Control of Hybrid Nonlinear Systems

Abstract

In this chapter, we develop hybrid nonlinear control methodologies for various classes of hybrid nonlinear processes. Initially, switched processes whose dynamics are both constrained and uncertain are considered. These are systems that consist of a finite family of continuous uncertain nonlinear dynamical subsystems, subject to hard constraints on their manipulated inputs, together with a higher–level supervisor that governs the transitions between the constituent modes. The key feature of the proposed control methodology is the integrated synthesis, via multiple Lyapunov functions (MLFs), of: (1) a family of lower-level robust bounded nonlinear feedback controllers that enforce robust stability in the constituent uncertain modes, and provide an explicit characterization of the stability region for each mode under uncertainty and constraints, and (2) upper-level robust switching laws that orchestrate safe transitions between the modes in a way that guarantees robust stability in the overall switched closed–loop system. Next, we consider switched nonlinear systems with scheduled mode transitions. These are systems that transit between their constituent modes at some predetermined switching times, following a prescribed switching sequence. For such systems, we develop a Lyapunov–based predictive control strategy that enforces both the required switching schedule and closed–loop stability. The main idea is to design a Lyapunov–based predictive controller for each mode, and incorporate transition constraints in the predictive controller design to ensure that the prescribed transitions between the modes occur in a way that guarantees stability of the switched closed–loop system. The proposed control methods are demonstrated through applications to chemical process examples. Finally, the chapter concludes with a demonstration of how hybrid systems techniques – in particular, the idea of coupling the switching logic to stability regions – can be applied for the analysis and control of mode transitions in biological networks. The results in this chapter were first presented in [82, 85, 196].