Keywords: Biologically-inspired methods, Neural networks, Nonlinear systems
Abstract: We present a novel framework for central pat- tern generator design that leverages the intrinsic rebound excitability of neurons in combination with winner-takes- all computation. Our approach unifies decision-making and rhythmic pattern generation within a simple yet powerful network architecture that employs all-to-all inhibitory con- nections enhanced by designable excitatory interactions. This design offers significant advantages regarding ease of implementation, adaptability, and robustness. We demon- strate its efficacy through a ring oscillator model, which exhibits adaptive phase and frequency modulation, making the framework particularly promising for applications in neuromorphic systems and robotics.

Keywords: Biologically-inspired methods, Hybrid systems, Stability of linear systems
Abstract: We present a systematic design method for a class of neuromorphic controllers for single-input single-output linear time-invariant systems. The proposed controller consists of two integrate-and-fire neurons, whose input is the measured output from the plant, and generates a spiking control signal, i.e., a sequence of fixed-amplitude spikes, which stabilizes the plant. To establish a practical stability property for the closed-loop system, we follow a two-step emulation-based design approach. In the first step, we provide conditions on the neuron parameters to ensure that the spiking signal generated by the neuromorphic controller emulates any signal with arbitrary accuracy. This can be linked to the well-known universal approximation properties of neural networks, but now on the level of spiky signals and neurons. In the second step, we exploit a novel and natural stability notion, called integral spiking-input-to-state stability, that a (precompensated) version of the plant needs to satisfy to be practically stabilized by a spiking controller. By combining these steps, we can prove a practical stability property of the closed-loop system. The proposed approach is illustrated in a numerical case study.

Keywords: Modeling, Systems biology, Neural networks
Abstract: This paper introduces a model that unifies the mechanisms of neuronal excitability in both time and space. As a starting point, we revisit both a key model of temporal excitability, proposed by Hodgkin and Huxley, and a key model of spatial excitability, proposed by Amari. We then propose a novel model that captures the temporal and spatial properties of both models. Our aim is to regard neuronal excitability as a property across scales, and to explore the benefits of modeling excitability with one and the same mechanism, whether at the cellular or the population level.

Keywords: Hybrid systems, Biologically-inspired methods, Stability of hybrid systems
Abstract: Neuromorphic engineering is an emerging research domain that aims to realize important implementation advantages that brain-inspired technologies can offer over classical digital technologies, including energy efficiency, adaptability, and robustness. For the field of systems and control, neuromorphic controllers could potentially bring many benefits, but their advancement is hampered by lack of systematic analysis and design tools. In this paper, the objective is to show that hybrid systems methods can aid in filling this gap. We do this by formally analyzing rhythmic neuromorphic control of a pendulum system, which was recently proposed as a prototypical setup. The neuromorphic controller generates spikes, which we model as a Dirac delta pulse, whenever the pendulum angular position crosses its resting position, with the goal of inducing a stable limit cycle. This leads to modeling the closed-loop system as a hybrid dynamical system, which in between spikes evolves in open loop and where the jumps correspond to the spiking control actions. Exploiting the hybrid system model, we formally prove the existence, uniqueness, and a stability property of the hybrid limit cycle for the closed-loop system. We finally elaborate on a possible spiking adaptation mechanism on the pulse amplitude to generate a hybrid limit cycle of a desired maximal angular amplitude.

Keywords: Modeling, Nonlinear systems, Networked control systems
Abstract: We introduce a gradient modeling framework for memristive systems. Our focus is on memristive systems as they appear in neurophysiology and neuromorphic systems. Revisiting the original definition of Chua, we regard memristive elements as gradient operators of quadratic functionals with respect to a metric determined by the memristance. We explore the consequences of gradient properties for the analysis and design of neuromorphic circuits

Keywords: Biologically-inspired methods, Nonlinear systems, Autonomous systems
Abstract: We introduce a generalized excitable system in which spikes can happen in a continuum of directions, therefore drastically enriching the expressivity and control capability of the spiking dynamics. In this generalized excitable system, spiking trajectories happen in a Hilbert space with an excitable resting state at the origin and spike responses that can be triggered in any direction as a function of the system's state and inputs. State-dependence of the spiking direction provide the system with a vanishing spiking memory trace, which enables robust tracking and integration of inputs in the spiking direction history. The model exhibits generalized forms of both Hodgkin's Type I and Type II excitability, capturing their usual bifurcation behaviors in an abstract setting. When used as the controller of a two-dimensional navigation task, this model facilitates both the sparseness of the actuation and its sensitivity to environmental inputs. These results highlight the potential of the proposed generalized excitable model for excitable control in high- and infinite-dimensional spaces.

Keywords: Biologically-inspired methods, Hybrid systems, Control applications
Abstract: In biology, homeostasis is the process of maintaining a stable internal environment, which is crucial for optimal functioning of organisms. One of the key homeostatic mechanisms is thermoregulation that allows the organism to maintain its core temperature within tight bounds despite being exposed to a wide range of varying external temperatures. Instrumental in thermoregulation is the presence of thermosensitive neurons at multiple places throughout the body, including muscles, the spinal cord, and the brain, which provide spiking sensory signals for the core temperature. In response to these signals, thermoeffectors are activated, creating a negative spiking feedback loop. Additionally, a feedforward signal is provided by warmth and cold-sensitive neurons in the skin, offering a measure for the external temperature. This paper presents an electronic circuit-based architecture design to replicate the biological process of thermoregulation, combined with a formal mathematical analysis. The considered architecture consists of four temperature sensitive neurons and a single actuator, configured in a negative feedback loop with feedforward control. To model the overall system mathematically, hybrid dynamical system descriptions are proposed that are used to analyze and simulate the performance of the design. The analysis and numerical case study illustrate the crucial role of feedforward control in reducing the dependency on the external temperature.

Keywords: Hybrid systems, Biologically-inspired methods, Energy systems
Abstract: In reactor-grade tokamaks, pellet injection is the best candidate for core plasma fuelling. However, density control schemes that can handle the hybrid nature of this type of fuelling, i.e., the discrete impact of the pellets on the continuously evolving plasma density, are lacking. This paper proposes a neuromorphic controller, inspired by the integrate-and-fire neuronal model, to address this problem. The overall system is modelled as a hybrid system, and we analyse the proposed controller in closed loop with a single-input single-output linear time-invariant plasma model. The controller generates spikes, representing pellet launches, when the neuron variable reaches a certain threshold. Between the control actions, or spikes, the system evolves in open loop. We establish conditions on the controller variables and minimum actuator speed, depending on the reference value for the desired density, the pellet size and the time-constant of the plasma density, that guarantee a practical stability property for the closed-loop system. The results are illustrated in a numerical example.

Keywords: Identification, Statistical learning, Linear systems
Abstract: 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 {Omega(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.

Keywords: Data driven control, Identification
Abstract: Affine systems are ubiquitous in modeling and emerge naturally from the

linearization of nonlinear dynamics. Despite their relevance in applications, their identification remains largely ad hoc, relying on centering the data before applying linear identification methods. This heuristic approach assumes constant offset and can introduce bias. We develop a dedicated framework for affine system identification, deriving identifiability conditions and identification methods based on

difference equation representations. Unlike the classical two-step approach, our method identifies the data-generating system under conditions verifiable from data and system complexity. For noisy data in the errors-in-variables setting, we recast the problem as a structured low-rank approximation, leveraging existing optimization techniques for efficient computation.

Keywords: Identification, Statistical learning
Abstract: The goal of this work is to accelerate the identification of an unknown ARX system from trajectory data through online input design. Specifically, we present an active learning algorithm that sequentially selects the input to excite the system according to an experiment design criterion using the past measured data. The adopted criterion yields a non-convex optimization problem, but we provide an exact convex reformulation allowing to find the global optimizer in a computationally tractable way. Moreover, we give sample complexity bounds on the estimation error due to the stochastic noise. Numerical studies showcase the effectiveness of our algorithm and the benefits of the convex reformulation.

Keywords: Statistical learning, Identification, Subspace methods
Abstract: This paper addresses the problem of identifying linear systems from noisy input-output trajectories. We introduce Thresholded Ho-Kalman, an algorithm that leverages a rank-adaptive procedure to estimate a Hankel-like matrix associated with the system. This approach optimally balances the trade-off between accurately inferring key singular values and minimizing approximation errors for the rest. We establish finite-sample Frobenius norm error bounds for the estimated Hankel matrix. Our algorithm further recovers both the system order and its Markov parameters, and we provide upper bounds for the sample complexity required to identify the system order and finite-time error bounds for estimating the Markov parameters. Interestingly, these bounds match those achieved by state-of-the-art algorithms that assume prior knowledge of the system order.

Keywords: Uncertain systems, Statistical learning, Data driven control
Abstract: In this paper, we introduce a targeted exploration strategy for the non-asymptotic, finite-time case. The proposed strategy is applicable to uncertain linear time-invariant systems subject to sub-Gaussian disturbances. As the main result, the proposed approach provides a priori guarantees, ensuring that the optimized exploration inputs achieve a desired accuracy of the model parameters. The technical derivation of the strategy (i) leverages existing non-asymptotic identification bounds with self-normalized martingales, (ii) utilizes spectral lines to predict the effect of sinusoidal excitation, and (iii) effectively accounts for spectral transient error and parametric uncertainty. A numerical example illustrates how the finite exploration time influences the required exploration energy.

