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.
Research in @cite_5 relates Ramadge-Wonham supervisory control to an equivalent model-checking problem, resulting in important observations regarding the mutual exchangeability and complexity analysis of both problems. Despite the fact that research in @cite_5 is limited to a deterministic setting, and synthesis results are not guaranteed to be maximally permissive, it does incorporate a quite expressible set of @math -calculus requirements. Other research based upon a dual approach between control synthesis and model checking studies the incremental effects of transition removal upon the validity of @math -calculus formulas @cite_14 , based on @cite_2 .
@cite_5 @cite_14 @cite_2
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Model checking and supervisor synthesis have been successful in solving different design problems related to discrete systems in the last decades. In this paper, we analyze some advantages and drawbacks of these approaches and combine them for mutual improvement. We achieve this through a generalization of the supervisory control problem proposed by Ramadge and Wonham. The objective of that problem is to synthesize a supervisor which constrains a system's behavior according to a given specification, ensuring controllability and coaccessibility. By introducing a new representation of the solution using systems of μ-calculus equations, we are able to handle these two conditions separately and thus to exchange the coaccessibility requirement by any condition that could be used in model checking. Well-known results on μ-calculus model checking allow us to easily assess the computational complexity of any generalization. Moreover, the model checking approach also delivers algorithms to solve the generalized synthesis problem. We include an example in which the coaccessibility requirement is replaced by fairness constraints. The paper also contains an analysis of related work by several authors. 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. This paper addresses the optimal control problem known as the Linear Quadratic Regulator in the case when the dynamics are unknown. We propose a multi-stage procedure, called Coarse-ID control, that estimates a model from a few experimental trials, estimates the error in that model with respect to the truth, and then designs a controller using both the model and uncertainty estimate. Our technique uses contemporary tools from random matrix theory to bound the error in the estimation procedure. We also employ a recently developed approach to control synthesis called System Level Synthesis that enables robust control design by solving a convex optimization problem. We provide end-to-end bounds on the relative error in control cost that are nearly optimal in the number of parameters and that highlight salient properties of the system to be controlled such as closed-loop sensitivity and optimal control magnitude. We show experimentally that the Coarse-ID approach enables efficient computation of a stabilizing controller in regimes where simple control schemes that do not take the model uncertainty into account fail to stabilize the true system. A traditional counterexample to a linear-time safety property shows the values of all signals at all times prior to the error. However, some signals may not be critical to causing the failure. A succinct explanation may help human understanding as well as speed up algorithms that have to analyze many such traces. In Bounded Model Checking (BMC), a counterexample is constructed from a satisfying assignment to a Boolean formula, typically in CNF. Modern SAT solvers usually assign values to all variables when the input formula is satisfiable. Deriving minimal satisfying assignments from such complete assignments does not lead to concise explanations of counterexamples because of how CNF formulae are derived from the models. Hence, we formulate the extraction of a succinct counterexample as the problem of finding a minimal assignment that, together with the Boolean formula describing the model, implies an objective. We present a two-stage algorithm for this problem, such that the result of each stage contributes to identify the “interesting” events that cause the failure. We demonstrate the effectiveness of our approach with an example and with experimental results.