranteeing closed loop stability. The scheme becomes specifically useful when extended to linear plants whose parameters are piecewise constants while changing abruptly to new constant parameterizations or in the case when the parameters are slowly time varying rather than constant. Thus, the scheme becomes attractive from a modelling point of view since the plant, while being potentially time varying, or in particular, possessing several operation points, is modelled as a set of time-invariant plant unknown parameterizations each possessing its own estimation scheme. In that way, the model description becomes conceptually simple and easy to implement concerned with both estimation and control issues. A description of the controller architecture with multiple parameterizations, together with its associated multi-estimation scheme is given. In addition, the proofs of boundedness of all the relevant signals are given so that the closed-loop system is proved to be stable.