Keywords: Learning, Linear systems, Predictive control for linear systems
Abstract: Compounding error, where small prediction mistakes accumulate over time, presents a major challenge in learning-based control. For example, this issue often limits the performance of model-based reinforcement learning and imitation learning. One common approach to mitigate compounding error is to train multi-step predictors directly, rather than relying on autoregressive rollout of a single-step model. However, it is not well understood when the benefits of multi-step prediction outweigh the added complexity of learning a more complicated model. In this work, we provide a rigorous analysis of this trade-off in the context of linear dynamical systems. We show that when the model class is well-specified and accurately captures the system dynamics, single-step models achieve lower asymptotic prediction error. On the other hand, when the model class is misspecified due to partial observability, direct multi-step predictors can significantly reduce bias and thus outperform single-step approaches. These theoretical results are supported by numerical experiments, wherein we also (a) empirically evaluate an intermediate strategy which trains a single-step model using a multi-step loss and (b) evaluate performance of single step and multi-step predictors in a closed loop control setting.

Keywords: Neural networks, Observers for nonlinear systems
Abstract: Beyond the traditional neural network training methods based on gradient descent and its variants, state estimation techniques have been proposed to determine a set of ideal weights from a control-theoretic perspective. Hence, the concept of observability becomes relevant in neural network training. In this paper, we investigate local observability of a class of two-layer feedforward neural networks (FNNs) with rectified linear unit (ReLU) activation functions. We analyze local observability of FNNs by evaluating an observability rank condition with respect to the weight matrix and the input sequence. First, we show that, in general, the weights of FNNs are not locally observable. Then, we provide sufficient conditions on the network structures and the weights that lead to local observability. Moreover, we propose an input design approach to render the weights distinguishable and show that this input also excites other weights inside a neighborhood. Finally, we validate our results through a numerical example.

Keywords: Kalman filtering, Machine learning, Observers for nonlinear systems
Abstract: State estimation in control and systems engineering traditionally requires extensive manual system identification or data-collection effort. However, transformer-based foundation models in other domains have reduced data requirements by leveraging pre-trained generalist models. Ultimately, developing zero-shot foundation models of system dynamics could drastically reduce manual deployment effort. While recent work shows that transformer-based end-to-end approaches can achieve zero-shot performance on unseen systems, they are limited to sensor models seen during training. We introduce the foundation model unscented Kalman filter (FM-UKF), which combines a transformer-based model of system dynamics with analytically known sensor models via an UKF, enabling generalization across varying dynamics without retraining for new sensor configurations. We evaluate FM-UKF on a new benchmark of container ship models with complex dynamics, demonstrating a competitive accuracy, effort, and robustness trade-off compared to classical methods with approximate system knowledge and to an end-to-end approach. The benchmark and dataset are open sourced to further support future research in zero-shot state estimation via foundation models.

Keywords: Distributed parameter systems, Modeling, Mechatronics
Abstract: This paper presents a mathematical analysis of the (regularized) distributed LuGre friction model, focusing on its stability and dissipativity properties. Compared to its lumped counterpart, it is shown that these key features are preserved in the distributed formulation under certain assumptions regarding the contact pressure distribution and micro-stiffness coefficient. An alternative definition of the damping term as a true deformation velocity is also proposed, with important implications on stability and dissipativity. Additionally, a linearized version of the model is derived, which may facilitate analysis and control design.

Keywords: Distributed parameter systems
Abstract: This paper studies the static output feedback stabilization of constant coefficients heat equations by means of a proportional controller. We consider the case of a Dirichlet boundary control and Dirichlet boundary measurement. In this setting, we show that a simple proportional static output feedback control strategy can be successfully implemented for sufficiently small reaction terms. By duality, the same result applies to the case of a Neumann boundary control and Neumann boundary measurement.

Keywords: Robust adaptive control, Distributed parameter systems, Adaptive control
Abstract: This paper presents the first robust adaptive backstepping control system for dynamical systems whose functional uncertainties are assumed to lie in a user-defined native space (also known as reproducing kernel Hilbert space). This work generalizes classical adaptive backstepping control systems and their non-adaptive counterparts by freeing the user from providing a parametric representation of the functional uncertainties. Such representations are usually in the form of regressor vectors, or some equivalent structure, to be provided a priori or reconstructed online, and without employing conservative upper bounds on the functional uncertainties. The adaptive laws for the proposed control system are shown to form a distributed parameter system (DPS) evolving over the native space. Finite-dimensional approximations of such adaptive laws enable their applications to problems of practical interest, as shown by the proposed numerical examples.

Keywords: Distributed parameter systems, Backstepping, Observers for Linear systems
Abstract: Motivated by the fact that control and observer designs constructed based on a continuum counterpart may provide computationally tractable control laws for large-scale, n+m systems, we develop an output-feedback control design for large-scale, n+m, linear hyperbolic PDE systems, utilizing continuum-based control/observer kernels and observer dynamics. We establish exponential stability of the closed-loop system, consisting of a mixed n+m-continuum PDE system (comprising the plant-observer dynamics), via introduction of a virtual continuum system with resets, which enables utilization of the continuum approximation property of the solutions of the n+m system by its continuum counterpart (for large n). We illustrate the potential computational complexity/flexibility benefits of our approach via a numerical example of stabilization of a large-scale n+m system, for which we employ the continuum observer-based controller, while the continuum-based stabilizing control/observer kernels can be computed in closed form.

Keywords: Optimization algorithms, Distributed parameter systems, Sensor networks
Abstract: A fast computational technique is proposed for sensor location maximizing the parameter estimation accuracy for spatiotemporal processes in the presence of correlated measurement noise. In the setting of a linearized Bayesian formulation incorporating prior information about the parameters, a general concave design criterion is utilized to quantify the anticipated estimation accuracy. This design criterion is maximized by selecting a best subset of gauged sites from among a given and possibly very large finite set of candidate sites. To circumvent the inherent combinatorial nature of this problem combined with the correlation structure of the errors, a convex relaxation is proposed here, which results from the decomposition of the covariance kernel into the sum of a positive definite matrix and a scalar multiple of the identity matrix. A relaxed problem is then formulated and solved using extremely efficient simplicial decomposition. Since the optimal relaxed solution is a measure on the set of candidate sites, randomization is used to convert it into a nearly optimal sensor configuration. Simulation experiments regarding a process of induction heating are reported to validate the presented approach.

Keywords: Distributed parameter systems, Computational methods, Flexible structures
Abstract: In this work, the classical equivalence between Schrödinger and Euler-Bernoulli beam partial differential equations (PDEs) as closed physical systems is extended to open physical systems using the port-Hamiltonian framework: first, a damped version of both these models is presented; second, the possible collocated inputs and outputs of the two models are parameterized in the most general way; and third, a structure-preserving discretization method for a class of one-dimensional Boundary-Controlled Port-Hamiltonian System (BC-PHS) with collocated boundary actuation and sensing is developed. Unlike the classical Partitioned Finite Element Method (PFEM) approach, the proposed discretization method makes it possible to obtain an ordinary differential equation regardless of the boundary conditions, preventing the emergence of a differential-algebraic equation in the case of mixed boundary conditions. This novelty, recently validated for the wave and Timoshenko beam equations, is now extended to PDEs with a second-order differential operator. On the Schrödinger and Euler-Bernoulli equations, it is shown that the proposed numerical scheme can deal with a large type of boundary inputs and outputs.

Keywords: Distributed parameter systems, Computational methods
Abstract: Controller design for distributed parameter systems is often accomplished using a lumped approximation. For a system that is exponentially stable, it is reasonable to expect the approximation to preserve this decay rate. Preservation of the decay rate is important for realistic simulations and also for reliable controller design. We show that a simple mixed finite element method conserves exponential stability for a class of boundary-damped systems that are port-Hamiltonian. The results are illustrated by LQ-optimal controller design for a wave equation with spatially varying physical parameters. The convergence and performance of the controllers obtained using this mixed finite element method are compared to those obtained using a standard finite-element method approximation, which does not preserve the stability margin.

Keywords: Distributed parameter systems, Lyapunov methods, Nonlinear systems
Abstract: In this paper, we propose a feedback control strategy to protect vulnerable areas from wildfires. We consider a system of coupled partial differential equations (PDEs) that models heat propagation and fuel depletion in wildfires and study two cases. First, when the wind velocity is known, we design a Neumann-type boundary controller guaranteeing that the temperature of some protected region converges exponentially, in the L2 norm, to the ambient temperature. Second, when the wind velocity is unknown, we design an adaptive Neumann-type boundary controller guaranteeing the asymptotic convergence, in the L2 norm, of the temperature of the protected region to the ambient temperature. In both cases, the controller acts along the boundary of the protected region and relies solely on temperature measurements along that boundary. Our results are supported by numerical simulations.

