This paper presents a novel approach to including non-instantaneous discrete control transitions in the linear hybrid automaton approach to simulation and verification of hybrid control systems. In this paper we study the control of a continuously evolving analog plant using a controller programmed in a synchronous programming language. We provide extensions to the synchronous subset of the SystemJ programming language for modeling, implementation, and verification of such hybrid systems. We provide a sound rewrite semantics that approximate the evolution of the continuous variables in the discrete domain inspired from the classical supervisory control theory. The resultant discrete time model can be verified using classical model-checking tools. Finally, we show that systems designed using our approach have a higher fidelity than the ones designed using the hybrid automaton approach.
Finally, the work closest to the one described in this article is done by: (1) @cite_2 , where they extend the Esterel language to model timed automata @cite_1 , i.e., ODEs with rate of change always equal to 1. In this proposal we are able to model the more general hybrid rather than its subset timed automaton and (2) @cite_12 , which is a seminal work in extending synchronous imperative languages to model hybrid automaton. This work is extended further and completed by giving a formal treatment by @cite_13 . The work described herein differs significantly from both; @cite_13 and @cite_12 in that they do not approximate the continuous behavior of the plant, instead all discrete transitions are carried out and then a so called continuous phase is launched, which models the continuous evolution of the plant until the invariant condition holds, just like in hybrid automaton. Since these approaches derive their semantics from hybrid automaton, they inherit the same problem described in , i.e., non-zero mode-switch transitions cannot be captured in the semantics.
@cite_13 @cite_1 @cite_12 @cite_2
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Abstract A hallmark of the Esterel language is the combination of perfect synchrony with total orthogonality and powerful constructs for preemption, suspension and trap handling. It is desirable to make this kind of expressiveness available for the description of hybrid systems, that is, systems whose evolution is understood in terms of segment-wise continuous functions over the real time axis. Our approach consists of modifying Esterel concepts, most notably by replacing the discrete time frame by a continuously advancing one. We are then able to state a semantics made up of transitions with closed execution intervals of non-zero length. By an instant we understand an execution interval within this framework. Hybrid signals may change their value during such an instant, non-hybrid ones, that is, classical signals immediately settle to a specific state and keep it the whole time. Time consumption still has to be specified explicitly, namely in that instants reflect jumps among control flow locations defined by pause statements; all other statements take no time in the sense that arbitrarily many of them may be sequentially executed regardless of the instant's duration. A transfer of perfect synchrony from the discrete to the continuous is in this way accomplished. We also consider an example, which is from the automotive domain, traces, bisimilarity and compositionality. Abstract We present an approximation technique, that can render real-time model checking of safety and universal path properties more efficient. It is beneficial, when loops lead to repetition of control situations. Basically we augment a timed automata model with carefully selected extra transitions. This increases the size of the state-space, but potentially decreases the number of symbolic states to be explored by orders of magnitude. We give a formal definition of a timed automata formalism, enriched with basic data types, hand-shake synchronization, urgency, and committed locations. We prove by means of a trace semantics, that if a safety property can be established in the augmented model, it also holds for the original model. We extend our technique to a richer set of properties, that can be decided via a set of traces (universal path properties). In order for universal path properties to carry over to the original model, the semantics of the timed automata formalism is formulated relative to the applied augmentation. Our technique is particularly useful in systems, where a scheduler dictates repetition of control over elapsing time. As a typical example we mention translations of LEGO® RCX™ programs to U ppaal models, where the Round-Robin scheduler is a static entity. We allow scheduler and associated tasks to “park”, until some timing or environmental conditions are met. We apply our technique on a brick-sorter model for a safety property and report run-time data. This paper presents a new algorithm for generating finite-state automata models of hybrid systems in which the continuous-state dynamics can be switched when the continuous-state trajectory generates threshold events. The automata state transitions correspond to threshold events and the automata states correspond to portions of the threshold surfaces in the continuous state space. The hybrid system dynamics are approximated by the automata models in the sense that the languages of threshold event sequences generated by the automata contain the threshold event language for the hybrid system. Properties of the algorithm for constructing and refining the approximating automata are demonstrated and the application of approximating automata for system verification is illustrated for a switching controller for an inverted pendulum. Relationships to other approaches to hybrid system synthesis and verification are also discussed. The paper concerns the synthesis of supervisory controllers for a class of continuous-time hybrid systems with discrete-valued input signals that select differential inclusions for continuous-valued state trajectories and event-valued output signals generated by threshold crossings in the continuous state space, the supervisor is allowed to switch the input signal value when threshold events are observed. The objective is to synthesize a nonblocking supervisor such that the set of possible sequences of control and threshold event pairs for the closed-loop system lies between given upper and lower bounds in the sense of set containment. We show how this problem can be converted into a supervisor synthesis problem for a standard controlled discrete-event system (DES). A finite representation may not exist for the exact DES model of the hybrid system, however. To circumvent this difficulty, we present an algorithm for constructing finite-state Muller automata that accept outer approximations to the exact controlled threshold-event language, and we demonstrate that supervisors that solve the synthesis problem for the approximating automata achieve the control specifications when applied to the original hybrid system.