Supervisory target control for hybrid systems

Abstract

The problem of systematically synthesizing supervisory control laws that satisfy eventuality and efficiency requirements for hybrid systems modelled by hybrid automata is considered. Here, the efficiency requirement is specified by weighting the discrete transitions of the system. The optimization of the efficiency requirement is considered in the min-max sense due to the existence of disturbance inputs. Adopting a game theoretic approach, the high priority eventuality requirement is considered first and the class of controls, in which the low priority efficiency requirement should be optimized, is obtained. Then, a dynamic programming algorithm, which determines the value function of the optimization problem, is derived. A synthesis problem on a simplified batch process plant is considered to illustrate a potential application of the approach

Hybrid control synthesis for eventuality specifications using level set methods

“…The results of the paper can be seen as the extension of the results presented in Trontis and Spathopoulos (2003) and Xia et al (2002) on the supervisory control synthesis for eventuality specifications. Recall that in supervisory control synthesis problems no control over the continuous dynamics of the system is considered.…”

“…Obviously, C is not the unique solution to the eventuality synthesis problem ðA; ÅFÞ. In Trontis and Spathopoulos (2003), by defining a cost function with respect to the discrete transitions of the system, we derived a different eventuality controller for hybrid automata that do not accept continuous inputs.…”

“…In Xia et al (2002) a solution is derived for hybrid automata that accept discrete control inputs only. In Trontis and Spathopoulos (2003) an optimization criterion related with the discrete transitions of the system was considered on top of the standard eventuality specification and the result of Xia et al (2002) was extended for the same class of hybrid automata. Also, the application of level set methods for the design of a supervisor for the batch evaporator has been previously presented in Trontis and Spathopoulos (2002), where a simplified solution to the eventuality synthesis problem is proposed in the case the set of initial states is known.…”

Synthesis of controllers for target problems of hybrid systems using approximate computation

“…The target control problem for hybrid automata has been studied in and , 2003a, 2003b and the solution is derived using reachability analysis. The basic idea here, instead of using the whole state space for reachability, is to find the shortest discrete path that has the minimal discrete cost from the initial set to the target set.…”

“…Programmable Logic Controllers (PLCs) or Distributed Control Systems (DCSs). Design problems in such systems can be seen as target control problems Spathopoulos 2003b), where given the initial set and the target set of states, one asks to derive the switching strategy of the controller such that the system eventually reaches the desired target set. As the same time, a discrete controller must be designed in the process to ensure safe start up, shut down and correct batch sequences.…”