Keywords: Neural networks, Machine learning, Nonlinear systems
Abstract: The rapid integration of large language models (LLMs) into our everyday lives has outpaced safety considerations aimed at protecting users from toxic outputs and preventing malicious actors from generating harmful text at scale. As a result, LLMs have been exploited by bots capable of producing vast amounts of harmful and toxic content, enabling users to manipulate online opinions and, in some cases, create dangerous online environments.

Our work addresses this issue by developing a framework for designing safety filters that preclude toxic outputs. To achieve this, we leverage Control Barrier Functions (CBFs) which enable the design of closed-loop systems that remain safe. We consider the continuous-time model of an LLM, where tokens are regarded as the state of the model, and prove that by only controlling the first token, any function satisfying mild assumptions becomes a CBF. Our approach can be utilized to design LLMs capable of ensuring safety of its outputs without significantly affecting the original model’s behavior.

Keywords: Stability of nonlinear systems, Reinforcement learning, Optimal control
Abstract: This paper presents a novel framework for analyzing Incremental-Input-to-State Stability (dISS) based on the idea of using rewards as "test functions." Whereas control theory traditionally deals with Lyapunov functions that satisfy a time-decrease condition, reinforcement learning (RL) value functions are constructed by exponentially decaying a Lipschitz reward function that may be non-smooth and unbounded on both sides. Thus, these RL-style value functions cannot be directly understood as Lyapunov certificates. We develop a new equivalence between a variant of incremental input-to-state stability of a closed-loop system under given a policy, and the regularity of RL-style value functions under adversarial selection of a Holder-continuous reward function. This result highlights that the regularity of value functions, and their connection to incremental stability, can be understood in a way that is distinct from the traditional Lyapunov-based approach to certifying stability in control theory.

Keywords: Neural networks, Predictive control for linear systems, Nonlinear systems
Abstract: Recent advances in state-space model architectures have shown great promise for efficient sequence modeling, but challenges remain in balancing computational efficiency with model expressiveness. We propose the Flash STU architecture, a hybrid model that interleaves spectral state space model layers with sliding window attention, enabling scalability to billions of parameters for language modeling while maintaining a near-linear time complexity. We evaluate the Flash STU and its variants on diverse sequence prediction tasks, including linear dynamical systems, robotics control, and language modeling. We find that, given a fixed parameter budget, the Flash STU architecture consistently outperforms the Transformer and other leading state-space models such as S4 and Mamba-2.

Keywords: Control applications, Predictive control for linear systems
Abstract: Model Predictive Control (MPC) is a powerful control strategy widely utilized in domains like energy management, building control, and autonomous systems. However, its effectiveness in real-world settings is challenged by the need to incorporate context-specific predictions and expert instructions, which traditional MPC often neglects. We propose InstructMPC, a novel framework that addresses this gap by integrating real-time human instructions through a Large Language Model (LLM) to produce context-aware predictions for MPC. Our method employs a Language-to-Distribution (L2D) module to translate contextual information into predictive disturbance trajectories, which are then incorporated into the MPC optimization. Unlike existing context-aware and language-based MPC models, InstructMPC enables dynamic human-LLM interaction and fine-tunes the L2D module in a closed loop with theoretical performance guarantees, achieving a regret bound of O(sqrt{Tlog T}) for linear dynamics when optimized via advanced fine-tuning methods such as Direct Preference Optimization (DPO) using a tailored loss function.

Keywords: Emerging control applications, Sensor fusion, Sensor networks
Abstract: This paper models information diffusion in a network of Large Language Models (LLMs) that is designed to answer queries from distributed datasets, where the LLMs can hallucinate the answer. We introduce a two-time-scale dynamical model for the centrally administered network, where opinions evolve faster while the network's degree distribution changes more slowly. Using a mean-field approximation, we establish conditions for a locally asymptotically stable equilibrium where all LLMs remain truthful. We provide approximation guarantees for the mean-field approximation and a singularly perturbed approximation of the two-time-scale system. To mitigate hallucination and improve the influence of truthful nodes, we propose a reputation-based preferential attachment mechanism that reconfigures the network based on LLMs' evaluations of their neighbors. Numerical experiments on an open-source LLM (LLaMA-3.1-8B) validate the efficacy of our preferential attachment mechanism and demonstrate the optimization of a cost function for the two-time-scale system.

Keywords: Chemical process control, Manufacturing systems and automation, Neural networks
Abstract: Predictive maintenance (PDM) plays a crucial role in minimizing resource loss and ensuring production continuity in advanced manufacturing by optimizing equipment health management strategies. To effectively capture the non-stationary dynamic behavior of industrial processes and quantify uncertainty, this paper proposes a Multi-Scale Mixing Condition Diffusion Denoising Probabilistic Model (MSM-DDPM). The proposed method leverages multiscale decomposition mixing to efficiently learn complex time-domain variations in time series while modeling the distribution of the prediction window in the frequency domain by means of a channeled self-attentive encoder. Experimental results on two representative non-stationary datasets demonstrate that MSM-DDPM outperforms 9 state-of-the-art algorithms. This study provides a novel technical pathway for health state assessment and the development of preventive maintenance strategies for complex industrial equipment.

Keywords: Machine learning, Robotics, Data driven control
Abstract: This paper addresses the problem of generating dynamically admissible trajectories for control tasks using diffusion models, particularly in scenarios where the environment is complex and system dynamics are crucial for practical application. We propose a novel framework that integrates system dynamics directly into the diffusion model's denoising process through a sequential prediction and projection mechanism. This mechanism, aligned with the diffusion model's noising schedule, ensures generated trajectories are both consistent with expert demonstrations and adhere to underlying physical constraints. Notably, our approach can generate maximum likelihood trajectories and accurately recover trajectories generated by linear feedback controllers, even when explicit dynamics knowledge is unavailable. We validate the effectiveness of our method through experiments on a complex non-convex optimal control problem involving waypoint tracking and collision avoidance, demonstrating its potential for efficient trajectory generation in practical applications. Our code repository is available at www.github.com/darshangm/dynamics-aware-diffusion.

Keywords: Neural networks, Learning, Filtering
Abstract: Sequential fine-tuning of transformers is useful when new data arrive sequentially, especially with shifting distributions. Unlike batch learning, sequential learning demands that training be stabilized despite a small amount of data by balancing new information and previously learned knowledge in the pre-trained models. This challenge is further complicated when training is to be completed in latency-critical environments and learning must additionally quantify and be mediated by uncertainty. Motivated by these challenges, we propose a novel method that frames sequential fine-tuning as a posterior inference problem within a Bayesian framework. Our approach integrates closed-form moment propagation of random variables, Kalman Bayesian Neural Networks, and Taylor approximations of the moments of softmax functions. By explicitly accounting for pre-trained models as priors and adaptively balancing them against new information based on quantified uncertainty, our method achieves robust and data-efficient sequential learning. The effectiveness of our method is demonstrated through numerical simulations involving sequential adaptation of a decision transformer to tasks characterized by distribution shifts and limited memory resources.

Keywords: Autonomous vehicles, Delay systems, Traffic control
Abstract: We provide experimental validation, in a pair of vehicles, of a recently introduced predictor-based cooperative adaptive cruise control (CACC) design, developed for achieving delay compensation in heterogeneous vehicular platoons subject to long actuation delays that may be distinct for each individual vehicle. We provide the explicit formulae of the control design that is implemented, accounting for the effect of zero-order hold and sampled measurements; as well as we obtain vehicle and string stability conditions numerically, via derivation of the transfer functions relating the speeds of pairs of consecutive vehicles. We also present consistent simulation results for a platoon with a larger number of vehicles, under digital implementation of the controller. Both the simulation and experimental results confirm the effectiveness of the predictor-based CACC design in guaranteeing individual vehicle stability, string stability, and tracking, despite long/distinct actuation delays. 

Keywords: Traffic control, Transportation networks, Modeling
Abstract: Network signal control is an important means to tackle congestion in urban networks. This study proposes a model predictive control (MPC) approach for optimizing road network signal timing by employing an extended link transmission model with dynamic queues, namely the link queue transmission model (LQM). The LQM circumvents the limitations of the link transmission model that only considers link-level cumulative inflows and outflows at road boundaries. By incorporating turn-level queue dynamics across multiple turning directions, the LQM captures time-varying queues and spillback effects over the prediction horizon and enables the network controller to determine the green time fraction for all links centrally to minimize total queue length and reduce oscillations in signal plans. Simulation experimental results conducted on a grid network with six intersections demonstrate the effectiveness of the proposed method in reducing congestion compared to conventional methods.

Keywords: Traffic control, Transportation networks, Decentralized control
Abstract: This paper presents a novel reformulation of the queue-based Max-Pressure (MP) traffic signal control strategy using a decentralized framework that leverages only local intersection data to dynamically determine optimal phase durations, maximizing traffic throughput. We critically analyze the conventional store-and-forward modeling approach and highlight its limitations in representing phase-switching gaps at intersections. To overcome these issues, we propose an enhanced store-and-forward model coupled with an improved MP control formulation that explicitly accounts for phase-switching losses. Additionally, we introduce a dynamic constraint on phase durations, challenging the traditional assumption that minimal green times are inherently optimal and stable. Simulation results demonstrate that the negative impact of switching gaps escalates with increasing demand, underscoring the necessity of adaptive phase timing. Our refined control strategy contributes to a more robust, realistic, and efficient traffic signal management, enhancing overall network performance.

