Feedback stabilization of nonlinear systems: "universal'' constructions towards real-life applications

Abstract

Various feedback stabilizers based on Sontag's ``universal'' formula for stabilizing control laws are presented, incorporating restrictions inspired by real-life applications. The first main contribution is an extension of Sontag's ``universal'' formula for positive nonlinear control systems. More specifically, an auxiliary function is introduced in the feedback interconnection, such that invariance of the positive orthant is retained for the system in closed loop with the ``universal'' stabilizer. We further state a ``universal'' event-based stabilizer for bounded controls and develop an extension of the controller for positive systems. In a motivating case study from systems biology, the methodology is shown to provide clinically realistic control inputs, which can be used for treatment in real life. The second main contribution is the construction of continuous and piecewise affine (CPA) feedback stabilizers for nonlinear control systems affine in the input, motivated by the ease of implementation of the resulting control law. A verification procedure for ``universal'' CPA stabilizers is provided, together with an alternative computational method for CPA stabilizers via linear programming. Two numerical examples are presented for illustration of the CPA method.

Date of Award	2 Dec 2016
Original language	English
Supervisor	Mircea Lazar (Supervisor 1)