Control Synthesis for a Class of Hybrid Systems Subject to Configuration-Based Safety Constraints

We examine a class of hybrid systems which we call Composite Hybrid Machines (CHM's) that consists of the concurrent (and partially synchronized) operation of Elementary Hybrid Machines (EHM's). Legal behavior, specified by a set of illegal configurations that the CHM may not enter, is to be achieved by the concurrent operation of the CHM with a suitably designed legal controller. In the present paper we focus on the problem of synthesizing a legal controller, whenever such a controller exists. More specifically, we address the problem of synthesizing the minimally restrictive legal controller. A controller is minimally restrictive if, when composed to operate concurrently with another legal controller, it will never interfere with the operation of the other controller and, therefore, can be composed to operate concurrently with any other controller that may be designed to achieve liveness specifications or optimality requirements without the need to reinvestigate or reverify legality of the composite controller. We confine our attention to a special class of CHM's where system dynamics is rate-limited and legal guards are conjunctions or disjunctions of atomic formulas in the dynamic variables (of the type x less than or equal to x(sub 0), or x greater than or equal to x(sub 0)). We present an algorithm for synthesis of the minimally restrictive legal controller. We demonstrate our approach by synthesizing a minimally restrictive controller for a steam boiler (the verification of which recently received a great deal of attention).