Anastasios Trontis

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.

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.

Eventuality synthesis for controlled linear automata

The synthesis of hybrid controllers that satisfy eventuality specifications is studied. Linear automata that accept continuous inputs are considered. The feedback control derivation is based on reachability analysis. A computational procedure for the reachable set, based on Fourier elimination and convexity analysis techniques, is derived. A feedback controller that guarantees the system will visit a given convex target set without violating state constraints is obtained.

Supervisory eventuality synthesis

This paper presents a study on the eventuality synthesis problem for hybrid automata. Given a hybrid automaton and a target set of states, we seek to compute a feedback controller as well as the maximal set of initial states from which all the trajectories of the closed system eventually reach the target set. Considering control action on the discrete event level only and applying reachability analysis, we derive a feedback eventuality controller Since, generally, there does not exist a least restrictive eventuality controller we propose a second controller and derive the necessary condition under which it becomes the least restrictive eventuality controller Finally, we investigate the relationship between eventuality and safety synthesis for hybrid automata and reach the conclusion that there is no duality in the extraction of the control law.

Target control for hybrid systems with linear continuous dynamics

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. This involves under-approximation of reachable sets under linear continuous dynamics. The algorithm is applied to a batch control problem.

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.

Target control for hybrid systems

This paper is concerned with the supervisory target control problem for hybrid systems modeled by hybrid automata. The problem is studied in a straightforward manner through reachability analysis. A switching controller is proposed such that all the trajectories of the controlled automaton, that initiate from a given initial set in the state space, reach a target set. At the same time a cost function, specified by weighting the discrete-event transitions of the automaton, is minimized. Emphasis is given to the control synthesis under event uncertainty modeled by uncontrollable transitions.

Hierarchical Control Synthesis for Eventuality Specifications in Hybrid Systems

Paper examining hierarchical control synthesis for eventuality specifications in hybrid systems.