This paper is about the design of control sequences of minimal time for a class of timed discrete event systems that behave in uncertain environment including unexpected and uncontrollable events. Such systems are modelled using partially controllable Transition-Timed Petri nets that encompass controllable deterministic, controllable stochastic and uncontrollable stochastic transitions. The main contribution of the work is to embed the timing aspect of such systems in Reconfigurable Timed Extended Reachability Graphs. As a consequence, the control problem is solved with standard optimization method. An application to the reactive scheduling of manufacturing systems highlights the advantages of the approach.

This paper presents a new method for sliding mode control to create a compromise between duration of reaching phase and response rate of the stochastic time-delay systems. A natural logarithm sliding surface is first constructed and then, the asymptotic stability with probability one for the closed-loop system has been analyzed by Lyapunov method. Some practical considerations are uncertain parameter variations, environmental matched disturbances, actuator degradation, stochastic environmental mismatched disturbances, and unmodeled dynamics. Finally, the simulation results show how to adjust the response rate and the sensitivity of the closed-loop system to the variations by regulating a special parameter.