arXiv subjects

Adnane Saoud

Publications and source records attributed to Adnane Saoud.

At least 37 records · Page 2Linked to original sources

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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arXiv2025

Bridging Robustness and Generalization Against Word Substitution Attacks in NLP via the Growth Bound Matrix Approach

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

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arXiv2025

Controller Synthesis of Collaborative Signal Temporal Logic Tasks for Multi-Agent Systems via Assume-Guarantee Contracts

This paper considers the problem of controller synthesis of signal temporal logic (STL) specifications for large-scale multi-agent systems, where the agents are dynamically coupled and subject to collaborative tasks. A compositional framework based on continuous-time assume-guarantee contracts is developed to break the complex and large synthesis problem into subproblems of manageable sizes. We first show how to formulate the collaborative STL tasks as assume-guarantee contracts by leveraging the idea of funnel-based control. The concept of contracts is used to establish our compositionality result, which allows us to guarantee the satisfaction of a global contract by the multi-agent system when all agents satisfy their local contracts. Then, a closed-form continuous-time feedback controller is designed to enforce local contracts over the agents in a distributed manner, which further guarantees the global task satisfaction based on the compositionality result. Finally, the effectiveness of our results is demonstrated by two numerical examples.

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arXiv2024

Energy Efficient Aerial RIS: Phase Shift Optimization and Trajectory Design

Reconfigurable Intelligent Surface (RIS) technology has gained significant attention due to its ability to enhance the performance of wireless communication systems. The main advantage of RIS is that it can be strategically placed in the environment to control wireless signals, enabling improvements in coverage, capacity, and energy efficiency. In this paper, we investigate a scenario in which a drone, equipped with a RIS, travels from an initial point to a target destination. In this scenario, the aerial RIS (ARIS) is deployed to establish a direct link between the base station and obstructed users. Our objective is to maximize the energy efficiency of the ARIS while taking into account its dynamic model including its velocity and acceleration along with the phase shift of the RIS. To this end, we formulate the energy efficiency problem under the constraints of the dynamic model of the drone. The studied problem is challenging to solve. To address this, we proceed as follows. First, we introduce an efficient solution that involves decoupling the phase shift optimization and the trajectory design. Specifically, the closed-form expression of the phase-shift is obtained using a convex approximation, which is subsequently integrated into the trajectory design problem. We then employ tools inspired by economic model predictive control (EMPC) to solve the resulting trajectory optimization. Our simulation results show a significant improvement in energy efficiency against the scenario where the dynamic model of the UAV is ignored.

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arXiv2024

Scenario Convex Programs for Dexterous Manipulation under Modeling Uncertainties

This paper proposes a new framework to design a controller for the dexterous manipulation of an object by a multi-fingered hand. To achieve a robust manipulation and wide range of operations, the uncertainties on the location of the contact point and multiple operating points are taken into account in the control design by sampling the state space. The proposed control strategy is based on a robust pole placement using LMIs. Moreover, to handle uncertainties and different operating points, we recast our problem as a robust convex program (RCP). We then consider the original RCP as a scenario convex program (SCP) and solve the SCP by sampling the uncertain grasp map parameter and operating points in the state space. For a required probabilistic level of confidence, we quantify the feasibility of the SCP solution based on the number of sampling points. The control strategy is tested in simulation in a case study with contact location error and different initial grasps.

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arXiv2024

How to discretize continuous state-action spaces in Q-learning: A symbolic control approach

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.

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arXiv2024

On Robust Controlled Invariants for Continuous-time Monotone Systems

This paper delves into the problem of computing robust controlled invariants for monotone continuous-time systems, with a specific focus on lower-closed specifications. We consider the classes of state monotone (SM) and control-state monotone (CSM) systems, we provide the structural properties of robust controlled invariants for these classes of systems and show how these classes significantly impact the computation of invariants. Additionally, we introduce a notion of feasible points, demonstrating that their existence is sufficient to characterize robust controlled invariants for the considered class of systems. The study further investigates the necessity of reducing the feasibility condition for CSM and Lipschitz systems, unveiling conditions that guide this reduction. Leveraging these insights, we construct an algorithm for the computation of robust controlled invariants. To demonstrate the practicality of our approach, we applied the developed algorithm to the coupled tank problem.

