Adaptive backstepping-based tracking control of a class of uncertain switched nonlinear systems

In this paper, we propose two adaptive control schemes to solve the output tracking control problem of a class of uncertain switched nonlinear systems. The first is a robust scheme constructed based on common Lyapunov function method, aiming to achieve the insensitivity of closed-loop system to parameter switches by estimating the bound on switching parameters. It is analyzed that the system stability under arbitrary switching is established with such a scheme, but the control input required may be relatively large since the estimate of the bound on switching parameters is utilized. To avoid this, we further propose a direct adaptive control scheme by estimating the switching parameters directly, and derive a dwell-time condition for parameter switches based on an extended multiple Lyapunov functions method newly developed, such that the global boundedness of all the closed-loop signals and the convergence of tracking error to a residual around zero are ensured. The effectiveness of the proposed control schemes is illustrated through simulation studies.