Towards Switched Control Under Input and State Constraints

Engineered systems which are safety-critical, high-risk, or expensive must often meet multiple objectives. In addition to guarantees of safe and reliable operation, other goals, such as stability, tracking, or optimality are also important. Indeed, a system which is guaranteed to be "safe" may not be implementable in practice unless it is also guaranteed to meet other performance objectives. In previous work, the problem of control design to meet multiple objectives was addressed through reachability analysis. For a feedback linearizable system subject to bounded control input and nonlinear state constraints, we synthesized a single controller guaranteed to 1) stabilize the nonlinear system despite input saturation, and 2) prevent violation of the state constraints. However, a single controller may be restrictive. Switching between multiple controllers may increase the region of operation for the system as well as improve its overall performance. We focus here on recent developments to synthesize a switched multi-objective controller through reachability analysis. The result provides a mathematical guarantee that for all states within the computed reachable set, there exists a switched control law that will simultaneously satisfy two separate goals: envelope protection (no violation of state constraints), and stabilization despite saturation. This is accomplished through a reachability calculation, in which the state is extended to incorporate input parameters for the switched system.