arXiv subjects

Giannis Delimpaltadakis

Publications and source records attributed to Giannis Delimpaltadakis.

At least 19 recordsLinked to original sources

arXiv2026

An Information Theory of Finite Abstractions and their Fundamental Scalability Limits

Finite abstractions are discrete models of dynamical systems, such that the set of abstraction trajectories contains all system trajectories. There is a consensus that abstractions suffer from a scalability bottleneck: to obtain a sufficient ``accuracy" (how closely the abstraction models the system), the required abstraction size often becomes very large, rendering computation infeasible. This is accentuated for complex, high-dimensional systems, due to the curse of dimensionality. Yet, after decades of research, there are no formal results on the size-accuracy tradeoff of abstractions. Here, we derive a statistical, quantitative theory of the size-accuracy tradeoff of abstractions of autonomous deterministic systems and uncover fundamental limits on their scalability, through rate-distortion theory---the information theory of lossy compression. Abstractions are viewed as encoder-decoder pairs, encoding trajectories of dynamical systems. Rate measures abstraction size, while distortion describes accuracy, defined as the spatial average deviation between abstract trajectories and system ones. We obtain a fundamental lower bound on the minimum achievable abstraction distortion, given the system dynamics and the abstraction size; and vice-versa a lower bound on the minimum required size, for given distortion. The bound depends on the complexity of the dynamics, through trajectory entropy and a constant depending on the trajectory manifold's geometry. We demonstrate its tightness on some dynamical systems. Finally, we showcase how this new theory enables constructing minimal abstractions, optimizing the size-accuracy tradeoff, through an example on a chaotic system.

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arXiv2026

Memory-Dependent Interval Markov Chain Abstractions of Stochastic Dynamics

Finite-state interval Markov-chain (IMC) abstractions provide sound verification and performance bounds for continuous-state stochastic systems by enclosing cell-to-cell transition probabilities and costs in intervals. Finite-state Markovian abstractions are generally lossy, as state aggregation often destroys the Markov property. Recently, memory-dependent Markov-chain (MC) abstractions of stochastic systems have been developed to mitigate this by recording recently visited cells. In this paper, we develop the memory-dependent extension of IMC abstractions. Building on the insight that memory narrows the family of state distributions that could occur inside the current cell, we prove that memory tightens the local intervals, at the price of a larger abstraction. We also formulate no-memory IMC abstractions, tightening classic IMC abstraction intervals without enlarging the state space. To characterize spatial refinement relative to memory, we derive two cost-guarantee tightness upper bounds. The bounds depend, respectively, on cell size, and on the worst-case remaining distributional ambiguity after filtering over the remembered past. We then specialize our result to linear-Gaussian systems, for which we derive a closed-form upper bound on this ambiguity. Numerical examples show that the memory-dependent and no-memory constructions can produce tighter expected-cost intervals than comparable partition refined models.

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arXiv2026

Formal Entropy-Regularized Control of Stochastic Systems

Analyzing and controlling system entropy is a powerful tool for regulating predictability of control systems. Applications benefiting from such approaches range from reinforcement learning and data security to human-robot collaboration. In continuous-state stochastic systems, accurate entropy analysis and control remains a challenge. In recent years, finite-state abstractions of continuous systems have enabled control synthesis with formal performance guarantees on objectives such as stage costs. However, these results do not extend to entropy-based performance measures. We solve this problem by first obtaining bounds on the entropy of system discretizations using traditional formal-abstractions results, and then obtaining an additional bound on the difference between the entropy of a continuous distribution and that of its discretization. The resulting theory enables formal entropy-aware controller synthesis that trades predictability against control performance while preserving formal guarantees for the original continuous system. More specifically, we focus on minimizing the linear combination of the KL divergence of the system trajectory distribution to uniform -- our system entropy metric -- and a generic cumulative cost. We note that the bound we derive on the difference between the KL divergence to uniform of a given continuous distribution and its discretization can also be relevant in more general information-theoretic contexts. A set of case studies illustrates the effectiveness of the method.

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arXiv2026

Safe Feedback Optimization through Control Barrier Functions

Feedback optimization refers to a class of methods that steer a control system to a steady state that solves an optimization problem. Despite tremendous progress on the topic, an important problem remains open: enforcing state constraints at all times. The difficulty in addressing it lies on mediating between the safety enforcement and the closed-loop stability, and ensuring the equivalence between closed-loop equilibria and the optimization problem's critical points. In this work, we present a feedback-optimization method that enforces state constraints at all times employing high-order control-barrier functions. We provide several results on the proposed controller dynamics, including well-posedness, safety guarantees, equivalence between equilibria and critical points, and local and global (in certain convex cases) asymptotic stability of optima. Various simulations illustrate our results.

