Adaptive Control of Piecewise Linear Systems with State Feedback for Output Tracking

A piecewise linear system consists of a set of linear time-invariant (LTI) subsystems, with a switching sequence specifying an active subsystem at each time instant. This paper studies the adaptive control problem of single-input, single-output (SISO) piecewise linear systems. By employing the knowledge of the time instant indicator functions of system parameter switches, a new controller structure parametrization is proposed for the development of a stable adaptive control scheme with reduced modeling error in the estimation error signal used for parameter adaptive laws. This key feature is achieved by the new control scheme's ability to avoid a major parameter swapping term in the error model, with the help of indicator functions whose knowledge is available in many applications. A direct state feedback model reference adaptive control (MRAC) scheme is presented for such systems to achieve closed-loop signal boundedness and small output tracking error in the mean square sense, under the usual slow system parameter switching condition. Simulation results on linearized NASA GTM models are presented to demonstrate the effectiveness of the proposed scheme.