Adaptive control of single-input single-output hybrid systems possessing interacting discrete- and continuous-time dynamics

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. As a result there are also mixed continuous-time and discrete signals present in the system associated either with the solutions of differential equations which depend at the same time on both discrete-time and continuous-time forcing terms and on generalized difference equations associated with discretized and digital signals. The estimation algorithm is of a continuous-time nature since the plant parameter estimates are updated for all time. It also incorporates a relative adaptation dead-zone as a robust stabilization mechanism which prevents against instability in the presence of a common class of unmodeled dynamics and bounded noise.