arXiv subjects

Necmiye Ozay

Publications and source records attributed to Necmiye Ozay.

At least 19 recordsLinked to original sources

arXiv2026

Benefits of Linear Dynamic State Feedback in Co-stabilization

Co-stabilization, i.e., designing a single controller that stabilizes multiple systems, is a fundamental problem in robust and data-driven control. While any stabilizable linear system admits a stabilizing linear static state feedback controller, this equivalence does not extend to co-stabilization. In particular, there exist system collections that cannot be co-stabilized by linear static state feedback but can be co-stabilized using linear dynamic state feedback. In this paper, we study the role of controller memory in co-stabilization. We show that linear dynamic state feedback strictly enlarges the set of co-stabilizable systems compared to static feedback, for both scalar systems and high-dimensional examples. At the same time, we identify structural limitations that cannot be overcome even with dynamic controllers. We also develop a path-integral-based algorithm for computing co-stabilizing controllers for a finite set of systems. Numerical results demonstrate that increasing controller memory enlarges the feasible co-stabilization region. These results highlight controller architecture as a key structural factor in co-stabilization, with potential implications for reducing the sample complexity of learning-based control.

eess.SY↗

arXiv2026

Expressive Power of WSTL Formulas for Learning to Rank

Weighted Signal Temporal Logic (WSTL) is increasingly used as a scoring function in learning-to-rank problems of trajectories with safety guarantees, where its weighted quantitative semantics serve as a parametrized utility function. Despite the growing interest, prior work only assumes the expressiveness of WSTL formulas and empirically demonstrates its utility in capturing diverse preferences. This work focuses on the correctness of this assumption and asks whether using WSTL formulas as scoring functions is theoretically justified. We formalize two concepts: first, rank-realizability, which asks whether all rankings of a given signal set are achievable by varying weights, and, second, rank-capacity, the maximum signal set size for which the formula is rank-realizable. We propose a Mixed-Integer Linear Program to decide rank-realizability, and derive constructive lower bounds for rank-capacity. Experiments on a robotic navigation task show that while a practical WSTL specification may fail to be rank-realizable on a set with similar trajectories, its rank-capacity exceeds the size of the trajectory set. Analysis of Boolean-equivalent formulas reveals that formula structure affects expressivity and that rank-capacity can be increased without altering qualitative semantics.

eess.SY↗

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, through experiments with state-of-the-art LLMs, we show that translation accuracy degrades systematically as the target specifications become more complex, across several measures including Abstract Syntax Tree (AST) size, temporal depth, and Büchi automaton size, while also accounting for the length of the NL input. These results reveal a scaling law that links LLM success rate to the intrinsic complexity of the underlying LTL formula. 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.

eess.SY↗

arXiv2026

On the Nonexistence of Continuous Immersions for Discrete-time Systems

Understanding when linear immersions of nonlinear dynamical systems exist is important since such immersions allow us to leverage the rich tools of linear system theory to analyze nonlinear dynamics. Recently, Liu et al. (2023) showed that continuous-time dynamical systems that admit countably many but more than one omega-limit sets cannot be immersed into finite dimensional linear systems with a one-to-one and continuous mapping. In this paper, we extend these results to discrete-time dynamics and show that similar obstructions exist also in discrete time. We further consider a generalization involving alpha-limit sets. Several examples are provided to demonstrate the results.

eess.SY↗

arXiv2026

On the Generalization Properties of Selective State-Space Models for Filtering Tasks for Unknown Systems

Selective State-Space Models (SSMs) such as Mamba have emerged as an alternative architecture to self-attention based transformers in sequence modeling tasks. Recent works have demonstrated the use of transformers in some filtering and output prediction tasks via in-context learning. In this paper, we analyze whether structured SSMs can work equally well for filtering of unknown systems. In particular, we train the SSM on trajectory samples from a set of systems. At run-time, the SSM is given the outputs of an unknown system from the same set and is expected to predict the next output online. Theoretically, under appropriate assumptions, we derive generalization bounds as to why SSMs succeed in such tasks. Empirically, we demonstrate the performance via several numerical examples. We also discuss the advantages and disadvantages of SSMs versus transformers for this task.

eess.SY↗

arXiv2026

Active Reward Machine Inference From Raw State Trajectories

Reward machines are automaton-like structures that capture the memory required to accomplish a multi-stage task. When combined with reinforcement learning or optimal control methods, they can be used to synthesize robot policies to achieve such tasks. However, specifying a reward machine by hand, including a labeling function capturing high-level features that the decisions are based on, can be a daunting task. This paper deals with the problem of learning reward machines directly from raw state and policy information. As opposed to existing works, we assume no access to observations of rewards, labels, or machine nodes, and show what trajectory data is sufficient for learning the reward machine in this information-scarce regime. We then extend the result to an active learning setting where we incrementally query trajectory extensions to improve data (and indirectly computational) efficiency. Results are demonstrated with several grid world examples.

cs.RO↗

arXiv2026

Safe and Optimal Learning from Preferences via Weighted Temporal Logic with Applications in Robotics and Formula 1

