Switched Controller Synthesis for Constrained Nonlinear Systems

Abstract

Given a system's mathematical model, controller synthesis involves designing inputs to ensure desired responses. As models get more complicated to capture systems' behavior, so does synthesis. For instance, nonlinearities in differential equations invalidate linear design tools. Moreover, the state and input are typically constrained by physical limitations or safety concerns. Satisfying these constraints complicates the design. Further, since no model is perfect, the controller should account for the inevitable discrepancies. This thesis develops practical design tools by imposing specific structures on controllers and exploiting key structures in dynamical models.The first part of this dissertation develops an offline, Lyapunov-based synthesis method for constrained control-affine systems that ensures stability and safety alongside secondary performance objectives. By limiting the search for the controller and Lyapunov function to continuous piecewise affine (CPA) functions, the Lyapunov conditions that must hold at all points in a compact set are turned into a non-convex program with a finite number of constraints defined on the vertices of a triangulated region. The non-convex program is then solved using a sequence of conservative, but well-posed semi-definite programs. This eliminates a priori design choices as well as taxing, non-convex optimizations common to existing methods. Two techniques to enlarge the region of attraction are discussed, including a state-dependent switched controller that further alleviates computations. Together with triangulation refinements, the method provides an efficient synthesis tool for constrained control-affine systems.The second part focuses on systems modeled by a combination of subsystems. First, the previous part's method is adjusted to design for piecewise affine systems. For these systems, an important source of conservatism in design by CPA functions is eliminated, making the method competitive to those that rely on S-procedure or complex optimizations. Second, a method of constraint enforcement in presence of mode-dependent, additive disturbances for time-dependent switched systems is given. This approach extends an existing method that solves the problem for the deterministic case. The dwell-time characteristic of the external switching signal is exploited to design recursively feasible, switched tube-based model predictive controllers (MPCs). The online computations remain the same as that of a non-switched tube-based MPC.