arXiv subjects

Youssef Ait Si

Publications and source records attributed to Youssef Ait Si.

6 recordsLinked to original sources

arXiv2026

Specification-aware Robustness Margins for Symbolic Controllers

We address the problem of robust controller synthesis for a class of linear temporal logic (LTL) specifications over families of perturbed systems using symbolic control techniques. Given a dynamical system, a specification, and a symbolic controller synthesized using the fixed-point algorithm of the specification, the objective is to find the maximal perturbation we can apply to the system while the system continues to satisfy the same specification under the same controller. We first provide general results, by demonstrating that controllers synthesized based on the symbolic model can be refined back to a perturbed version of the concrete system while preserving their correctness. Focusing on four fundamental temporal logic specifications, namely safety, reachability, persistence, and recurrence, we introduce a general measure of the maximal robustness margin. Then, for each class of specifications, we derive a customized version of the measure and establish the corresponding theoretical guarantees. Importantly, the robustness margin depends explicitly on the sequence of sets generated during the fixed-point computation, allowing for specification-dependent and less conservative bounds compared to generic abstraction-based approaches. The theoretical developments are illustrated on two examples, demonstrating the practical applicability and effectiveness of the proposed approach.

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arXiv2026

Temporal Logic Resilience for Continuous-time Systems

In this paper, we present a novel framework for quantifying a lower bound on resilience in continuous-time (non)linear systems subject to external disturbances while ensuring satisfaction of signal temporal logic specifications. Unlike robustness, which evaluates how well a system satisfies a specification under a given disturbance, resilience measures the maximum disturbance a system can tolerate from a given initial state while maintaining specification satisfaction. We first derive bounds on the perturbed trajectories and then use them to formulate a computational method based on scenario optimization to efficiently compute the maximum admissible disturbance. We validate our approach through case studies, including dc motor, temperature regulation, a nonlinear numerical example, and a vehicle collision avoidance case.

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arXiv2026

Resilient and Effort-Optimal Controller Synthesis under Temporal Logic Specifications

In this paper, we consider the notions of effort and resilience of a dynamical control system defined by the maximum disturbance the system can withstand while satisfying given finite temporal logic specifications. Given a dynamical system and a specification, the objective is to synthesize the controller such that the system satisfies the specification while maximizing its resilience, taking into account input constraints. In addition, we introduce a new metric, called the effort metric, which characterizes the minimal input bound necessary to satisfy a given specification for a perturbed system. The problem for both metrics is formulated as a robust optimization program where the objective is to compute the maximum resilience for the system with input constraints or the minimal effort while simultaneously synthesizing the corresponding controller parameters. Moreover, we study the trade-off between resilience and effort, where we seek to maximize resilience and minimize the control effort. For linear systems and linear controllers, exact solutions are provided for the class of time-varying polytopic specifications for the closed-loop and open-loop systems. For the case of nonlinear systems, nonlinear controllers, and more general specifications, we leverage tools from the scenario optimization approach, offering a probabilistic guarantee of the solution as well as computational feasibility. Different case studies are presented to illustrate the theoretical results.

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arXiv2025

Computation of Feasible Assume-Guarantee Contracts: A Resilience-based Approach

We propose a resilience-based framework for computing feasible assume-guarantee contracts that ensure the satisfaction of temporal specifications in interconnected discrete-time systems. Interconnection effects are modeled as structured disturbances. We use a resilience metric, the maximum disturbance under which local specifications hold, to refine assumptions and guarantees across subsystems iteratively. We first demonstrate correctness and monotone refinement of guarantees for two subsystems. Then, we extend our approach to general networks of L subsystems using weighted combinations of interconnection effects. We instantiate the framework on linear systems by meeting finite-horizon safety, exact-time reachability, and finite-horizon reachability specifications, and on nonlinear systems by fulfilling general finite-horizon specifications. Our approach is demonstrated through numerical linear examples and a nonlinear DC microgrid case study, showcasing the impact of our framework on verifying temporal logic specifications with compositional reasoning.

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arXiv2025

Maximally Resilient Controllers under Temporal Logic Specifications

In this paper, we consider the notion of resilience of a dynamical system, defined by the maximum disturbance a controlled dynamical system can withstand while satisfying given temporal logic specifications. Given a dynamical system and a specification, the objective is to synthesize the controller such that the closed-loop system satisfies this specification while maximizing its resilience. The problem is formulated as a robust optimization program where the objective is to compute the maximum resilience while simultaneously synthesizing the corresponding controller parameters. For linear systems and linear controllers, exact solutions are provided for the class of time-varying polytopic specifications. For the case of nonlinear systems, nonlinear controllers and more general specifications, we leverage tools from the scenario optimization approach, offering a probabilistic guarantee of the solution as well as computational feasibility. Different case studies are presented to illustrate the theoretical results.

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arXiv2025

Symbolic Control: Unveiling Free Robustness Margins

This paper addresses the challenge of ensuring robustness in the presence of system perturbations for symbolic control techniques. Given a discrete-time control system that is related to its symbolic model by an alternating simulation relation. In this paper, we focus on computing the maximum robustness margin under which the symbolic model remains valid for a perturbed-version of the discrete-time control system. We first show that symbolic models are inherently equipped with a certain free robustness margins. We then provide constructive procedures to compute uniform and non-uniform (state and input dependent) robustness margins. We also show that the tightness of the robustness margin depends on the tightness of the reachability technique used to compute the symbolic model. We then explain how the computed robustness margin can be used for the sake of controller synthesis. Finally, we present two illustrative examples to demonstrate the effectiveness of our approach.

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