7th Biannual Meeting on System and Control Theory
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چکیده
– We discuss a class of control problems for continuous time dynamical systems featuring synthesis of controllers to meet certain logic specifications. Such problems fall in the area of hybrid systems. Hybrid systems have been studied for some time; unfortunately the area has not delivered all that it promised: a theory of control synthesis has remained elusive. Some work has been done at the high level on synthesis of controllers for logic specifications inspired by discrete event system theory. These approaches do not confront where the true challenge lies: a (hopefully structural) characterization of the intrinsic limits of a continuous time control system to achieve a non-equilibrium specification. We study affine systems and logic specifications encoded as inequality constraints. Mathematically, the model is an affine system defined on a polytopic state space, and control synthesis typically yields piecewise affine controllers. By studying this special model, synthesis tools have been recoverable. The core synthesis problem has been distilled in the so-called Reach Control Problem (RCP). Roughly speaking, the problem is for an affine system xdot = A x + B u + a defined on a simplex to reach a pre-specified facet (boundary) of the simplex in finite time without first exiting the simplex. The significance of the problem stems from its capturing the essential requirements of logic specifications: state constraints and the notion of trajectories reaching a goal set of states in finite-time. In the talk I will give highlights of nearly 10 years of research on RCP: solvability by affine feedback, continuous state feedback, timevarying affine feedback, and piecewise affine feedback; an associated Lyapunov theory; a geometric structure theory; and emerging applications.
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تاریخ انتشار 2016