A multiestimation-based scheme for modelling single-input–single-output discrete adaptive control systems

A pole-placement multiestimation-based adaptive controller is synthesised for linear single-input–single-output time-invariant plants. A higher level switching structure between the various estimation schemes is used to supervise the reparameterisation 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 parameterisations 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 in a conceptually simple way as a set of time-invariant plant unknown parameterisations each one possessing its corresponding estimation scheme. A description of the controller architecture with multiple parameterisations, together with its associated multiestimation scheme is given. Moreover, graph theory is used to describe in a formal and concise way the switching mechanism between the various plant parameterisations of the switched system. Thus, the switching rule is formally represented by a graph (or finite automaton). Also, the proofs of boundedness of all the relevant signals are given.