Keywords: Transportation networks, Stability of nonlinear systems, Nonlinear systems
Abstract: We study a class of dynamical multi-commodity flow networks in transportation networks. These are modeled as dynamical systems describing the evolution of the densities of a number of different commodities across the cells of a transportation network. Each cell is characterized by commodity-specific increasing demand functions returning the maximum outflow of each commodity from the cell as a function of the current density of that commodity, as well as a decreasing supply function returning the total maximum inflow that is allowed in the cell as a function of the current aggregate density in the cell. Every commodity is characterized by a different routing matrix, whose entries describe the turning ratios between adjacent cells. We identify a (typically convex) capacity region: for exogenous inflow vectors belonging to that region, we prove the existence of a locally asymptotically stable free-flow equilibrium point. Building on a contraction argument, we also provide an estimate of the basin of attraction of such free-flow equilibrium point. Finally, we analyze a simple special case showing that, when the exogenous inflow vector does not belong to the region of stability, non-free flow equilibrium points might arise.

Keywords: Traffic control
Abstract: In this paper, we present a novel control strategy for autonomous vehicles traveling on a circular road. The proposed approach employs continuation methods to relate microscopic driver dynamics to macroscopic flow representations. By transforming second-order microscopic vehicle models into a system of 2 times 2 partial differential equations, we derive a continuum-based control framework designed to steer the system toward a desired equilibrium configuration. This macroscopic control strategy is later discretized to enable practical implementation at the microscopic level. Different discretization strategies will lead to different local controllers with different communication patterns. In that, our approach can be seen as a generic controller allowing for a family of intervehicle control laws with different connectivity patterns. Numerical simulations are conducted to illustrate the effectiveness of the approach.

Keywords: Machine learning, Observers for nonlinear systems, Traffic control
Abstract: Recent works on applying Physics-Informed Neural Networks to traffic density estimation have shown promise for future developments due to their robustness to model errors and noisy data. In this paper, we introduce a methodology for online approximation of the traffic density using measurements from probe vehicles in two settings: one using the Greenshield model and the other considering a high-fidelity traffic simulation. The proposed method continuously estimates the real-time traffic density in space and performs model identification with each new set of measurements. The density estimate is updated in almost real-time using gradient descent and adaptive weights. In the case of full model knowledge, the resulting algorithm performs similarly to the classical open-loop one. However, in the case of model mismatch, the iterative solution behaves as a closed-loop observer and outperforms the baseline method. Similarly, the proposed algorithm correctly reproduces the traffic characteristics in the high-fidelity setting.

Keywords: Traffic control, Model Validation, Agents-based systems
Abstract: This paper presents an analysis and validation of a control-oriented macroscopic moving bottleneck model with an agent-based traffic simulator. The moving bottleneck approach uses a partial differential equation (PDE) to model traffic flow and an ordinary differential equation (ODE) to model the behavior of connected and automated vehicles (CAVs). On the other hand, the agent-based simulation uses AGAMAS, which is a framework integrated into SUMO using JADE, to define controlled agents in microscopic traffic flow. The coupled PDE-ODE model is extended from previous work to incorporate more realistic fundamental diagrams validated on real-world data taken from motorway A20 in the Netherlands. The two models are compared, and the moving bottleneck model is validated on several different scenarios including CAV-free operation, the presence of a stationary bottleneck (accident), and the presence of a moving bottleneck. Overall, the improved macroscopic moving bottleneck approach is shown to capture the average behavior of the agent-based approach, namely the location of the bottleneck, the density values upstream and downstream and of the bottleneck, and the speed of the backward propagation of the bottleneck. In addition, the macroscopic model is shown to be less computationally intensive which is paramount in light of real-time control applications.

Keywords: Autonomous vehicles, Nonlinear systems, Traffic control
Abstract: This article proposes a nonlinear microscopic dynamical model for autonomous electric vehicles (A-EVs) that considers battery energy efficiency in the car-following dynamics. The model builds upon the Optimal Velocity Model (OVM), with the control term based on the battery dynamics to enable thermally optimal and energy-efficient driving. We rigorously prove that the proposed model achieves lower energy consumption compared to the Optimal Velocity Follow-the-Leader (OVFL) model. Through numerical simulations, we validate the analytical results on the energy efficiency. We additionally investigate the stability properties of the proposed model.

Keywords: Discrete event systems, Petri nets, Optimization algorithms
Abstract: The concept of K-step non-interference for discrete event systems deals with the possibility of inferring a secret after at most K observations following the occurrence of the secret itself. K-step non-interference accounts for the possibility of not being able to infer a secret in due time to threaten system's security. Indeed, if a secret is detected after a maximum delay, the inferred information may be no longer useful, hence nullifying the malicious intrusion. From this point-of-view, the concept of K-step non-interference deals with practical security. This paper formally introduces the concept of K-step non-interference and gives a necessary and sufficient condition to verify such a property when discrete event systems are modeled as bounded, live, and reversible Petri nets. The effectiveness of the proposed approach is shown by means of two examples.

Keywords: Discrete event systems, Automata
Abstract: Confidentiality is a security model for discrete-event systems that uses an encryption function to obscure communications so the original information can be recovered by any agent with the decryption key. In this work we introduce the idea of stealthy confidentiality, namely when the set of possible behaviours of the encrypted system appears to be possible behaviours of the actual plant. We then present conditions that must be satisfied for stealthy confidentiality enforcing encryption functions to exist under the assumptions from our previous work and under generalized assumptions that permit the existence of strings that are neither secret nor non-secret.

Keywords: Discrete event systems, Supervisory control, Automata
Abstract: We investigate the problem of synthesizing safe supervisors for discrete-event systems under actuator attacks, where an adversary can partially override control commands at vulnerable states. We introduce a novel dynamic-eventprotection mechanism, where the system can defend itself from attacks by taking defense actions when it meets certain required safety levels. To achieve this, the system employs two policies: a safety-enhancement policy that dynamically manipulates protecting events to increase the safety level, and a state-defense policy that determines whether to defend against attacks when sufficient safety levels are accumulated. Our goal is to synthesize a attack-resilient supervisor, along with compatible safety-enhancement and state-defense policies, to ensure the closed-loop system remains safe under any possible attacks on vulnerable states. We provide a sound and complete approach for synthesizing the supervisor and policies by formulating the problem as a safety game played on a multilayered duplication structure of the original system. We illustrate the proposed approach by running examples.

Keywords: Discrete event systems, Supervisory control, Automata
Abstract: Many property verification and enforcement problems of partially observed discrete event systems (DES) are typically addressed solely from the outside observer's perspective. However, systems may be monitored not only by a designated observer but also by a potentially malicious intruder when deployed in complex and open environments. The observer infers the information of the system based on its observation, which is referred to as knowledge. In addition, the intruder not only eavesdrops on the system's behaviors but also attempts to infer the observer's knowledge from its own observation. Notably, the information flow from the system to the observer and the intruder is asymmetric, resulting in incomparable observable events for each agent. Such an inference scenario has recently been formalized as the epistemic property. This paper addresses the enforcement of the epistemic property in a partially observed DES through supervisory control. Specifically, we propose a game-theoretic framework involving the observer/supervisor, the intruder, and the environment. A bipartite structure named all-protect structure is constructed as the game area, from which we solve the game and synthesize maximally permissive controllable and observable supervisors to enforce the epistemic properties.

Keywords: Discrete event systems, Automata, Fault diagnosis
Abstract: This paper addresses the problem of fault diagnosis in discrete event systems under a decentralized observation setting where information processing is based on partially ordered observation sequences. Specifically, we consider a system modeled as a nondeterministic finite automaton, observed by a set of observation sites, each capable of recording sequences of (possibly different) events. When prompted, these recorded sequences are transmitted to a coordinator, which utilizes the received information to diagnose faults that may have occurred in the system. To capture and interpret the relationship between the possible system states and faults, and the received information at the coordinator, we introduce the notion of the Complete Synchronizing Sequence structure (CSS structure). Based on this structure, we propose two methods for diagnosability verification: an observer-based approach and a verifier-based approach, both of which would be highly impractical without the CSS structure.

Keywords: Discrete event systems, Automata, Supervisory control
Abstract: In this paper, we propose a method to verify the existence of weakly harmful actuator-enabling attacks, a property of resiliency in discrete-event systems. An external attacker has knowledge of the plant model and is aware of the existence of the supervisor and the language of the closed-loop system via an observation mask, but it does not have any knowledge of the supervisor nor the specification. We show that weakly harmful actuator-enabling attacks cannot be verified through a direct state analysis in the corresponding supremal consistent supervisor. To verify the existence of such weakly harmful actuator-enabling attacks, we develop a method based on language consistency.

