A new Lyapunov design method for nonlinear process control

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 introduces a notion of short-horizon model-based prediction and optimization of the rate of ``energy dissipation'' of the system, as it is realized through the derivative of an appropriately selected control 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 control Lyapunov function and closed-loop performance characteristics. A set of key properties of the proposed control law is examined. Key properties include continuity, unity static (steady-state) gain in closed-loop, closed-loop internal stability and enlargement of the quadratic closed-loop stability region estimates. The proposed Laypunov design method is evaluated in a representative chemical reactor example which exhibits nonminimum-phase behaviour, and the main design aspects are illustrated through simulation studies.