arXiv subjects

Raphael M. Jungers

Publications and source records attributed to Raphael M. Jungers.

At least 19 recordsLinked to original sources

arXiv2026

End-to-End Abstraction-Based Control with LLM-Enhanced NL-to-LTL Translation

Abstraction-Based Controller Design (ABCD) offers a principled framework for the safe control of complex Cyber-Physical Systems (CPSs), but interfacing real-world requirements with its formal synthesis machinery remains a major bottleneck: such requirements are most naturally expressed in Natural Language (NL), whereas ABCD requires formal specifications such as Linear Temporal Logic (LTL). Large Language Models (LLMs) offer a promising way to bridge this gap by translating NL requirements into formal specifications. This paper makes three contributions. First, we formalize an LLM-enhanced pipeline for ABCD, in which NL requirements are translated into LTL and used within a formal synthesis workflow. Second, we implement this pipeline in the Dionysos toolbox and introduce a benchmark for evaluating NL-to-LTL translation under both logical diversity and linguistic variation. Third, experiments with state-of-the-art LLMs reveal a consistent relationship between LTL complexity and translation success: translation accuracy decreases as the target specification becomes more complex in terms of Abstract Syntax Tree (AST) size, temporal depth, and Büchi automaton size, while accounting for NL input length. Together, these contributions provide both an evaluation framework and a practical integration pathway for making ABCD more accessible while preserving the rigor of formal methods.

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arXiv2026

On Tikhonov Regularization for Direct and Indirect Data-Driven LQR Control

In recent years, the so-called `direct data-driven control' has been a topic of intense research, and it is expected that it will become prominent in future complex dynamical systems control. Within this framework, regularization not only implicitly enforces system identification, but also plays a crucial role in ensuring reliable closed-loop behavior. To further enhance the performance of data-driven controllers, we propose a new regularization method for direct data-driven LQR control of unknown LTI systems, based on a regularized covariance parameterization. Unlike existing data-driven techniques, the proposed method remains effective in handling ill-conditioned cases, such as when the data matrix has a large condition number. Then, we demonstrate that our method is equivalent to the indirect certainty-equivalence LQR combined with Tikhonov regularization. Furthermore, we extend our method to the design of controllers for unknown nonlinear systems using Koopman linear embedding. Finally, the simulation results validate the effectiveness and advantages of the proposed regularization method.

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arXiv2025

LLM-Enhanced Symbolic Control for Safety-Critical Applications

Motivated by Smart Manufacturing and Industry 4.0, we introduce a framework for synthesizing Abstraction-Based Controller Design (ABCD) for reach-avoid problems from Natural Language (NL) specifications using Large Language Models (LLMs). A Code Agent interprets an NL description of the control problem and translates it into a formal language interpretable by state-of-the-art symbolic control software, while a Checker Agent verifies the correctness of the generated code and enhances safety by identifying specification mismatches. Evaluations show that the system handles linguistic variability and improves robustness over direct planning with LLMs. The proposed approach lowers the barrier to formal control synthesis by enabling intuitive, NL-based task definition while maintaining safety guarantees through automated validation.

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arXiv2024

Zonotope-based Symbolic Controller Synthesis for Linear Temporal Logic Specifications

This paper studies the controller synthesis problem for nonlinear control systems under linear temporal logic (LTL) specifications using zonotope techniques. A local-to-global control strategy is proposed for the desired specification expressed as an LTL formula. First, a novel approach is developed to divide the state space into finite zonotopes and constrained zonotopes, which are called cells and allowed to intersect with the neighbor cells. Second, from the intersection relation, a graph among all cells is generated to verify the realization of the accepting path for the LTL formula. The realization verification determines if there is a need for the control design, and also results in finite local LTL formulas. Third, once the accepting path is realized, a novel abstraction-based method is derived for the controller design. In particular, we only focus on the cells from the realization verification and approximate each cell thanks to properties of zonotopes. Based on local symbolic models and local LTL formulas, an iterative synthesis algorithm is proposed to design all local abstract controllers, whose existence and combination establish the global controller for the LTL formula. Finally, the proposed framework is illustrated via a path planning problem of mobile robots.