Keywords: Cyber-Physical Security, Computer/Network Security, Discrete event systems
Abstract: We propose a novel cyber-attack detection scheme for control schemes regulated via Stochastic Event-Triggered Control, to detect packets that are maliciously injected by an adversary. The diagnosis scheme relies on assessing whether the arrival time of the information packets received from the controller are compatible with the nominal probability distribution of triggering, or whether they are anomalous. To contrast the threat of an eavesdropping adversary capable of estimating the nominal triggering distribution, we propose a switching scheme, whereby the probability of triggering is drawn among a set of stochastic triggering mechanisms, which is such that the reconstruction of the communication pattern by an eavesdropper becomes computationally infeasible. We design the set of stochastic triggering mechanisms via the solution of an optimization problem, which embeds an explicit trade-off between the properties of the nominal Stochastic Event-Triggered Controller and the detection scheme. The results are illustrated through a numerical example.

Keywords: Discrete event systems, Hybrid systems, Switched systems
Abstract: Stability analysis of switched systems, characterized by multiple operational modes and switching signals, is a challenging task due to their inherently nonlinear dynamics. While theoretical frameworks such as multiple Lyapunov functions (MLF) provide a foundation for stability analysis, their computational applicability remains limited for general systems lacking favorable structural properties. This paper investigates stability analysis for switched systems under state-dependent switching conditions. We propose neural multiple Lyapunov functions (NMLF), a unified framework that combines the theoretical guarantees of MLF with the computational efficiency of neural Lyapunov functions (NLF). Our approach leverages a set of tailored loss functions and a counter-example guided inductive synthesis (CEGIS) scheme to train neural networks that rigorously satisfy MLF conditions. Through comprehensive simulations and theoretical analysis, we demonstrate NMLF’s effectiveness and its potential for practical deployment in complex switched systems.

Keywords: Mean field games
Abstract: We address in this paper a fundamental question that arises in mean-field games (MFGs), namely whether mean-field equilibria (MFE) for discrete-time finite-horizon MFGs can be used to obtain approximate stationary as well as non-stationary MFE for similarly structured infinite-horizon MFGs. We provide a rigorous analysis of this relationship, and show that any accumulation point of MFE of a discounted finite-horizon MFG constitutes, under weak convergence as the time horizon goes to infinity, a non-stationary MFE for the corresponding infinite-horizon MFG. Further, under certain conditions, these non-stationary MFE converge to a stationary MFE, establishing the appealing result that finite-horizon MFE can serve as approximations for stationary MFE. Additionally, we establish improved contraction rates for iterative methods used to compute regularized MFE in finite-horizon settings, extending existing results in the literature. As a byproduct, we obtain that when two MFGs have finite-horizon MFE that are close to each other, the corresponding stationary MFE are also close. As one application of the theoretical results, we show that finite-horizon MFGs can facilitate learning-based approaches to approximate infinite-horizon MFE when system components are unknown.

Keywords: Stochastic optimal control, Reinforcement learning, Filtering
Abstract: We study reinforcement learning using linear function approximation and finite memory approximations for partially observed Markov decision processes (POMDPs). We first present an algorithm for the value evaluation of finite memory feedback policies. We provide error bounds derived from filter stability and projection errors. We then study the learning of finite memory based near-optimal Q values. Convergence in this case requires further assumptions on the exploration policy when using general basis functions. We then show that these assumptions can be relaxed for specific models such as those with perfectly linear cost and dynamics, or when using discretization based basis functions.

Keywords: Markov processes, Stochastic optimal control
Abstract: In this paper, we present a generalization of the certainty equivalence principle of stochastic control. One interpretation of the classical certainty equivalence principle for linear systems with output feedback and quadratic costs is as follows: the optimal action at each time is obtained by evaluating the optimal state-feedback policy of the stochastic linear system at the minimum mean square error (MMSE) estimate of the state. Motivated by this interpretation, we consider certainty equivalent policies for general (non-linear) partially observed stochastic systems and allow for any state estimate rather than restricting to MMSE estimates. In such settings, the certainty equivalent policy is not optimal. For models with Lipschitz cost and dynamics, we derive upper bounds on the sub-optimality of certainty equivalent policies in terms of expected error of the proposed estimator. We present several examples to illustrate the results.

Keywords: Stochastic optimal control, Robust control, Optimal control
Abstract: We introduce the Kernel Mean Embedding Topology, a novel topology for stochastic kernels in both weak and strong forms, defined on integrable functions from a signal space to a Hilbert-structured space of probability measures. The weak formulation connects with the Young narrow and Borkar ((w^*))-topologies, revealing that while the (w^*)-topology and kernel mean embedding topology are relatively compact but not closed, the Young narrow topology is closed but lacks relative compactness. The strong form offers a natural framework for defining topologies on system models characterized by stochastic kernels, with implications for robustness and learning in optimal stochastic control under discounted or average cost criteria. The topology's Hilbert space structure facilitates stochastic kernel approximation via simulation data, making it ideal for studying optimality, approximations, robustness, and continuity properties.

Keywords: Stochastic optimal control, Predictive control for nonlinear systems, Stochastic systems
Abstract: In this paper, we present performance estimates for stochastic economic MPC schemes with risk-averse cost formulations. For MPC algorithms with costs given by expectations, it was recently shown that the guaranteed near-optimal performance of abstract MPC in random variables coincides with its implementable variant using pathwise feedback. In general, this property does not extend to costs formulated in terms of risk measures. However, through a turnpike-based analysis, this paper demonstrates that for a particular class of risk measures, this result can still be leveraged to formulate an implementable risk-averse MPC scheme, resulting in near-optimal averaged performance.

Keywords: Stochastic optimal control, Stability of linear systems, Lyapunov methods
Abstract: We analyze the stability properties of stochastic linear systems in closed-loop with an optimal policy that minimizes a discounted quadratic cost in expectation. In particular, the linear system is perturbed by both additive and multiplicative stochastic disturbances. We provide conditions under which mean-square boundedness, mean-square stability and recurrence properties hold for the closed-loop system. We distinguish two cases, when these properties are verified for any value of the discount factor sufficiently close to 1, or when they hold for a fixed value of the discount factor in which case tighter conditions are derived as illustrated in an example. The analysis exploits properties of the optimal value function, as well as a detectability property of the system with respect to the stage cost, to construct a Lyapunov function for the stochastic linear quadratic regulator problem.

Keywords: Stochastic optimal control, Markov processes, Filtering
Abstract: In Markov Decision Processes (MDPs) with intermittent state information, decision-making becomes challenging due to periods of missing observations. Linear programming (LP) methods can play a crucial role in solving MDPs, in particular, with constraints. However, the resultant belief MDPs lead to infinite dimensional LPs, even when the original MDP is with a finite state and action spaces. The verification of strong duality becomes non-trivial. This paper investigates the conditions for no duality gap in average-reward finite Markov decision process with intermittent state observations. We first establish that in such MDPs, the belief MDP is unichain if the original Markov chain is recurrent. Furthermore, we establish strong duality of the problem, under the same assumption. Finally, we provide a wireless channel example, where the belief state depends on the last channel state received and the age of the channel state. Our numerical results indicate interesting properties of the solution.

Keywords: Stochastic optimal control, Filtering, Sampled-data control
Abstract: This paper is concerned with the error analysis of two types of sampling algorithms, namely model predictive path integral (MPPI) and an interacting particle system (IPS) algorithm, that have been proposed in the literature for numerical approximation of the stochastic optimal control. The analysis is presented through the lens of Gibbs variational principle. For an illustrative example of a single-stage stochastic optimal control problem, analytical expressions for approximation error and scaling laws, with respect to the state dimension and sample size, are derived. The analytical results are illustrated with numerical simulations.

Keywords: Data driven control, Learning
Abstract: In the online non-stochastic control problem, an agent sequentially selects control inputs for a linear dynamical system when facing unknown and adversarially selected convex costs and disturbances. A common metric for evaluating control policies in this setting is policy regret, defined relative to the best-in-hindsight linear feedback controller. However, for general convex costs, this benchmark may be less meaningful since linear controllers can be highly suboptimal. To address this, we introduce an alternative, more suitable benchmark—the performance of the best fixed input. We show that this benchmark can be viewed as a natural extension of the standard benchmark used in online convex optimization and propose a novel online control algorithm that achieves sublinear regret with respect to this new benchmark. We also discuss the connections between our method and the original one proposed by Agarwal et al. in their seminal work introducing the online non-stochastic control problem, and compare the performance of both approaches through numerical simulations.

