Permissive Controller Synthesis for Probabilistic Systems

We propose novel controller synthesis techniques for probabilistic systems modelled using stochastic two-player games: one player acts as a controller, the second represents its environment, and probability is used to capture uncertainty arising due to, for example, unreliable sensors or faulty system components. Our aim is to generate robust controllers that are resilient to unexpected system changes at runtime, and flexible enough to be adapted if additional constraints need to be imposed. We develop a permissive controller synthesis framework, which generates multi-strategies for the controller, offering a choice of control actions to take at each time step. We formalise the notion of permissivity using penalties, which are incurred each time a possible control action is disallowed by a multi-strategy. Permissive controller synthesis aims to generate a multi-strategy that minimises these penalties, whilst guaranteeing the satisfaction of a specified system property. We establish several key results about the optimality of multi-strategies and the complexity of synthesising them. Then, we develop methods to perform permissive controller synthesis using mixed integer linear programming and illustrate their effectiveness on a selection of case studies

Substructural controller synthesis

A decentralized design procedure which combines substructural synthesis, model reduction, decentralized controller design, subcontroller synthesis, and controller reduction is proposed for the control design of flexible structures. The structure to be controlled is decomposed into several substructures, which are modeled by component mode synthesis methods. For each substructure, a subcontroller is designed by using the linear quadratic optimal control theory. Then, a controller synthesis scheme called Substructural Controller Synthesis (SCS) is used to assemble the subcontrollers into a system controller, which is to be used to control the whole structure

Lazy Abstraction-Based Controller Synthesis

We present lazy abstraction-based controller synthesis (ABCS) for continuous-time nonlinear dynamical systems against reach-avoid and safety specifications. State-of-the-art multi-layered ABCS pre-computes multiple finite-state abstractions of varying granularity and applies reactive synthesis to the coarsest abstraction whenever feasible, but adaptively considers finer abstractions when necessary. Lazy ABCS improves this technique by constructing abstractions on demand. Our insight is that the abstract transition relation only needs to be locally computed for a small set of frontier states at the precision currently required by the synthesis algorithm. We show that lazy ABCS can significantly outperform previous multi-layered ABCS algorithms: on standard benchmarks, lazy ABCS is more than 4 times faster

On the Control of Asynchronous Automata

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 automataand the controllers have causal memoryis 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