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arXiv2026

Predictable Interval MDPs through Entropy Regularization

Regularization of control policies using entropy can be instrumental in adjusting predictability of real-world systems. Applications benefiting from such approaches range from, e.g., cybersecurity, which aims at maximal unpredictability, to human-robot interaction, where predictable behavior is highly desirable. In this paper, we consider entropy regularization for interval Markov decision processes (IMDPs). IMDPs are uncertain MDPs, where transition probabilities are only known to belong to intervals. Lately, IMDPs have gained significant popularity in the context of abstracting stochastic systems for control design. In this work, we address robust minimization of the linear combination of entropy and a standard cumulative cost in IMDPs, thereby establishing a trade-off between optimality and predictability. We show that optimal deterministic policies exist, and devise a value-iteration algorithm to compute them. The algorithm solves a number of convex programs at each step. Finally, through an illustrative example we show the benefits of penalizing entropy in IMDPs.

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arXiv2025

Tempering the Bayes Filter towards Improved Model-Based Estimation

Model-based filtering is often carried out while subject to an imperfect model, as learning partially-observable stochastic systems remains a challenge. Recent work on Bayesian inference found that tempering the likelihood or full posterior of an imperfect model can improve predictive accuracy, as measured by expected negative log likelihood. In this paper, we develop the tempered Bayes filter, improving estimation performance through both of the aforementioned, and one newly introduced, modalities. The result admits a recursive implementation with a computational complexity no higher than that of the original Bayes filter. Our analysis reveals that -- besides the well-known fact in the field of Bayesian inference that likelihood tempering affects the balance between prior and likelihood -- full-posterior tempering tunes the level of entropy in the final belief distribution. We further find that a region of the tempering space can be understood as interpolating between the Bayes- and MAP filters, recovering these as special cases. Analytical results further establish conditions under which a tempered Bayes filter achieves improved predictive performance. Specializing the results to the linear Gaussian case, we obtain the tempered Kalman filter. In this context, we interpret how the parameters affect the Kalman state estimate and covariance propagation. Empirical results confirm that our method consistently improves predictive accuracy over the Bayes filter baseline.

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arXiv2025

Feedback Optimization with State Constraints through Control Barrier Functions

Recently, there has been a surge of research on a class of methods called feedback optimization. These are methods to steer the state of a control system to an equilibrium that arises as the solution of an optimization problem. Despite the growing literature on the topic, the important problem of enforcing state constraints at all times remains unaddressed. In this work, we present the first feedback-optimization method that enforces state constraints. The method combines a class of dynamics called safe gradient flows with high-order control barrier functions. We provide a number of results on our proposed controller, including well-posedness guarantees, anytime constraint-satisfaction guarantees, equivalence between the closed-loop's equilibria and the optimization problem's critical points, and local asymptotic stability of optima.

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arXiv2025

Predictable Reinforcement Learning Dynamics through Entropy Rate Minimization

In Reinforcement Learning (RL), agents have no incentive to exhibit predictable behaviors, and are often pushed (through e.g. policy entropy regularisation) to randomise their actions in favor of exploration. This often makes it challenging for other agents and humans to predict an agent's behavior, triggering unsafe scenarios (e.g. in human-robot interaction). We propose a novel method to induce predictable behavior in RL agents, termed Predictability-Aware RL (PARL), employing the agent's trajectory entropy rate to quantify predictability. Our method maximizes a linear combination of a standard discounted reward and the negative entropy rate, thus trading off optimality with predictability. We show how the entropy rate can be formally cast as an average reward, how entropy-rate value functions can be estimated from a learned model and incorporate this in policy-gradient algorithms, and demonstrate how this approach produces predictable (near-optimal) policies in tasks inspired by human-robot use-cases.

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arXiv2025

Memory-dependent abstractions of stochastic systems through the lens of transfer operators

With the increasing ubiquity of safety-critical autonomous systems operating in uncertain environments, there is a need for mathematical methods for formal verification of stochastic models. Towards formally verifying properties of stochastic systems, methods based on discrete, finite Markov approximations -- abstractions -- thereof have surged in recent years. These are found in contexts where: either a) one only has partial, discrete observations of the underlying continuous stochastic process, or b) the original system is too complex to analyze, so one partitions the continuous state-space of the original system to construct a handleable, finite-state model thereof. In both cases, the abstraction is an approximation of the discrete stochastic process that arises precisely from the discretization of the underlying continuous process. The fact that the abstraction is Markov and the discrete process is not (even though the original one is) leads to approximation errors. Towards accounting for non-Markovianity, we introduce memory-dependent abstractions for stochastic systems, capturing dynamics with memory effects. Our contribution is twofold. First, we provide a formalism for memory-dependent abstractions based on transfer operators. Second, we quantify the approximation error by upper bounding the total variation distance between the true continuous state distribution and its discrete approximation.