Keywords: Data driven control, Optimal control, Machine learning
Abstract: We propose a novel self-supervised learning framework for solving nonlinear optimal control problems (OCPs) with input constraints in real-time. In this framework, a neural network (NN) learns to predict the optimal co-state trajectory that minimizes the control Hamiltonian for a given system, at any system's state, based on the Pontryagin's Minimum Principle (PMP). Specifically, the NN is trained to find the optimal co-state solution that simultaneously satisfies the nonlinear system dynamics and minimizes a quadratic regulation cost. The control input is then extracted from the predicted optimal co-state trajectory by solving a quadratic program (QP) to satisfy input constraints and optimality conditions. We coin the term neural co-state regulator (NCR) to describe the combination of the co-state NN and the control input QP solver. To demonstrate the effectiveness of the NCR, we compare its feedback control performance with that of an expert nonlinear model predictive control (MPC) solver on a unicycle model. Because the NCR's training does not rely on expert nonlinear control solvers, which are often suboptimal, the NCR is able to produce solutions that outperform the nonlinear MPC solver in terms of convergence error and input trajectory smoothness even for system conditions that are outside its original training domain. At the same time, the NCR offers two orders of magnitude less computational time than the nonlinear MPC.

Keywords: Data driven control
Abstract: Data-driven controller design based on the data informativity framework has gained popularity due to its straightforward applicability, while providing rigorous guarantees. However, applying this framework to the estimator synthesis problem introduces technical challenges, which can only be solved so far by adding restrictive assumptions. In this work, we remove these restrictions by directly deriving a suitable parameterization in primal space. Moreover, this allows the integration of additional structural knowledge, such as bounds on parameters. Our findings are validated using numerical examples.

Keywords: Reduced order modeling, Data driven control, Robotics
Abstract: High-dimensional nonlinear systems pose considerable challenges for modeling and control across many domains, from fluid mechanics to advanced robotics. Such systems are typically approximated with reduced-order models, which often rely on orthogonal projections, a simplification that may lead to large prediction errors. In this work, we derive optimality of fiber-aligned projections onto spectral submanifolds, preserving the nonlinear geometric structure and minimizing long-term prediction error. We propose a data-driven procedure to learn these projections from trajectories and demonstrate its effectiveness through a 180-dimensional robotic system. Our reduced-order models achieve up to fivefold improvement in trajectory tracking accuracy under model predictive control compared to the state of the art.

Keywords: Data driven control, Nonlinear systems, Neural networks
Abstract: Controlling rhythmic systems, typically modeled as limit-cycle oscillators, is an important subject in real-world problems. Phase reduction theory, which simplifies the multidimensional oscillator state under weak input to a single phase variable, is useful for analyzing the oscillator dynamics. In the control of limit-cycle oscillators with unknown dynamics, the oscillator phase should be estimated from time series under partial observation in real time. In this study, we present an autoencoder-based method for estimating the oscillator phase using delay embedding of observed state variables. We evaluate the order of the phase estimation error under weak inputs and apply the method to phase-reduction-based feedback control of mutual synchronization of two oscillators under partial observation. The effectiveness of our method is illustrated by numerical examples using two types of limit-cycle oscillators, the Stuart-Landau and Hodgkin-Huxley models.

Keywords: Data driven control, Learning, Differential-algebraic systems
Abstract: Kolmogorov-Arnold networks (KANs) have been gaining attention as promising alternatives to multi-layer perceptions (MLPs). In this work, we propose a novel KAN-based Koopman operator (KO) learning framework (i.e., KAN-Extended Dynamic Mode Decomposition (KAN-EDMD)) for predicting the state trajectories dominated by complex nonlinear dynamics of power systems after faults. Furthermore, based on the construction of a KO predictor, we formulate a model predictive control (MPC) strategy that effectively stabilizes the system after faults. The linearity of the KO assures that the MPC optimization problem is convex quadratic, even if the original problem has non-convex constraints and nonlinear dynamics. The method benefits from efficient training and accurate prediction due to the expressibility of KANs. Comparing the performance of KAN-EDMD and Deep-EDMD (using regular MLPs) also showcases the superiority of the former approach in terms of predicting system trajectories on high-dimensional, highly nonlinear systems. Simulation results on the WECC 9-bus system are provided to verify the effectiveness of the proposed method.

Keywords: Nonlinear output feedback, Data driven control, Stability of nonlinear systems
Abstract: We present conditions of stability for an output feedback control framework of (unknown) nonlinear systems using Koopman operator theory, integrating derivative estimation via high-gain observers (HGOs) and gain synthesis through linear quadratic tracking (LQT) optimal controller. We show that this modeling process can be done effectively using output data only, the whole control strategy is output-driven. Closed-loop stability is proven under conditions where the residual errors from the HGO estimation and the Koopman model truncation effects are bounded. The accuracy of the Koopman model depends solely on these residuals, relying instead on the quality of the data-driven model and observer performance. Numerical simulations of a nonlinear system validate the theoretical results.

Keywords: Neural networks, Learning, Model Validation
Abstract: Deep learning models have emerged as powerful tools for modeling complex dynamical systems, offering data-driven alternatives to traditional identification techniques. Among them, autoencoder-based architectures have gained popularity due to their ability to extract low-dimensional latent representations starting from high-dimensional information. However, a major challenge persists: assessing the reliability of these models, especially in control tasks where prediction errors can have critical consequences. In this work, we propose an optimization-based certification approach to quantify the worst-case prediction error of ReLU-activated autoencoder models of dynamical systems. By formulating a targeted Mixed-Integer Quadratic Programming, our approach identifies data sequences that maximize the deviation between the model’s predicted output and the true system response.

Keywords: Identification, Closed-loop identification, Identification for control
Abstract: Multivariable parametric models are critical for designing, controlling, and optimizing the performance of engineered systems. The main objective of this paper is to develop a parametric identification strategy that delivers accurate and physically relevant models of multivariable systems using time-domain data. The introduced approach adopts an additive model structure, offering a parsimonious and interpretable representation of many physical systems, and employs a refined instrumental variable-based estimation algorithm. The developed identification method enables the estimation of parametric continuous-time additive models and is applicable to both open- and closed-loop controlled systems. The performance of the estimator is demonstrated through numerical simulations and experimentally validated on a flexible beam system.

Keywords: Identification, Data driven control, Linear systems
Abstract: We consider the problem of incrementally identifying a deterministic linear time-invariant system based on sequentially collected input-state data. It is assumed that abundant data from another system that is similar, but not identical to the true system, is available at the start of the identification process. In the initial stages of data collection, the data set generated by the true system is not yet fully informative for accurate identification, and multiple models are consistent with the data recorded up until that instant. We propose a method to identify one such model at each time step, which is closest to the similar system among all possible systems consistent with the true system data collected up to that instant. As more data become available, the proposed model shifts away from the similar system sequentially. It finally converges onto the true system when the data set grows to be informative for the true system. We compare the effectiveness of this incremental transfer identification paradigm with other recent attempts to identify systems with online/minimal data.

Keywords: Identification for control, Nonlinear systems identification, Data driven control
Abstract: This paper proposes a framework called Iterative Residual Dynamic Mode Decomposition (IRDMD) to address a limitation of extended dynamic mode decomposition (EDMD)---the need to manually select observables. While EDMD provides rich nonlinear representations by embedding state variables into a higher-dimensional space, it suffers from sensitivity to the choice of observables and requires prior knowledge for their design. In contrast, IRDMD automatically constructs observables by iteratively capturing residuals that arise from basic dynamic mode decomposition (DMD) approximations. Furthermore, IRDMD updates the system matrix gradually, making it more computationally efficient than EDMD. We apply IRDMD to both autonomous and control systems and demonstrate its effectiveness in prediction and control tasks through numerical experiments. The results confirm that IRDMD not only enables accurate forecasting but also achieves computationally efficient system identification and control on various nonlinear systems compared to EDMD.

Keywords: Identification for control, Modeling, Nonlinear systems
Abstract: In recent years, we have proposed a singular value decomposition (SVD) based recursive PI-MOESP identification algorithm (PI-MOESP identification algorithm: the multiple-input multiple-output (MIMO) output-error state-space model (MOESP) identification algorithm using an instrumental variable (IV) consisting of past input (PI) data) with fixed input and output (I/O) data size and the matrix inversion lemma (MIL). In this paper, we prove that our SVD-based recursive PI-MOESP identification approach is exactly the same as the existing SVD-based recursive PI-MOESP identification approach with fixed I/O data size and LQ-factorization. In addition, we point out that our SVD-based recursive PI-MOESP identification algorithm (RPI-MOESP) has lower computational complexity than the existing SVD-based RPI-MOESP with fixed I/O data size and LQ-factorization (LQ-RPI-MOESP). Finally, we examine the computational efficiency and the accuracy of our SVD-based RPI-MOESP and the LQ-RPI-MOESP through numerical experiments.

Keywords: Power systems, Identification for control, Identification
Abstract: This article presents a fully non-invasive method for accurate line impedance estimation using only inverter-side measurements, without injecting signals into the power network. The proposed signal conditioning scheme employs a direct-quadrature (dq) transformation with a secondary Phase-Locked Loop (PLL) dedicated to impedance estimation. Estimation is performed primarily along the d-axis dynamics, which are less affected by inverter set-point changes than the q-axis, while the proposed filter provides frequency separation that further enhances robustness and accuracy. A Variable Direction Forgetting Recursive Least Squares (VDF-RLS) algorithm is then applied, enabling rapid and stable adaptation by selectively discarding redundant information. Simulations show up to 3times lower error under low excitation compared to conventional RLS and Kalman filter methods.

