Adnane Saoud

Yoshinari Takayama, Alessio Iovine, Bart Besselink et al.

Real-world control systems must achieve long-horizon objectives (liveness) while respecting continuous-time safety constraints, a combination that motivates hierarchical layered control architectures (LCAs). Existing LCA research, however, lacks (i) a uniform specification language across discrete planning and continuous execution, (ii) formal guarantees that specifications are preserved when interconnecting subsystems at heterogeneous time scales, and (iii) compositional separation between layers, owing to reliance on naive input-filtering laws. This paper addresses all three gaps by importing the safety--liveness decomposition into a heterogeneous assume--guarantee framework: \emph{safety is enforced by invariance} at the continuous-time layer, while \emph{liveness is achieved through refinement} at the discrete-time layer, with inter-layer coordination formalized via vertical refinement and timing-compatibility conditions. We instantiate this contract with a novel LCA combining an MPC planner, an input-to-state stabilizing (ISS) low-level controller, and a reference-governor bridge, and validate it on a Hybrid Energy Storage System (HESS) comprising a battery and a supercapacitor.

Ratnangshu Das, Negar Monir, Youssef Ait Si et al.

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.

Youssef Ait Si, Ratnangshu Das, Negar Monir et al.

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.

Mohammed Bouri, Adnane Saoud

Despite advancements in Natural Language Processing (NLP), models remain vulnerable to adversarial attacks, such as synonym substitutions. While prior work has focused on improving robustness for feed-forward and convolutional architectures, the robustness of recurrent networks and modern state space models (SSMs), such as S4, remains understudied. These architectures pose unique challenges due to their sequential processing and complex parameter dynamics. In this paper, we introduce a novel regularization technique based on Growth Bound Matrices (GBM) to improve NLP model robustness by reducing the impact of input perturbations on model outputs. We focus on computing the GBM for three architectures: Long Short-Term Memory (LSTM), State Space models (S4), and Convolutional Neural Networks (CNN). Our method aims to (1) enhance resilience against word substitution attacks, (2) improve generalization on clean text, and (3) providing the first systematic analysis of SSM (S4) robustness. Extensive experiments across multiple architectures and benchmark datasets demonstrate that our method improves adversarial robustness by up to 8.8% over existing baselines. These results highlight the effectiveness of our approach, outperforming several state-of-the-art methods in adversarial defense. Codes are available at https://github.com/BouriMohammed/GBM

Emmanuel Junior Wafo Wembe, Adnane Saoud

In this paper, we revisit the computation of controlled invariant sets for linear discrete-time systems through a trajectory-based viewpoint. We begin by introducing the notion of convex feasible points, which provides a new characterization of controlled invariance using finitely long state trajectories. We further show that combining this notion with the classical backward fixed-point algorithm allows us to compute the maximal controlled invariant set. Building on these results, we propose two MPC schemes that guarantee recursive feasibility without relying on precomputed terminal sets. Finally, we formulate the search for convex feasible points as an optimization problem, yielding a practical computational method for constructing controlled invariant sets. The effectiveness of the approach is illustrated through numerical examples.

Sadek Belamfedel Alaoui, Adnane Saoud

Q-learning is widely recognized as an effective approach for synthesizing controllers to achieve specific goals. However, handling challenges posed by continuous state-action spaces remains an ongoing research focus. This paper presents a systematic analysis that highlights a major drawback in space discretization methods. To address this challenge, the paper proposes a symbolic model that represents behavioral relations, such as alternating simulation from abstraction to the controlled system. This relation allows for seamless application of the synthesized controller based on abstraction to the original system. Introducing a novel Q-learning technique for symbolic models, the algorithm yields two Q-tables encoding optimal policies. Theoretical analysis demonstrates that these Q-tables serve as both upper and lower bounds on the Q-values of the original system with continuous spaces. Additionally, the paper explores the correlation between the parameters of the space abstraction and the loss in Q-values. The resulting algorithm facilitates achieving optimality within an arbitrary accuracy, providing control over the trade-off between accuracy and computational complexity. The obtained results provide valuable insights for selecting appropriate learning parameters and refining the controller. The engineering relevance of the proposed Q-learning based symbolic model is illustrated through two case studies.

Alex Devonport, Adnane Saoud, Murat Arcak

Symbolic control techniques aim to satisfy complex logic specifications. A critical step in these techniques is the construction of a symbolic (discrete) abstraction, a finite-state system whose behaviour mimics that of a given continuous-state system. The methods used to compute symbolic abstractions, however, require knowledge of an accurate closed-form model. To generalize them to systems with unknown dynamics, we present a new data-driven approach that does not require closed-form dynamics, instead relying only the ability to evaluate successors of each state under given inputs. To provide guarantees for the learned abstraction, we use the Probably Approximately Correct (PAC) statistical framework. We first introduce a PAC-style behavioural relationship and an appropriate refinement procedure. We then show how the symbolic abstraction can be constructed to satisfy this new behavioural relationship. Moreover, we provide PAC bounds that dictate the number of data required to guarantee a prescribed level of accuracy and confidence. Finally, we present an illustrative example.