Autonomous systems increasingly rely on human feedback to align their behavior, expressed as pairwise comparisons, rankings, or demonstrations. While existing methods can adapt behaviors, they often fail to guarantee safety in safety-critical domains. We propose a safety-guaranteed, optimal, and efficient approach for solving the learning problem from preferences, rankings, or demonstrations using Weighted Signal Temporal Logic (WSTL). WSTL learning problems, when implemented naively, lead to multi-linear constraints in the weights to be learned. By introducing structural pruning and log-transform procedures, we reduce the problem size and recast it as a Mixed-Integer Linear Program while preserving safety guarantees. Experiments on robotic navigation and real-world Formula 1 data demonstrate that the method captures nuanced preferences and models complex task objectives.

cs.RO↗

arXiv2025

Safe Control of Multi-Agent Systems with Minimal Communication

In many multi-agent systems, communication is limited by bandwidth, latency, and energy constraints. Designing controllers that achieve coordination and safety with minimal communication is critical for scalable and reliable deployment. This paper presents a method for designing controllers that minimize inter-agent communication in multi-agent systems while satisfying safety and coordination requirements, while conforming to communication delay constraints. The control synthesis problem is cast as a rank minimization problem, where a convex relaxation is obtained via system level synthesis. Simulation results on various tasks, including trajectory tracking with relative and heterogeneous sensing, demonstrate that the proposed method significantly reduces inter-agent transmission compared to baseline approaches.

eess.SY↗

arXiv2025

Learning Reward Machines from Partially Observed Policies

Inverse reinforcement learning is the problem of inferring a reward function from an optimal policy or demonstrations by an expert. In this work, it is assumed that the reward is expressed as a reward machine whose transitions depend on atomic propositions associated with the state of a Markov Decision Process (MDP). Our goal is to identify the true reward machine using finite information. To this end, we first introduce the notion of a prefix tree policy which associates a distribution of actions to each state of the MDP and each attainable finite sequence of atomic propositions. Then, we characterize an equivalence class of reward machines that can be identified given the prefix tree policy. Finally, we propose a SAT-based algorithm that uses information extracted from the prefix tree policy to solve for a reward machine. It is proved that if the prefix tree policy is known up to a sufficient (but finite) depth, our algorithm recovers the exact reward machine up to the equivalence class. This sufficient depth is derived as a function of the number of MDP states and (an upper bound on) the number of states of the reward machine. These results are further extended to the case where we only have access to demonstrations from an optimal policy. Several examples, including discrete grid and block worlds, a continuous state-space robotic arm, and real data from experiments with mice, are used to demonstrate the effectiveness and generality of the approach.

cs.LG↗

arXiv2025

Identification and Adaptive Control of Markov Jump Systems: Sample Complexity and Regret Bounds

Learning how to effectively control unknown dynamical systems is crucial for intelligent autonomous systems. This task becomes a significant challenge when the underlying dynamics are changing with time. Motivated by this challenge, this paper considers the problem of controlling an unknown Markov jump linear system (MJS) to optimize a quadratic objective. By taking a model-based perspective, we consider identification-based adaptive control of MJSs. We first provide a system identification algorithm for MJS to learn the dynamics in each mode as well as the Markov transition matrix, underlying the evolution of the mode switches, from a single trajectory of the system states, inputs, and modes. Through martingale-based arguments, sample complexity of this algorithm is shown to be $\mathcal{O}(1/\sqrt{T})$. We then propose an adaptive control scheme that performs system identification together with certainty equivalent control to adapt the controllers in an episodic fashion. Combining our sample complexity results with recent perturbation results for certainty equivalent control, we prove that when the episode lengths are appropriately chosen, the proposed adaptive control scheme achieves $\mathcal{O}(\sqrt{T})$ regret, which can be improved to $\mathcal{O}(polylog(T))$ with partial knowledge of the system. Our proof strategy introduces innovations to handle Markovian jumps and a weaker notion of stability common in MJSs. Our analysis provides insights into system theoretic quantities that affect learning accuracy and control performance. Numerical simulations are presented to further reinforce these insights.

cs.LG↗

arXiv2025

Initial Distribution Sensitivity of Constrained Markov Decision Processes

Constrained Markov Decision Processes (CMDPs) are notably more complex to solve than standard MDPs due to the absence of universally optimal policies across all initial state distributions. This necessitates re-solving the CMDP whenever the initial distribution changes. In this work, we analyze how the optimal value of CMDPs varies with different initial distributions, deriving bounds on these variations using duality analysis of CMDPs and perturbation analysis in linear programming. Moreover, we show how such bounds can be used to analyze the regret of a given policy due to unknown variations of the initial distribution.

cs.LG↗

arXiv2025

Efficient Reward Identification In Max Entropy Reinforcement Learning with Sparsity and Rank Priors