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arXiv2023

Stability Analysis of Switched Linear Systems with Neural Lyapunov Functions

Neural-based, data-driven analysis and control of dynamical systems have been recently investigated and have shown great promise, e.g. for safety verification or stability analysis. Indeed, not only do neural networks allow for an entirely model-free, data-driven approach, but also for handling arbitrary complex functions via their power of representation (as opposed to, e.g. algebraic optimization techniques that are restricted to polynomial functions). Whilst classical Lyapunov techniques allow to provide a formal and robust guarantee of stability of a switched dynamical system, very little is yet known about correctness guarantees for Neural Lyapunov functions, nor about their performance (amount of data needed for a certain accuracy). We thus formally introduce neural Lyapunov functions for the stability analysis of switched linear systems: we benchmark them on this paradigmatic problem, which is notoriously difficult (and in general Turing-undecidable), but which admits recently-developed technologies and theoretical results. Inspired by switched systems theory, we provide theoretical guarantees on the representative power of neural networks, leveraging recent results from the ML community. We additionally experimentally display how neural Lyapunov functions compete with state-of-the-art results and techniques, while admitting a wide range of improvement, both in theory and in practice. This study intends to improve our understanding of the opportunities and current limitations of neural-based data-driven analysis and control of complex dynamical systems.

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arXiv2022

Razumikhin and Krasovskii Approaches for Safe Stabilization

This paper studies the stabilization and safety problems of nonlinear time-delay systems. Following both Razumikhin and Krasovskii approaches, we propose novel control Lyapunov functions/functionals for the stabilization problem and novel control barrier functions/functionals for the safety problem. The proposed control Lyapunov and barrier functions/functionals extend the existing ones from the delay-free case to the time-delay case, and allow for designing the stabilizing and safety controllers in closed-form. Since analytical solutions to time-delay optimal control problems are hard to be achieved, a sliding mode control based approach is developed to merge the proposed control Lyapunov and barrier functions/functionals. Based on the sliding surface functional, a feedback control law is established to investigate the stabilization and safety objectives simultaneously. In particular, the properties of the sliding surface functional are analyzed, and further how to construct the sliding surface functional is discussed. Finally, the proposed approaches are illustrated via two numerical examples from the connected cruise control problem of automotive systems and the synchronization problem of multi-agent systems.

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arXiv2022

Optimal Resource Scheduling and Allocation under Allowable Over-Scheduling

This paper studies optimal scheduling and resource allocation under allowable over-scheduling. Formulating an optimisation problem where over-scheduling is embedded, we derive an optimal solution that can be implemented by means of a new additive increase multiplicative decrease (AIMD) algorithm. After describing the AIMD-like scheduling mechanism as a switching system, we show convergence of the scheme, based on the joint spectral radius of symmetric matrices, and propose two methods for fitting an optimal AIMD tuning to the optimal solution derived. Finally, we demonstrate the overall optimal design strategy via an illustrative example.

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arXiv2018

Data Driven Stability Analysis of Black-box Switched Linear Systems

Can we conclude the stability of an unknown dynamical system from the knowledge of a finite number of snapshots of trajectories? We tackle this black-box problem for switched linear systems. We show that, for any given random set of observations, one can give probabilistic stability guarantees. The probabilistic nature of these guarantees implies a trade-off between their quality and the desired level of confidence. We provide an explicit way of computing the best stability-like guarantee, as a function of both the number of observations and the required level of confidence. Our proof techniques rely on geometrical analysis, chance-constrained optimization, and stability analysis tools for switched systems, including the joint spectral radius.

