Logic-based switching control of nonlinear systems using high-gain observers

Sammanfattning: The design of robust output and state feedback controllers for practical track-ing and stabilization for nonlinear systems with large-scale parametric uncertainty is considered. We consider a class of single-input single-output systems that can be transformed into a special form, where unavailable states (if any) are derivatives of the measured outputs. We consider a large class of nonlinear systems that could be stabilized via a Lyapunov-based technique if the level of parametric uncertainty was much lower and if the unmeasured states were available for feedback. We propose and investigate a new approach based on subdividing the set of parameters into smaller subsets, designing candidate controllers for each subset, and implementing a logic-based switching between them. We use the output of an extended-order high-gain observer to substitute the unavailable states in the candidate controllers, check the inequality for the derivative of the Lyapunov function and switch if it is not satisfied, and to approximately identify the parameters. We discuss the issues of digital implementation and measurement noise and illustrate our design procedure on several examples.