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Timed automata (TA) is used for modeling systems with timing aspects. A TAextends a finite automaton with a set of real valued variables called clocks,that measure the time and constraints over the clocks guard the transitions. Aparametric TA (PTA) is a TA extension that allows parameters in clockconstraints. In this paper, we focus on synthesis of a control strategy andparameter valuation for a PTA such that each run of the resulting TA reaches atarget location within the given amount of time while avoiding unsafelocations. We propose an algorithm based on depth first analysis combined withan iterative feasibility check. The algorithm iteratively constructs a symbolicrepresentation of the possible solutions, and employs a feasibility check toterminate the exploration along infeasible directions. Once the construction iscompleted, a mixed integer linear program is solved for each candidate strategyto generate a parameter valuation and a control strategy pair. We present arobotic planning example to motivate the problem and to illustrate the results.

Control Synthesis for Parametric Timed Automata under Unavoidability Specifications