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arXiv2018

SOS-Convex Lyapunov Functions and Stability of Difference Inclusions

We introduce the concept of sos-convex Lyapunov functions for stability analysis of both linear and nonlinear difference inclusions (also known as discrete-time switched systems). These are polynomial Lyapunov functions that have an algebraic certificate of convexity and that can be efficiently found via semidefinite programming. We prove that sos-convex Lyapunov functions are universal (i.e., necessary and sufficient) for stability analysis of switched linear systems. We show via an explicit example however that the minimum degree of a convex polynomial Lyapunov function can be arbitrarily higher than a non-convex polynomial Lyapunov function. In the case of switched nonlinear systems, we prove that existence of a common non-convex Lyapunov function does not imply stability, but existence of a common convex Lyapunov function does. We then provide a semidefinite programming-based procedure for computing a full-dimensional subset of the region of attraction of equilibrium points of switched polynomial systems, under the condition that their linearization be stable. We conclude by showing that our semidefinite program can be extended to search for Lyapunov functions that are pointwise maxima of sos-convex polynomials.

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arXiv2017

Invariance in Constrained Switching

We study discrete time linear constrained switching systems with additive disturbances, in which the switching may be on the system matrices, the disturbance sets, the state constraint sets or a combination of the above. In our general setting, a switching sequence is admissible if it is accepted by an automaton. For this family of systems, stability does not necessarily imply the existence of an invariant set. Nevertheless, it does imply the existence of an invariant multi-set, which is a relaxation of invariance and the object of our work. First, we establish basic results concerning the characterization, approximation and computation of the minimal and the maximal admissible invariant multi-set. Second, by exploiting the topological properties of the directed graph which defines the switching constraints, we propose invariant multi-set constructions with several benefits. We illustrate our results in benchmark problems in control.

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arXiv2016

Path-complete positivity of switching systems

The notion of path-complete positivity is introduced as a way to generalize the property of positivity from one LTI system to a family of switched LTI systems whose switching rule is constrained by a finite automaton. The generalization builds upon the analogy between stability and positivity, the former referring to the contraction of a norm, the latter referring to the contraction of a cone (or, equivalently, a projective norm). We motivate and investigate the potential of path-positivity and we propose an algorithm for the automatic verification of positivity.

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arXiv2016

Observability and controllability analysis of linear systems subject to data losses

We provide algorithmically verifiable necessary and sufficient conditions for fundamental system theoretic properties of discrete time linear systems subject to data losses. More precisely, the systems in our modeling framework are subject to disruptions (data losses) in the feedback loop, where the set of possible data loss sequences is captured by an automaton. As such, the results are applicable in the context of shared (wireless) communication networks and/or embedded architectures where some information on the data loss behaviour is available a priori. We propose an algorithm for deciding observability (or the absence of it) for such systems, and show how this algorithm can be used also to decide other properties including constructibility, controllability, reachability, null-controllability, detectability and stabilizability by means of relations that we establish among these properties. The main apparatus for our analysis is the celebrated Skolem Theorem from linear algebra. Moreover, we study the relation between the model adopted in this paper and a previously introduced model where, instead of allowing dropouts in the feedback loop, one allows for time varying delays.

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arXiv2016

A Characterization of Lyapunov Inequalities for Stability of Switched Systems

We study stability criteria for discrete-time switched systems and provide a meta-theorem that characterizes all Lyapunov theorems of a certain canonical type. For this purpose, we investigate the structure of sets of LMIs that provide a sufficient condition for stability. Various such conditions have been proposed in the literature in the past fifteen years. We prove in this note that a family of languagetheoretic conditions recently provided by the authors encapsulates all the possible LMI conditions, thus putting a conclusion to this research effort. As a corollary, we show that it is PSPACE-complete to recognize whether a particular set of LMIs implies stability of a switched system. Finally, we provide a geometric interpretation of these conditions, in terms of existence of an invariant set.