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arXiv2024

Contract-Based Design for Hybrid Dynamical Systems and Invariance Properties

This work establishes fundamental principles for verifying contract for interconnected hybrid systems. When system's hybrid arcs conform to the contract for a certain duration but subsequently violate it, the composition of hybrid dynamical systems becomes challenging. The objective of this work is to analyze the temporal satisfaction of the contract, allowing us to reason about the compositions that do not violate the contract up to a certain point in a hybrid time. Notions of weak and strong satisfaction of an assume-guarantee contract are introduced. These semantics permits the compositional reasoning on hybrid systems of varying complexity depending on the interconnection's type, feedback or cascade. The results show that both semantics are compatible with cascade composition, while strong semantic is required for feedback composition. Moreover, we have shown how one can go from weak to strong contract satisfaction. Finally, we have studied a particular class of hybrid systems and we have shown that the concept of forward (pre-)invariant relative to a contract makes it possible to deal with feedback compositions. These results are demonstrated throughout the paper with simple numerical examples.

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arXiv2024

Temporal Logic Resilience for Dynamical Systems

We consider the notion of resilience for cyber-physical systems, that is, the ability of the system to withstand adverse events while maintaining acceptable functionality. We use finite temporal logic to express the requirements on the acceptable functionality and define the resilience metric as the maximum disturbance under which the system satisfies the temporal requirements. We fix a parameterized template for the set of disturbances and form a robust optimization problem under the system dynamics and the temporal specifications to find the maximum value of the parameter. Additionally, we introduce two novel classes of specifications: closed and convex finite temporal logics specifications, offering a comprehensive analysis of the resilience metric within these specific frameworks. From a computational standpoint, we present an exact solution for linear systems and exact-time reachability and finite-horizon safety, complemented by an approximate solution for finite-horizon reachability. Extending our findings to nonlinear systems, we leverage linear approximations and SMT-based approaches to offer viable computational methodologies. The theoretical results are demonstrated on the temperature regulation of buildings, adaptive cruise control and DC motors.

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arXiv2023

Symbolic Models for Interconnected Impulsive Systems

In this paper, we present a compositional methodology for constructing symbolic models of nonlinear interconnected impulsive systems. Our approach relies on the concept of "alternating simulation function" to establish a relationship between concrete subsystems and their symbolic models. Assuming some small-gain type conditions, we develop an alternating simulation function between the symbolic models of individual subsystems and those of the nonlinear interconnected impulsive systems. To construct symbolic models of nonlinear impulsive subsystems, we propose an approach that depends on incremental input-to-state stability and forward completeness properties. Finally, we demonstrate the advantages of our framework through a case study.

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arXiv2023

Safety verification of Neural-Network-based controllers: a set invariance approach

This paper presents a novel approach to ensure the safety of continuous-time linear dynamical systems controlled by a neural network (NN) based state-feedback. Our method capitalizes on the use of continuous piece-wise affine (PWA) activation functions (e.g. ReLU) which render the NN a PWA continuous function. By computing the affine regions of the latter and applying Nagumo's theorem, a subset of boundary points can effectively verify the invariance of a potentially non-convex set. Consequently, an algorithm that partitions the state space in affine regions is proposed. The scalability of our approach is thoroughly analyzed, and extensive tests are conducted to validate its effectiveness.

