Coordinating Feedback and Switching for Control of Hybrid Nonlinear Processes

A robust hybrid control strategy for a broad class of hybrid nonlinear processes with actuator constraints and uncertain dynamics is proposed. These ®ariable-structure processes comprise a finite family of constrained uncertain continuous nonlinear dynamical subsystems, together with discrete e®ents that trigger the transition between the continuous subsystems. The proposed control strategy is predicated on the idea of coordinating the hierarchical tasks of lower-le®el feedback-controller synthesis and upper-le®el switching logic design. Using multiple Lyapuno® functions, a family of bounded robust, nonlinear feedback controllers are initially designed to robustly stabilize the constituent modes of the hybrid process, subject to uncertainty and constraints. The region of guaranteed closed-loop stability is then explicitly characterized for each mode in terms of the magnitude of actuator constraints and the size of the uncertainty. A set of stabilizing switching laws that track the energy e®olution of the constituent modes are then deri®ed to orchestrate safe transitions between the stability regions of the constituent modes and their respecti®e controllers, in a way that respects actuator constraints and guarantees robust stability of the o®erall uncertain hybrid closed-loop system. This hybrid control method is applied through computer simulations to robustly stabilize an exothermic chemical reactor with switched dynamics, model uncertainty, and actuator constraints at an unstable steady-state and to design a fault-tolerant control system for chemical reactors through switching between multiple constrained control configurations.