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arXiv2015

On Primitivity of Sets of Matrices

A nonnegative matrix $A$ is called primitive if $A^k$ is positive for some integer $k>0$. A generalization of this concept to finite sets of matrices is as follows: a set of matrices $\mathcal M = \{A_1, A_2, \ldots, A_m \}$ is primitive if $A_{i_1} A_{i_2} \ldots A_{i_k}$ is positive for some indices $i_1, i_2, ..., i_k$. The concept of primitive sets of matrices comes up in a number of problems within the study of discrete-time switched systems. In this paper, we analyze the computational complexity of deciding if a given set of matrices is primitive and we derive bounds on the length of the shortest positive product. We show that while primitivity is algorithmically decidable, unless $P=NP$ it is not possible to decide primitivity of a matrix set in polynomial time. Moreover, we show that the length of the shortest positive sequence can be superpolynomial in the dimension of the matrices. On the other hand, defining ${\mathcal P}$ to be the set of matrices with no zero rows or columns, we give a simple combinatorial proof of a previously-known characterization of primitivity for matrices in ${\mathcal P}$ which can be tested in polynomial time. This latter observation is related to the well-known 1964 conjecture of Cerny on synchronizing automata; in fact, any bound on the minimal length of a synchronizing word for synchronizing automata immediately translates into a bound on the length of the shortest positive product of a primitive set of matrices in ${\mathcal P}$. In particular, any primitive set of $n \times n$ matrices in ${\mathcal P}$ has a positive product of length $O(n^3)$.

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arXiv2014

Resonance and marginal instability of switching systems

We analyse the so-called Marginal Instability of linear switching systems, both in continuous and discrete time. This is a phenomenon of unboundedness of trajectories when the Lyapunov exponent is zero. We disprove two recent conjectures of Chitour, Mason, and Sigalotti (2012) stating that for generic systems, the resonance is sufficient for marginal instability and for polynomial growth of the trajectories. We provide a characterization of marginal instability under some mild assumptions on the sys- tem. These assumptions can be verified algorithmically and are believed to be generic. Finally, we analyze possible types of fastest asymptotic growth of trajectories. An example of a pair of matrices with sublinear growth is given.

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arXiv2014

Stability of linear switching systems and Markov-Bernstein inequalities for exponents

We analyse the problem of stability of a continuous time linear switching system (LSS) versus the stability of its Euler discretization. It is well-known that the existence of a positive τ for which the corresponding discrete time system with step size τ is stable implies the stability of LSS. Our main goal is to obtain a converse statement, that is, to estimate the discretization step size τ > 0 up to a given accuracy ε > 0. This leads to a method of deciding the stability of continuous time LSS with a guaranteed accuracy. As the first step, we solve this problem for matrices with real spectrum and conjecture that our method stays valid for the general case. Our approach is based on Markov-Bernstein type inequalities for systems of exponents. We obtain universal estimates for sharp constants in those inequalities. Our work provides the first estimate of the computational cost of the stability problem for continuous-time LSS (though restricted to the real-spectrum case).

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arXiv2013

Efficient Computations of a Security Index for False Data Attacks in Power Networks

The resilience of Supervisory Control and Data Acquisition (SCADA) systems for electric power networks for certain cyber-attacks is considered. We analyze the vulnerability of the measurement system to false data attack on communicated measurements. The vulnerability analysis problem is shown to be NP-hard, meaning that unless $P = NP$ there is no polynomial time algorithm to analyze the vulnerability of the system. Nevertheless, we identify situations, such as the full measurement case, where it can be solved efficiently. In such cases, we show indeed that the problem can be cast as a generalization of the minimum cut problem involving costly nodes. We further show that it can be reformulated as a standard minimum cut problem (without costly nodes) on a modified graph of proportional size. An important consequence of this result is that our approach provides the first exact efficient algorithm for the vulnerability analysis problem under the full measurement assumption. Furthermore, our approach also provides an efficient heuristic algorithm for the general NP-hard problem. Our results are illustrated by numerical studies on benchmark systems including the IEEE 118-bus system.

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arXiv2012

Feedback stabilization of dynamical systems with switched delays

We analyze a classification of two main families of controllers that are of interest when the feedback loop is subject to switching propagation delays due to routing via a wireless multi-hop communication network. We show that we can cast this problem as a subclass of classical switching systems, which is a non-trivial generalization of classical LTI systems with timevarying delays. We consider both cases where delay-dependent and delay independent controllers are used, and show that both can be modeled as switching systems with unconstrained switchings. We provide NP-hardness results for the stability verification problem, and propose a general methodology for approximate stability analysis with arbitrary precision. We finally give evidence that non-trivial design problems arise for which new algorithmic methods are needed.

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