We propose a new method for controlled system synthesis on non-deterministic automata, which includes the synthesis for deadlock-freeness, as well as invariant and reachability expressions. Our technique restricts the behavior of a Kripke-structure with labeled transitions, representing the uncontrolled system, such that it adheres to a given requirement specification in an expressive modal logic. while all non-invalidating behavior is retained. This induces maximal permissiveness in the context of supervisory control. Research presented in this paper allows a system model to be constrained according to a broad set of liveness, safety and fairness specifications of desired behavior, and embraces most concepts from Ramadge-Wonham supervisory control, including controllability and marker-state reachability. Synthesis is defined in this paper as a formal construction, which allowed a careful validation of its correctness using the Coq proof assistant.
Ramadge-Wonham supervisory control @cite_4 defines a broadly-embraced meth-odology for controller synthesis on deterministic plant models for requirements specified using automata. It defines a number of key elements in the relationship between plant and controlled system, such as controllability, marker-state reachability, deadlock-freeness and maximal permissiveness. Despite the fact that a strictly separated controller offers advantages from a developmental or implementational point of view, we argue that increased abstraction and flexibility justifies research into control synthesis for non-deterministic models. In addition, we emphasize that the automata-based description of desired behavior in the Ramadge-Wonham framework @cite_4 does not allow the specification of requirements of existential nature. For instance, in this framework it is not possible to specify that a step labeled with a particular event exist, hence the choice of modal logic as our requirement formalism.
@cite_4
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The decidability of the distributed version of the Ramadge and Wonham controller synthesis problem, where both the plant and the controllers are modeled as asynchronous automata and the controllers have causal memory is a challenging open problem. There exist three classes of plants for which the existence of a correct controller with causal memory has been shown decidable: when the dependency graph of actions is series-parallel, when the processes are connectedly communicating and when the dependency graph of processes is a tree. We design a class of plants, called decomposable games, with a decidable controller synthesis problem. This provides a unified proof of the three existing decidability results as well as new examples of decidable plants. 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. We present a novel technique for synthesising behaviour models that works for an expressive subset of liveness properties and conforms to the foundational requirements engineering World Machine model, dealing explicitly with assumptions on environment behaviour and distinguishing controlled and monitored actions. This is the first technique that conforms to what is considered best practice in requirements specifications: distinguishing prescriptive and descriptive assertions. Most previous attempts at using synthesis of behavioural models were restricted to handling only safety properties. Those that did support liveness were inadequate for synthesis of operational event based models as they did not include the bespoke distinction between system goals and environment assumptions. Formal verification of a control system can be performed by checking if a model of its dynamical behavior conforms to temporal requirements. Unfortunately, adoption of formal verification in an industrial setting is a formidable challenge as design requirements are often vague, nonmodular, evolving, or sometimes simply unknown. We propose a framework to mine requirements from a closed-loop model of an industrial-scale control system, such as one specified in Simulink. The input to our algorithm is a requirement template expressed in parametric signal temporal logic: a logical formula in which concrete signal or time values are replaced with parameters. Given a set of simulation traces of the model, our method infers values for the template parameters to obtain the strongest candidate requirement satisfied by the traces. It then tries to falsify the candidate requirement using a falsification tool. If a counterexample is found, it is added to the existing set of traces and these steps are repeated; otherwise, it terminates with the synthesized requirement. Requirement mining has several usage scenarios: mined requirements can be used to formally validate future modifications of the model, they can be used to gain better understanding of legacy models or code, and can also help enhancing the process of bug finding through simulations. We demonstrate the scalability and utility of our technique on three complex case studies in the domain of automotive powertrain systems: a simple automatic transmission controller, an air-fuel controller with a mean-value model of the engine dynamics, and an industrial-size prototype airpath controller for a diesel engine. We include results on a bug found in the prototype controller by our method.