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arXiv2024

Continuous Approximations of Projected Dynamical Systems via Control Barrier Functions

Projected Dynamical Systems (PDSs) form a class of discontinuous constrained dynamical systems, and have been used widely to solve optimization problems and variational inequalities. Recently, they have also gained significant attention for control purposes, such as high-performance integrators, saturated control and feedback optimization. In this work, we establish that locally Lipschitz continuous dynamics, involving Control Barrier Functions (CBFs), namely CBF-based dynamics, approximate PDSs. Specifically, we prove that trajectories of CBF-based dynamics uniformly converge to trajectories of PDSs, as a CBF-parameter approaches infinity. Towards this, we also prove that CBF-based dynamics are perturbations of PDSs, with quantitative bounds on the perturbation. Our results pave the way to implement discontinuous PDS-based controllers in a continuous fashion, employing CBFs. We demonstrate this on numerical examples on feedback optimization and synchronverter control. Moreover, our results can be employed to numerically simulate PDSs, overcoming disadvantages of existing discretization schemes, such as computing projections to possibly non-convex sets. Finally, this bridge between CBFs and PDSs may yield other potential benefits, including novel insights on stability.

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arXiv2023

On the relationship between control barrier functions and projected dynamical systems

In this paper, we study the relationship between systems controlled via Control Barrier Function (CBF) approaches and a class of discontinuous dynamical systems, called Projected Dynamical Systems (PDSs). In particular, under appropriate assumptions, we show that the vector field of CBF-controlled systems is a Krasovskii-like perturbation of the set-valued map of a differential inclusion, that abstracts PDSs. This result provides a novel perspective to analyze and design CBF-based controllers. Specifically, we show how, in certain cases, it can be employed for designing CBF-based controllers that, while imposing safety, preserve asymptotic stability and do not introduce undesired equilibria or limit cycles. Finally, we briefly discuss about how it enables continuous implementations of certain projection-based controllers, that are gaining increasing popularity.

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arXiv2023

Interval Markov Decision Processes with Continuous Action-Spaces

Interval Markov Decision Processes (IMDPs) are finite-state uncertain Markov models, where the transition probabilities belong to intervals. Recently, there has been a surge of research on employing IMDPs as abstractions of stochastic systems for control synthesis. However, due to the absence of algorithms for synthesis over IMDPs with continuous action-spaces, the action-space is assumed discrete a-priori, which is a restrictive assumption for many applications. Motivated by this, we introduce continuous-action IMDPs (caIMDPs), where the bounds on transition probabilities are functions of the action variables, and study value iteration for maximizing expected cumulative rewards. Specifically, we decompose the max-min problem associated to value iteration to $|\mathcal{Q}|$ max problems, where $|\mathcal{Q}|$ is the number of states of the caIMDP. Then, exploiting the simple form of these max problems, we identify cases where value iteration over caIMDPs can be solved efficiently (e.g., with linear or convex programming). We also gain other interesting insights: e.g., in certain cases where the action set $\mathcal{A}$ is a polytope, synthesis over a discrete-action IMDP, where the actions are the vertices of $\mathcal{A}$, is sufficient for optimality. We demonstrate our results on a numerical example. Finally, we include a short discussion on employing caIMDPs as abstractions for control synthesis.

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arXiv2022

ETCetera: beyond Event-Triggered Control

We present ETCetera, a Python library developed for the analysis and synthesis of the sampling behaviour of event triggered control (ETC) systems. In particular, the tool constructs abstractions of the sampling behaviour of given ETC systems, in the form of timed automata (TA) or finite-state transition systems (FSTSs). When the abstraction is an FSTS, ETCetera provides diverse manipulation tools for analysis of ETC's sampling performance, synthesis of communication traffic schedulers (when networks shared by multiple ETC loops are considered), and optimization of sampling strategies. Additionally, the TA models may be exported to UPPAAL for analysis and synthesis of schedulers. Several examples of the tool's application for analysis and synthesis problems with different types of dynamics and event-triggered implementations are provided.

