An adaptive learning regulator for uncertain minimum phase systems with undermodeled unknown exosystems

The design of an adaptive learning regulator is addressed for uncertain minimum phase linear systems (with known bounds, known upper bound on system order, known relative degree, known high frequency gain sign) and for unknown exosystems (with unknown order, uncertain frequencies). On the basis of a known bound on system uncertainties and a known bound on the modeled exosystem frequencies, a new adaptive output error feedback control algorithm is proposed which guarantees exponential convergence of both the output and the control input errors into residual bounds which decrease as the exosystem modeling error decreases. Exponential convergence of both errors to zero is obtained when the regulator exactly models all exosystem excited frequencies, while asymptotic convergence of both errors to zero is achieved when the actual exosystem is overmodeled by the regulator. The new algorithm generalizes existing learning controllers since, in the case of periodic references and/or disturbances, the knowledge of the period is not required.