On synthesizing tolerable and permissive controllers for labeled transition systems

Control systems should enforce a desired property for both expected/modeled situations as well as unexpected/unmodeled environmental situations. Existing methods focus on designing maximally permissive controllers to enforce the desired property only when the environment behaves as expected. However, these methods lack discussion on how the system behaves when the environment is perturbed. We propose an approach for analyzing discrete-state systems with respect to their permissiveness and tolerance against environmental perturbations. There is an inherent trade-off between permissiveness and tolerance that we capture via Pareto optimality conditions. We investigate this trade-off by defining Pareto optimality between permissiveness and tolerance for invariance properties. We show that memoryless controllers are sufficient to describe the Pareto front. We also study the problem of synthesizing Pareto optimal controllers that achieve a minimum level of tolerance and permissiveness.