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arXiv2022

Isochronous Partitions for Region-Based Self-Triggered Control

In this work, we propose a region-based self-triggered control (STC) scheme for nonlinear systems. The state space is partitioned into a finite number of regions, each of which is associated to a uniform inter-event time. The controller, at each sampling time instant, checks to which region does the current state belong, and correspondingly decides the next sampling time instant. To derive the regions along with their corresponding inter-event times, we use approximations of isochronous manifolds, a notion firstly introduced in [1]. This work addresses some theoretical issues of [1] and proposes an effective computational approach that generates approximations of isochronous manifolds, thus enabling the region-based STC scheme. The efficiency of both our theoretical results and the proposed algorithm are demonstrated through simulation examples.

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arXiv2022

Formal Analysis of the Sampling Behaviour of Stochastic Event-Triggered Control

Analyzing Event-Triggered Control's (ETC) sampling behaviour is of paramount importance, as it enables formal assessment of its sampling performance and prediction of its sampling patterns. In this work, we formally analyze the sampling behaviour of stochastic linear periodic ETC (PETC) systems by computing bounds on associated metrics. Specifically, we consider functions over sequences of state measurements and intersampling times that can be expressed as average, multiplicative or cumulative rewards, and introduce their expectations as metrics on PETC's sampling behaviour. We compute bounds on these expectations, by constructing appropriate Interval Markov Chains equipped with suitable reward structures, that abstract stochastic PETC's sampling behaviour. Our results are illustrated on a numerical example, for which we compute bounds on the expected average intersampling time and on the probability of triggering with the maximum possible intersampling time in a finite horizon.

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arXiv2021

Abstracting the Sampling Behaviour of Stochastic Linear Periodic Event-Triggered Control Systems

Recently, there have been efforts towards understanding the sampling behaviour of event-triggered control (ETC), for obtaining metrics on its sampling performance and predicting its sampling patterns. Finite-state abstractions, capturing the sampling behaviour of ETC systems, have proven promising in this respect. So far, such abstractions have been constructed for non-stochastic systems. Here, inspired by this framework, we abstract the sampling behaviour of stochastic narrow-sense linear periodic ETC (PETC) systems via Interval Markov Chains (IMCs). Particularly, we define functions over sequences of state-measurements and interevent times that can be expressed as discounted cumulative sums of rewards, and compute bounds on their expected values by constructing appropriate IMCs and equipping them with suitable rewards. Finally, we argue that our results are extendable to more general forms of functions, thus providing a generic framework to define and study various ETC sampling indicators.

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arXiv2021

Abstracting the Traffic of Nonlinear Event-Triggered Control Systems

Scheduling communication traffic in networks of event-triggered control (ETC) systems is challenging, as their sampling times are unknown, hindering application of ETC in networks. In previous work, finite-state abstractions were created, capturing the sampling behaviour of LTI ETC systems with quadratic triggering functions. Offering an infinite-horizon look to all sampling patterns of an ETC system, such abstractions can be used for scheduling of ETC traffic. Here we significantly extend this framework, by abstracting perturbed uncertain nonlinear ETC systems with general triggering functions. To construct an ETC system's abstraction: a) the state space is partitioned into regions, b) for each region an interval is determined, containing all intersampling times of points in the region, and c) the abstraction's transitions are determined through reachability analysis. To determine intervals and transitions, we devise algorithms based on reachability analysis. For partitioning, we propose an approach based on isochronous manifolds, resulting into tighter intervals and providing control over them, thus containing the abstraction's non-determinism. Simulations showcase our developments.

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arXiv2021

Region-Based Self-Triggered Control for Perturbed and Uncertain Nonlinear Systems

In this work, we derive a region-based self-triggered control (STC) scheme for nonlinear systems with bounded disturbances and model uncertainties. The proposed STC scheme is able to guarantee different performance specifications (e.g. stability, boundedness, etc.), depending on the event-triggered control (ETC) triggering function that is chosen to be emulated. To deal with disturbances and uncertainties, we employ differential inclusions (DIs). By introducing ETC/STC notions in the context of DIs, we extend well-known results on ETC/STC to perturbed uncertain systems. Given these results, and adapting tools from our previous work, we derive inner-approximations of isochronous manifolds of perturbed uncertain ETC systems. These approximations dictate a partition of the state-space into regions, each of which is associated to a uniform inter-sampling time. At each sampling time instant, the controller checks to which region the measured state belongs and correspondingly decides the next sampling instant.

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