Control of Timed Discrete Event Systems with Ticked Linear Temporal Logic Constraints

This paper presents a novel method of synthesizing a fragment of a timed discrete event system(TDES),introducing a novel linear temporal logic(LTL), called ticked LTL$_f$. The ticked LTL$_f$ is given as an extension to LTL$_f$, where the semantics is defined over a finite execution fragment. Differently from the standard LTL$_f$, the formula is defined as a variant of metric temporal logic formula, where the temporal properties are described by counting the number of tick in the fragment of the TDES. Moreover, we provide a scheme that encodes the problem into a suitable one that can be solved by an integer linear programming (ILP). The effectiveness of the proposed approach is illustrated through a numerical example of a path planning.