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arXiv2023

Barrier Function-based Distributed Symbolic Controller for Multi-Agent Systems

Because of the scalability issues associated with the symbolic controller synthesis approach, employing it in a multi-agent system (MAS) framework becomes difficult. In this paper, we present a novel approach for synthesizing distributed symbolic controllers for MAS, that enforces a local Linear Temporal Logic (LTL) specification on each agent and global safety specifications on the MAS, in a computationally efficient manner by leveraging the concept of control barrier functions (CBF). In addition, we also provide an analysis on the effect of the CBF parameters on the conservatism introduced by our proposed approach in the size and domain of the synthesized controller. The effectiveness of this approach is demonstrated through a comparison with the conventional monolithic symbolic control, using simulation as well as hardware demonstrations.

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arXiv2023

Characterization, Verification and Computation of Robust Controlled Invariants for Monotone Dynamical Systems

In this paper, we consider the problem of computing robust controlled invariants for discrete-time monotone dynamical systems. We consider different classes of monotone systems depending on whether the sets of states, control inputs and disturbances respect a given partial order. Then, we present set-based and trajectory-based characterizations of robust controlled invariants for the considered class of systems. Based on these characterizations, we propose algorithmic approaches for the verification and computation of robust controlled invariants. Finally, illustrative examples are provided showing the merits of the proposed approach.

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arXiv2023

Sufficient Conditions for Robust Safety in Differential Inclusions Using Barrier Functions

In this brief paper we introduce a robust-safety notion for differential inclusions, and we propose a general framework to certify such a notion in terms of barrier functions. While existing literature studied only what we designate by uniform robust safety, in this paper, we make a clear distinction between the uniform and the non-uniform robust-safety notions. For both cases, we establish sufficient (infinitesimal) conditions on the nominal (unperturbed) system. That is, our conditions involve only the barrier function and the system's right-hand side. Our results allow for unbounded safety regions as well as nonsmooth barrier functions. Throughout the paper, simple examples are provided to illustrate our results.

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arXiv2023

Hybrid Persistency of Excitation in Adaptive Estimation for Hybrid Systems

We propose a framework to analyze stability for a class of linear non-autonomous hybrid systems, where the continuous evolution of solutions is governed by an ordinary differential equation and the instantaneous changes are governed by a difference equation. Furthermore, the jumps are triggered by the influence of an external hybrid signal. The proposed framework builds upon a generalization of the well-known persistency of excitation (PE) and uniform observability (UO) notions to the realm of hybrid systems. That is, we establish conditions, under which, hybrid PE implies hybrid UO and, in turn, uniform exponential stability (UES) and input-to-state stability (ISS). Our proofs rely on an original statement for hybrid systems, expressed in terms of Lp bounds on the solutions. We demonstrate the utility of our results on generic adaptive estimation problems. The first one concerns the so-called gradient systems, reminiscent of the popular gradient-descent algorithm. The second one pertains to designing adaptive observers/identifiers for a class of hybrid systems that are nonlinear in the input and the output, and linear in the unknown parameters. In both cases, we illustrate through examples that the proposed hybrid framework succeeds when the classic purely continuous- or discrete-time counterparts fail.

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arXiv2022

Compositional Approximately Bisimilar Abstractions of Interconnected Systems

This paper formulates and studies the concepts of approximate (alternating) bisimulation relations characterizing equivalence relations between interconnected systems and their abstractions. These equivalence relations guarantee that the symbolic model conserves the original model's dynamics. We develop a compositional approach for abstraction-based controller synthesis by relying on the notions of approximate composition and incremental input-to-state stability. In particular, given a large-scale system consisting of interconnected components, we provide conditions under which the concept of approximate (alternating) simulation relation is preserved when going from the subsystems to the large-scale interconnected system. The engineering relevance of the theoretical results has been evaluated through an application in traffic congestion control.

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arXiv2022

Funnel-based Reachability Control of Unknown Nonlinear Systems using Gaussian Processes

This paper aims to synthesize a reachability controller for an unknown dynamical system. We first learn the unknown system using Gaussian processes and the (probabilistic) guarantee on the learned model. Then we use the funnel-based controller synthesis approach using this approximated dynamical system to design the controller for a reachability specification. Finally, the merits of the proposed method are shown using a numerical example.

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