A new Lyapunov design approach for nonlinear systems based on Zubov's method

Abstract

The present research work proposes a new nonlinear controller synthesis approach that is based on the methodological principles of Lyapunov design. In particular, it relies on a short-horizon model-based prediction and optimization of the rate of “energy dissipation” of the system, as it is realized through the time derivative of an appropriately selected Lyapunov function. The latter is computed by solving Zubov's partial differential equation based on the system's drift vector field. A nonlinear state feedback control law with two adjustable parameters is derived as the solution of an optimization problem that is formulated on the basis of the aforementioned Lyapunov function and closed-loop performance characteristics. A set of system-theoretic properties of the proposed control law are examined as well. Finally, the proposed Lyapunov design method is evaluated in a chemical reactor example which exhibits nonminimum-phase behaviour.