Multiobjective bounded control of uncertain nonlinear systems: An inverted pendulum example

Given a class of nonlinear, parameter-dependent, perturbed systems, we propose a methodology for the synthesis of an output-feedback controller such that the closed-loop system satisfies a number of specifications. Our specifications include stability, disturbance rejection, command input and output peak bounds. Some parameters and/or states that appear in the nonlinearities are measured in real time. The controller is allowed to depend on this measured information, if any. Furthermore, our specifications must be satisfied robustly with respect to the remaining unmeasured ones. Sufficient conditions that ensure the existence of this so-called "robust measurement-scheduled" controller are derived. These conditions are LMIs. associated with a set of non-convex conditions. We propose an efficient heuristic to solve them, and illustrate our design method with an inverted pendulum example.