Keywords: Identification, Statistical learning, Linear systems
Abstract: This paper addresses the problem of learning linear dynamical systems from noisy observations. In this setting, existing algorithms either yield biased parameter estimates or have large sample complexities. We resolve these issues by adapting the instrumental variable method and the bias compensation method, originally proposed for error-in-variables models, to our setting. We provide refined non-asymptotic analysis for both methods. Under mild conditions, our algorithms achieve superior sample complexities that match the best-known sample complexity for learning a fully observable system without observation noise.

Keywords: Identification, Linear systems, Numerical algorithms
Abstract: Numerically efficient and stable implementation of algorithms is essential for the kernel-based regularized system identification in practice. The state of art algorithms explore the semiseparable structure of the kernel and are based on the generator representation of the kernel matrix. However, as will be shown from both the theory and the practice, the algorithms based on the generator representation are sometimes numerically unstable, and thus limits its application in practice. In this paper, we aim to address this issue, and we consider the alternative Givens-vector representation of semiseparable kernels instead, which is numerically more stable but often much harder to derive. In particular, we derive the Givens-vector representation of some widely used kernel matrices. Then, we design algorithms based on the Givens-vector representation. Monte Carlo simulations show that the proposed algorithms admit the same order of computational complexity as the state of art ones based on generator representation, but with more stable and accurate implementation.

Keywords: Fault diagnosis, Identification, Electrochemical processes
Abstract: Chlor-alkali electrolysis is a cornerstone of chemical manufacturing, enabling global production of chlorine and related chemicals while consuming over 10% of industrial electricity. However, impurity-driven degradation—caused by calcium and magnesium hydroxides—remains a critical challenge, escalating energy costs and shortening system lifespans due to the lack of real-time impurity monitoring and adaptive predictive maintenance strategies. Here, we propose a unified framework integrating physics-informed Dynamic Mode Decomposition with Control (piDMDc). Our method reduces resistance prediction errors by 61% compared to baseline and quantifies degradation trends through deviation models validated against historical resistance data. Applied to a 3 MW industrial electrolyzer in Italy, the framework demonstrates stable, interpretable degradation tracking by enforcing physical constraints on system dynamics. While direct RUL validation awaits maintenance records, the approach establishes a methodology to reconcile sparse laboratory measurements with operational data for impurity-driven failure forecasting. This work advances predictive maintenance in electrochemical systems by balancing data-driven insights with domain-specific constraints, offering a pathway to optimize maintenance costs.

Keywords: Kalman filtering, Estimation, LMIs
Abstract: This paper introduces an optimal stochastic filter designed for systems with state-dependent noise. It utilizes the Maximum A Posteriori Estimation (MAP) approach to refine predicted estimates during the measurement assimilation phase. The key contribution is the establishment of sufficient conditions ensuring a global minimum, leading to an optimal MAP filter for dealing with state-dependent measurement noise. The optimization involves minimizing the log-posterior distribution through a relaxation method using Schur's complement. We prove that this optimization results in a unique and strictly local minimum coinciding with the global minimum of the log-posterior distribution, thereby ensuring global optimality. Additionally, a numerical example highlights the benefits of the proposed MAP filter, demonstrating significant improvements over a naive Kalman Filter implementation in the state-dependent measurement noise scenario.

Keywords: Kalman filtering, Estimation, Algebraic/geometric methods
Abstract: The characterization and propagation of uncertainties on the Special Euclidean Lie groups SE(2) and SE(3) are crucial in robotics and state estimation. Applications such as navigation and SLAM require accurate modeling of pose uncertainty involving both position and attitude. Lie groups offer a structured state space that preserves system properties and improves consistency in nonlinear estimation. Kalman filters on Lie groups improve robustness but rely on a Gaussian assumption, which fails for large uncertainties. To overcome these limitations, we used an alternative probability density function, based on a maximum entropy criterion, leading to a filter that we call vMG-UKF-LG. The resulting method is validated on experimental datasets against four benchmark filters and indicates improved accuracy when dealing with complex trajectories and overestimating the process noise.

Keywords: Estimation, Filtering, Kalman filtering
Abstract: This work addresses the problem of state estimation in multivariable dynamic systems with quantized outputs, a common scenario in applications involving low-resolution sensors or communication constraints. A novel method is proposed to explicitly construct the probability mass function associated with the quantized measurements by approximating the indicator function of each region defined by the quantizer using Gaussian mixture models. Unlike previous approaches, this technique generalizes to any number of quantized outputs without requiring case-specific numerical solutions, making it a scalable and efficient solution. Simulation results demonstrate that the proposed filter achieves high accuracy in state estimation, both in terms of fidelity of the filtering distributions and mean squared error, while maintaining significantly reduced computational cost.

Keywords: Kalman filtering, Stochastic systems, Algebraic/geometric methods
Abstract: In this paper, we introduce the Enhanced Polynomial Extended Kalman Filter (ePEKF), a filtering methodology for stochastic discrete-time nonlinear systems. Building upon the idea underlying the existing Polynomial Extended Kalman Filter (PEKF), we introduce a trade-off by augmenting only the output of the original system using Kronecker powers and by employing specific approximations. By doing so, we address some intrinsic approximation limitations observed in the polynomial formulation, while also reducing the associated computational burden. Furthermore, we propose a consistency-enhancing solution that ensures the reliability of the filter outcomes. Numerical examples demonstrate the superior performance of the ePEKF compared to both the classical Extended Kalman Filter and the previous PEKF, validating its effectiveness in various non-Gaussian scenarios.

Keywords: Estimation, Identification
Abstract: Within Bayesian state estimation, considerable effort has been devoted to incorporating constraints into state estimation for process optimization, state monitoring, fault detection and control. Nonetheless, in the domain of state-space system identification, the prevalent practice entails constructing models under Gaussian noise assumptions, which can lead to inaccuracies when the noise follows bounded distributions. With the aim of generalizing the Gaussian noise assumption to potentially truncated densities, this paper introduces a method for estimating the noise parameters in a state-space model subject to truncated Gaussian noise. Our proposed data-driven approach is rooted in maximum likelihood principles combined with the Expectation-Maximization algorithm. The efficacy of the proposed approach is supported by a simulation example.

Keywords: Kalman filtering, Sensor fusion, Optimization
Abstract: Sensors’ stochastic error modeling is of utmost importance for sensitive navigation applications. Accelerometers, rate gyros and barometers are examples, whose measurements needs to be calibrated in real-time for high-performance estimation. This work revisits the sensors aiding/integration/fusion problem via Extended Kalman Filter (EKF) to reliably estimate a given vehicle state. Historically, Allan Variance (AV) has been used to characterize the stochastic errors affecting the sensors and then tune the EKF, which involves a trade-off between optimal stochastic error characterization and optimal navigation performance. In this sense, a novel Genetic Algorithm (GA)-based EKF-tuning methodology is investigated, and results from experimentally conducted tests show improvements, when compared to traditional techniques, for stabilizing the vertical channel error response. In this work, an EKF-based baro-aided Inertial Navigation System (INS) under Global Navigation Satellite System (GNSS)-denied conditions is considered and the navigation performance is evaluated via altitude Root Mean Square Error (RMSE).

Keywords: Computational methods, Kalman filtering, Machine learning
Abstract: Tuning of Kalman Filters typically requires time-consuming manual iteration. Efficient and scalable tools to guide this process are valuable in practice. In this work, an automatically differentiable loss function (of cross-validation type) is developed for the tuning of linear time/parameter-varying state-space system representations, which reliably handles long time-series, and interfaces with the computational graph machinery in PyTorch, therefore accessing machine-learning compute infrastructure. The custom loss function operates internally with a specialized square-root Kalman Filter/Smoother which caches matrix factors during its first solve and which is modified to solve an adjoint equation in its second solve. The algorithms are potentially highly optimizable. Numerical experiments are provided.

Keywords: Kalman filtering, Fault detection, Nonlinear systems
Abstract: This paper presents a methodology for joint state and fault estimation utilizing a self-tuning extended Kalman filter (EKF). The EKF algorithm builds upon the classical Kalman filter and recursive least squares (RLS) to facilitate simultaneous state and fault estimation. The self-tuning characteristic is incorporated through adaptive mechanisms that address the influence of faults by recursively estimating process and measurement noise covariances using innovation-based covariance matching, as well as by adaptively updating the fault profile matrix via a scaling algorithm. These adaptive strategies are employed to enhance the accuracy of the joint estimation. The effectiveness of the proposed methodology is validated through numerical simulations of a submersible injection pump in a subsea seawater injection system. The results demonstrate significant improvements in estimation performance through adaptive measures, ensuring convergence and robustness. These findings highlight the potential of the proposed approach for real-world fault diagnosis in nonlinear systems.

