Logic-based switching algorithms in control

This thesis deals with the use of logic-based switching in the control of imprecisely modeled nonlinear systems. Each control system considered consists of a continuous-time dynamical process to be controlled, a family of candidate controllers, and an event-driven switching logic. The need for switching arises when no single candidate controller is capable, by itself, of guaranteeing good performance when connected with a poorly modeled process. In this thesis we develop provably correct switching strategies capable of determining in real-time which candidate controller should be put in feedback with a process so as to achieve a desired closed-loop performance. The resulting closed-loop systems are hybrid in the sense that in each case, continuous dynamics interact with event-driven logic. In the process of designing these switching algorithms, we develop several tools for the analysis and synthesis of hybrid systems. Some of these tools also find application in the design of nonadaptive logic-based switching controllers for systems like the “nonholonomic integrator”, a model that, although locally null controllable, is not stabilizable by smooth, time-invariant control laws. Poorly modeled sensors are also considered in this thesis. In our study of imprecisely modeled sensors we focus on the problem of positioning a robot using a pair of cameras acting as a position measuring device. We derive conditions that enable one to decide on the basis of images acquired by an imprecisely modeled two-camera system, whether or not a prescribed robot positioning task has been precisely accomplished. This line of research represents an initial step towards the design of feedback control systems capable of precise robot positioning using visual feedback, in spite of camera miscalibration.