In this paper, we consider the problem of recovering time-varying reward functions from either optimal policies or demonstrations coming from a max entropy reinforcement learning problem. This problem is highly ill-posed without additional assumptions on the underlying rewards. However, in many applications, the rewards are indeed parsimonious, and some prior information is available. We consider two such priors on the rewards: 1) rewards are mostly constant and they change infrequently, 2) rewards can be represented by a linear combination of a small number of feature functions. We first show that the reward identification problem with the former prior can be recast as a sparsification problem subject to linear constraints. Moreover, we give a polynomial-time algorithm that solves this sparsification problem exactly. Then, we show that identifying rewards representable with the minimum number of features can be recast as a rank minimization problem subject to linear constraints, for which convex relaxations of rank can be invoked. In both cases, these observations lead to efficient optimization-based reward identification algorithms. Several examples are given to demonstrate the accuracy of the recovered rewards as well as their generalizability.

cs.LG↗

arXiv2025

Mode-Prefix-Based Control of Switched Linear Systems with Applications to Fault Tolerance

In this paper, we consider the problem of designing prefix-based optimal controllers for switched linear systems over finite horizons. This problem arises in fault-tolerant control, when system faults result in abrupt changes in dynamics. We consider a class of mode-prefix-based linear controllers that depend only on the history of the switching signal. The proposed optimal control problems seek to minimize both expected performance and worst-case performance over switching signals. We show that this problem can be reduced to a convex optimization problem. To this end, we synthesize one controller for each switching signal under a prefix constraint that ensures consistency between controllers. Then, system level synthesis is used to obtain a convex program in terms of the system-level parameters. In particular, it is shown that the prefix constraints are linear in terms of the system-level parameters. Finally, we apply this framework for optimal control of a fighter jet model suffering from system faults, illustrating how fault tolerance is ensured.

math.OC↗

arXiv2025

System Identification Under Bounded Noise: Optimal Rates Beyond Least Squares

System identification is a fundamental problem in control and learning, particularly in high-stakes applications where data efficiency is critical. Classical approaches, such as the ordinary least squares estimator (OLS), achieve an $O(1/\sqrt{T})$ convergence rate under Gaussian noise assumptions, where $T$ is the number of samples. This rate has been shown to match the lower bound. However, in many practical scenarios, noise is known to be bounded, opening the possibility of improving sample complexity. In this work, we establish the minimax lower bound for system identification under bounded noise, proving that the $O(1/T)$ convergence rate is indeed optimal. We further demonstrate that OLS remains limited to an $Ω(1/\sqrt{T})$ convergence rate, making it fundamentally suboptimal in the presence of bounded noise. Finally, we instantiate two natural variations of OLS that obtain the optimal sample complexity.

eess.SY↗

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.

eess.SY↗

arXiv2024

Noise Sensitivity of the Semidefinite Programs for Direct Data-Driven LQR

In this paper, we study the noise sensitivity of the semidefinite program (SDP) proposed for direct data-driven infinite-horizon linear quadratic regulator (LQR) problem for discrete-time linear time-invariant systems. While this SDP is shown to find the true LQR controller in the noise-free setting, we show that it leads to a trivial solution with zero gain matrices when data is corrupted by noise, even when the noise is arbitrarily small. We then study a variant of the SDP that includes a robustness promoting regularization term and prove that regularization does not fully eliminate the sensitivity issue. In particular, the solution of the regularized SDP converges in probability also to a trivial solution.

math.OC↗

arXiv2024

Ankle Exoskeletons May Hinder Standing Balance in Simple Models of Older and Younger Adults

Humans rely on ankle torque to maintain standing balance, particularly in the presence of small to moderate perturbations. Reductions in maximum torque (MT) production and maximum rate of torque development (MRTD) occur at the ankle with age, diminishing stability. Ankle exoskeletons are powered orthotic devices that may assist older adults by compensating for reduced muscle force and power production capabilities. They may also be able to assist with ankle strategies used for balance. However, no studies have investigated the effect of such devices on balance in older adults. Here, we model the effect ankle exoskeletons have on stability in physics-based models of healthy young and old adults, focusing on the mitigation of age-related deficits such as reduced MT and MRTD. We show that an ankle exoskeleton moderately reduces feasible stability boundaries in users who have full ankle strength. For individuals with age-related deficits, there is a trade-off. While exoskeletons augment stability in low velocity conditions, they reduce stability in some high velocity conditions. Our results suggest that well-established control strategies must still be experimentally validated in older adults.

physics.med-ph↗

arXiv2024

Properties of Immersions for Systems with Multiple Limit Sets with Implications to Learning Koopman Embeddings

Linear immersions (such as Koopman eigenfunctions) of a nonlinear system have wide applications in prediction and control. In this work, we study the properties of linear immersions for nonlinear systems with multiple omega-limit sets. While previous research has indicated the possibility of discontinuous one-to-one linear immersions for such systems, it has been unclear whether continuous one-to-one linear immersions are attainable. Under mild conditions, we prove that any continuous immersion to a class of systems including finite-dimensional linear systems collapses all the omega-limit sets, and thus cannot be one-to-one. Furthermore, we show that this property is also shared by approximate linear immersions learned from data as sample size increases and sampling interval decreases. Multiple examples are studied to illustrate our results.

eess.SY↗