Hybrid Control System Design Based on Natural Invariants - Decision and Control, 1995., Proceedings of the 34th IEEE Conference on

The hybrid control systems considered here consist of a continuous plant under the control of a discrete event system. Communication between the plant and controller is provided by an interface that can convert signals from the continuous domain to the symbolic domain, and vise-versa. Hybrid control system design generally involves designing a controller, possibly designing some or all of the interface, and in some cases, designing a continuous controller that will become part of the continuous-time plant. This paper examines the case where the interface is partially given, along with the plant and a set of control goals. A method is presented which designs the symbol generating portion of the interface and also yields a controller for the system. The method is based on the natural invariants of the plant. This technique is illustrated by an example in which the design process is simulated via a computer program for an unmanned underwater vehicle. 1 Hybrid Control System Modeling A hybrid control system, can be divided into three parts, the plant, interface, and controller as shown in Figure 1. The plant is a nonlinear, time-invariant system represented by a set of ordinary differential equations, q t ) = f(x(t), r(t>), (1) where x ( t ) E X and r(t) E R are the state and input vectors respectively, and X c Rn, R C Rml with t E (a, b ) some time interval. For any r(t) E R, the function f : X x R + X is continuous in x and meets the conditions for existence and uniqueness of solutions for initial states, xg E X. Note that the plant input and state are continuous-time vector valued signals. Boldface letters are used here to denote vectors and vector valued signals. The controller is a discrete event system which is modeled as a deterministic automaton, (s,x, R, 6, 4) , where 3 is the set of states, is the 0-7803-2685-7/95 $4.00