Switched Concurrent Learning Adaptive Control of Switched Systems With Nonlinear Matched Uncertainties

This paper investigates the model reference adaptive control (MRAC) problem of switched systems with nonlinear matched uncertainties based on mode-dependent average dwell time method. A novel switched MRAC scheme is proposed, which simultaneously uses both current and recorded data from the switched system, to study the convergence of the state tracking error and the weight error without depending on the persistency of excitation. It is critical to establish the relationship among the nonlinear matched uncertainties, the switched concurrent learning(CL) algorithm, the average dwell time of each subsystem, and the convergence domains of the state tracking error and the weight error. First, we find a class of switching signals characterized by mode-dependent average dwell time conditions such that the switched reference model is bounded-input bounded-state stable. Second, in the case of time-invariant nonlinear uncertainties, we design a switched CL adaptive law that ensures that the tracking error converges to zero, and the adaptive weights exponentially converge to their ideal values. Subsequently, in the case of nonlinear time-varying uncertainties, we estimate the convergence rates of the state tracking error and the weight error of each subsystem outside a ball, and thus obtain sufficient conditions that ensure the convergence of the trajectories of the state tracking error and the weight error to a ball centered at the origin with a given radius. Finally, the proposed approach is applied to an electro-hydraulic system, and its effectiveness is demonstrated.