Logic-based switching for the control of a class of nonlinear systems

We consider a nonlinear single-input-single-output minimum phase system with large parametric uncertainty. The system can be represented globally in the normal form and our goal is to find an output dynamic feedback control law to ensure that the output (practically) asymptotically tracks a bounded smooth reference signal. Earlier work used high-gain observers with saturation to derive adaptive as well as robust control laws for this problem. The adaptive control law requires the nonlinear functions to be linearly parameterized in the unknown parameters and could have unsatisfactory transient performance for a large parameter set. The robust control law is based on a worst-case design and could be overly conservative for a large parameter set. In this paper we propose a new approach based on partitioning the set of uncertain parameters into smaller subsets. Robust control laws are designed for each subset and logic based switching is used to choose the appropriate control law. The switching rule uses an estimate of the derivative of a Lyapunov function, which is estimated using a high-gain observer.