On the adaptive control of a class of SISO dynamic hybrid systems

Abstract

This paper deals with the problem of synthesizing a robust adaptive controller for a specific class of single-input single-output (SISO) time-invariant hybrid controlled object (plant) which can operate under bounded disturbances and/or unmodeled dynamics. The hybrid plant dealt with is composed of two coupled subsystems, one of them being of continuous-time type while the other is digital. The estimation algorithm is of a continuous-time nature since the plant parameter estimates are updated for all time. The adaptive scheme is pole-placement based and it is of indirect type since the controller parameters are re-updated at all time based on the calculated plant parameter estimates. An input–output model is first directly obtained from a state-space description which involves filtered signals for the hybrid plant from an initial state-space description. Such a model is simultaneously driven by the standard continuous-time input plus an extra signal. The extra input is composed for all time of a signal which involves the contribution of the input and output over a finite number of preceding sampling instants plus a driving signal which involves the contribution of the weighted integral of the continuous-time input on a set of preceding sampling intervals. Such a driving signal is due to the existing couplings between the continuous-time and digital substates of the hybrid plant. A relative adaptation dead zone is used in the parameter estimation scheme whose role is the robust adaptive stabilization in the presence of uncertainties. The hybrid nature of the system becomes apparent since the plant is simultaneously driven by the continuous time input plus its samples at sampling instants. As a result, its input–output differential equation has forcing terms generated by the system description at sampling instants.