The batch evaporator: A case study of target control for hybrid systems using level set methods

Trontis, A.; Spathopoulos, M.P.

doi:10.1109/cdc.2002.1184748

Cited by 2 publications

(2 citation statements)

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“…The idea is to solve the reachability problem without considering any state constraints first and then remove from W Ã the states that can reach states which do not satisfy the constraints. This idea has been presented briefly in Trontis and Spathopoulos (2002) for the computation of the reachable set W Ã under state constraints for systems of the form _ x x ¼ f ðxÞ. Such systems appear in supervisory control problems for hybrid systems, where it is assumed that the continuous control strategies of the plant have already been determined in each control location and the design is restricted to the discrete transitions of the system.…”

Section: Reachability With State Constraintsmentioning

confidence: 99%

“…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.…”

Section: Introductionmentioning

confidence: 99%

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Hybrid control synthesis for eventuality specifications using level set methods

Trontis¹,

Spathopoulos²

2003

International Journal of Control

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This paper is concerned with the extraction of controllers for hybrid systems with respect to eventuality specifications. Given a hybrid system modelled by a hybrid automaton and a target set of states, the objective is to compute the maximal set of initial states together with the hybrid control policy such that all the trajectories of the controlled system reach the target in finite time. Due to the existence of set-valued disturbance inputs, the problem is studied in a game-theoretic framework. Having shown that a least restrictive solution does not exist, we propose a dynamic programming algorithm that computes the maximal initial set and a controller with the desired property. To implement the algorithm, reachable sets of pursuit-evasion differential games need to be computed. For that reason level set methods are employed, where the boundary of the reachable set is characterized as the zero level set of a Hamilton-Jacobi equation. The procedure for the numerical extraction of the controller is presented in detail and examples illustrate the methodology. Finally, to demonstrate the practical character of our results, a control design problem in the benchmark system of the batch evaporator is considered as an eventuality synthesis problem and solved using the proposed methodology

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Section: Reachability With State Constraintsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%