Robust discrete-time adaptive control subject to a control input amplitude constraint

Abstract

Subject to a control input amplitude constraint, an adaptive algorithm is proposed to control discrete-time plants with unmodelled dynamics. By introducing an additional feedback signal, it is shown that the uniform boundedness of all signals in the adaptive loop can be guaranteed. The nominal plant is assumed to be stable but unnecessarily minimum phase. Various properties of this adaptive algorithm are analysed. It is shown that the performance which can be achieved with no control input amplitude constraint in the non-adaptive case (i.e. the case when the true nominal plant is known a priori) is asymptotically well maintained in the adaptive system. The analysis is supported by computer simulation results.