Hybrid target control design

We consider the target control problem for hybrid systems with linear continuous dynamics. The system is modelled as a hybrid automaton. Control action is applied on the discrete level, while the continuous dynamics is subject to constant or set valued disturbance. The proposed controller ensures that the system can be transferred from any point of an initial set to a target set of the hybrid state space. A control design algorithm based on reachability analysis is proposed. For the implementation of the algorithm, approximate reachability analysis is employed

On supervisory control for timed automata using urgency - invited session

The supervisory controller is state feedback and disables discrete-event transitions in order to solve the non-blocking forbidden state problem. The non-blocking problem is defined under both strong and weak conditions. For the latter maximally permissive solutions that are computable on a finite quotient space characterised by language equivalence are derived

On the control synthesis for target problems in continuous and hybrid systems using level set methods

The focus of this paper is on the numerical solution of target control problems in continuous systems using level set methods. Such control problems appear naturally in hybrid control synthesis when specifications with respect to reachable states of the system are considered. To account for the existence of disturbance inputs the problem is studied as a pursuit-evasion differential game. The boundary of the reachable set, i.e. the set of states from which the problem is feasible, is characterized as the zero level set of the viscosity solution of a Hamilton-Jacobi PDE. Our contribution is the detailed presentation of the procedure for the computation of the control and worst-case disturbance policies together with the reachable set using level set methods

Hybrid control synthesis for eventuality specifications using level set methods

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

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

The batch evaporator is employed as a benchmark example of supervisory control synthesis for hybrid systems. The control objective is the design of an emergency shut-down sequence. The specification is translated into a target control problem on hybrid automata and a switching controller is proposed such that all the trajectories of the controlled automaton, which initiate from a given initial set in the state space, reach a target set. The problem is studied in a straightforward manner, through reachability analysis, considering nonlinear continuous dynamics. Level set methods are utilized, where the boundary of the reachable set is characterized as the zero level set of the viscosity solution of a Hamilton-Jacobi equation

Discussion on: Supervisory control of discrete event systems with flexible marking

This paper proposes a new class of Discrete Event Systems endowed with control called DES with flexible marking (DESFM). The DESFM is modeled by a language and a control structure. The language contains all the strings of events that the system can generate. The control structure is a function that associates a set of controls to each string generated by the system. A control encapsulates information of event-enabling and marking for the string. The model is shown to be suitable for systems with abstraction for hierarchical control. The condition for existence of a supervisor and the synthesis of an optimal supervisory control scheme, in the sense of maximal permissiveness, are given. An illustrative example where the DESFM is naturally applied is presented

Supervisory target control for hybrid systems

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

Hierarchical control synthesis for eventuality specifications in hybrid systems - Invited Session

Paper examining hierarchical control synthesis for eventuality specifications in hybrid systems

Some Issues on Control of Discrete Event Systems Using Model Specifications

In this paper the control of a logical discrete-event system is introduced using predicates and associated blocking events. The blocking occurs when a predicate concerning the system behaviour becomes true. It is shown that model specifications can be transformed into control objectives involving predicates and blocking events. Next, we consider the control problem when events are unobservable and uncontrollable. It is shown that when the control objectives are decidable a separation principle holds, i.e., the problems of uncontrollability and unobservability can be solved separately and independently.