Keywords: Networked control systems, Numerical algorithms, Communication networks
Abstract: We propose a multi-sender, multi-receiver over-the-air computation (OAC) framework for wireless networked control systems (WNCS) with structural constraints. Our approach enables actuators to directly compute and apply control signals from sensor measurements, eliminating the need for a centralized controller. We use an iterative and convexifying procedure to obtain a control law that is structured with respect to the network topology and minimizes the overall system energy-to-energy gain. Furthermore, we solve a constrained matrix factorization problem to find the optimal OAC configuration with respect to power consumption, robustness, and stability of the WNCS. We prove the convergence of our proposed algorithms and present numerical results that validate our approach to preserve closed-loop stability with robust control performance and constrained power.

Keywords: Networked control systems, Estimation, Fault tolerant systems
Abstract: Distributed state estimation for large-scale networked systems remains a crucial challenge due to dynamically reconfiguring network topologies caused by link failures, scheduling changes, or environmental interference. To address this issue, we propose the distributed Kalman-IMM estimator (DKIE), which combines different estimator models by subsystem type and incorporates them into a fully distributed and localized design. We focus on switching systems modeled as networked Markovian jump linear systems (MJLS), and propose a systematic way to distinguish subsystem types as either reconfigurable (capable of switching links between neighboring nodes) or static. Then, leveraging system level synthesis (SLS), we design type-specific sub-estimators where reconfigurable subsystems use a variant of the interacting multiple model (IMM) estimator, while static subsystems use a variant of the Kalman filters. By introducing a cooperative protocol, we further develop an extension of DKIE, called DKICE, which enables local coordination of IMM sub-estimators using topology information under Bayesian inference. We compare our approach against an existing distributed estimation baseline on a power grid network with 24 possible topologies, and demonstrate DKICE as a scalable solution for reliable state and mode identification across the entire switching network.

Keywords: Networked control systems, Distributed control, Agents-based systems
Abstract: Multi-agent systems are often employed in applications requiring coordinated behavior. Potential-based control, based on driving agents toward critical points of predefined potential functions, is a widely adopted approach for its simplicity, flexibility, and intrinsic stability. While well-studied in continuous-time, applying it in discrete-time systems, common in real-world applications, can introduce challenges related to stability and approximation accuracy. This paper proposes a novel framework for distributed discrete-time potential-based coordination control that, under the mild assumption of convexity of the potential functions, preserves key properties of the continuous-time formulation while accommodating heterogeneous systems with actuator saturation. Numerical results validate the theoretical findings.

Keywords: Networked control systems, Control over communications, Network analysis and control
Abstract: Optimal sensor sampling—a key design aspect in sensor and control networks and Internet-of-Things (IoT)— aims for reducing communication load and energy usage. In networked systems where multiple (possibly a large number of) heterogeneous agents use a common communication network to exchange data, network load can be reduced by sampling data only when necessary. Sampling instances are typically optimized such that individual agent’s performance is not substantially degraded, i.e., independent of network conditions. In this letter, we address a network-aware, jointly optimal sampling-control problem for stochastic networked control systems, modeling the network as a dynamical system with memory whose ser- viceability depends on network input, capacity, delays, and dropouts. We define the network state as an indicator of quality and cost of service. The network broadcasts its current and predicted states to agents, who optimize their sampling and control policies accordingly. Agents submit communication requests through their sampling profiles, enabling the network to update its state, and service as many requests as possible in real time. We derive an analytical solution to the optimal control policy, which is independent of network dynamics. In contrast, the optimal sampling policy is tightly coupled with the network state and dynamics, and is the solution of a mixed- integer nonlinear problem. Our theoretical analysis shows that the integer constraint can be relaxed without affecting the optimality.

Keywords: Networked control systems, Network analysis and control, Boolean control networks and logic networks
Abstract: In the analysis and design of large network systems, we often face the problem that the dynamics of each node is not fully known. In such a case, a structural approach can be taken to solve a given problem. The “structural approach” refers to solving a problem without using the exact model of each node, i.e., using only the information about the network structure and very limited information about the nodes. This paper addresses a sensor placement problem by a structural approach, which aims to find sensor nodes whose measurements can determine whether the states of the pre-specified target nodes converge to zero. To do this, we classify the nodes into four categories in terms of the induced subgraph of the original network structure on the target nodes and present all the solutions parameterized by the target nodes and free parameters.

Keywords: Networked control systems, Agents-based systems, Modeling
Abstract: Limited range of phase measurements motivates the analysis of coupled oscillators that interact if their geodesic distances are within a prescribed bound. Steady state behaviors of this system depend on the natural frequencies of the oscillators and on the underlying graph structure. A necessary and sufficient condition is provided for the graph to remain complete. If the graph is connected over time, it is proved that phase ordering is preserved among the oscillators according to their natural frequencies. The asymptotic convergence to frequency synchronization is proved if the graph is assumed to stay connected and all natural frequencies are the same. A comprehensive analysis of the three-oscillator case shows that phase ordering is not necessary for frequency synchronization, and that graph connectivity, together with an appropriate bound on the range of natural frequencies, ensures frequency synchronization.

Keywords: Control over communications, Networked control systems, Information theory and control
Abstract: In many modern control applications, the controller is connected to the sensor via a digital communication channel. Such digital communication channels require the consideration of quantization of measurements and to cope with limitations in the amount of data which can be communicated. This raises the fundamental question of how much data needs to be communicated for achieving a desired control objective. In this work, we consider generalized H2-performance and derive an exact expression for the minimal data-rate needed to achieve this control performance objective. The results show that the minimal data-rate is the same as that required to render a fixed but arbitrary star-shaped and compact set containing the origin in its interior of the state-space strongly invariant. Moreover, the minimal data-rate cannot be decreased by accepting suboptimal performance.

Keywords: Energy systems, Networked control systems, Stability of nonlinear systems
Abstract: Hydrogen's growing role in the transition towards climate-neutral energy systems necessitates structured modeling frameworks. Existing gas network models, largely developed for natural gas, fail to capture hydrogen systems distinct properties, particularly the coupling of hydrogen pipes with electrolyzers, fuel cells, and electrically driven compressors. In this work, we present a unified systematic port-Hamiltonian (pH) framework for modeling hydrogen systems. The proposed pH model ensures structure-preserving interconnections among system components, for each of which a dedicated pH representation is derived. The results demonstrate that hydrogen systems admit a compositional pH structure, which inherently provides a passive input-output map of the overall interconnected system and, thus, a promising foundation for structured analysis, control and optimization of this type of newly emerging energy systems.

Keywords: Optimization, Optimization algorithms
Abstract: This work proposes and studies the distributed resource allocation problem in asynchronous and stochastic settings. We consider a distributed system with multiple workers and a coordinating server with heterogeneous computation and communication times. We explore an approximate stochastic primal-dual approach with the aim of 1) adhering to the resource budget constraints, 2) allowing for the asynchronicity between the workers and the server, and 3) relying on the locally available stochastic gradients. We analyze our Asynchronous stochastic Primal-Dual (Asyn-PD) algorithm and prove its convergence in the second moment to the saddle point solution of the approximate problem at the rate of {cal O}(1/t), where t is the iteration number. Furthermore, we verify our algorithm numerically to validate the analytically derived convergence results, and demonstrate the advantages of utilizing our asynchronous algorithm rather than deploying a synchronous algorithm where the server must wait until it gets update from all workers.

Keywords: Optimization, Optimization algorithms
Abstract: We consider a general constrained problem with black-box objective and constraints, which is short for efficient solution methods because the gradient information is unavailable. To solve it, we reformulate it as a min-max problem and propose a zeroth-order extra gradient (ZOEG) algorithm. The proposed ZOEG integrates the extra gradient method with a stochastic gradient estimator that only uses input-output information to estimate the gradients. We establish finite-sample convergence guarantees for ZOEG in convex settings and achieve the oracle complexity bound with the best-known dependence on the dimension of the variable space. Finally, numerical experiments on a practical problem further illustrate our theoretical results and the effectiveness of ZOEG.

Keywords: Optimization, Optimization algorithms
Abstract: This paper proposes a novel algorithmic design procedure for online constrained optimization grounded in control-theoretic principles. By integrating the Internal Model Principle (IMP) with an anti-windup compensation mechanism, the proposed Projected-Internal Model Anti-Windup (P-IMAW) gradient descent exploits a partial knowledge of the temporal evolution of the cost function to enhance tracking performance. The algorithm is developed through a structured synthesis procedure: first, a robust controller leveraging the IMP ensures asymptotic convergence in the unconstrained setting. Second, an anti-windup augmentation guarantees stability and performance in the presence of the projection operator needed to satisfy the constraints. The effectiveness of the proposed approach is demonstrated through numerical simulations comparing it against other classical techniques.

Keywords: Optimization, Constrained control, Optimization algorithms
Abstract: This paper presents a computationally-efficient method for evaluating the feasibility of Quadratic Programs (QPs) for online constrained control. Based on the duality principle, we first show that the feasibility of a QP can be determined by the solution of a properly-defined Linear Program (LP). Our analysis yields a LP that can be solved more efficiently compared to the original QP problem, and more importantly, is simpler in form and can be solved more efficiently compared to existing methods that assess feasibility via LPs. The computational efficiency of the proposed method compared to existing methods for feasibility evaluation is demonstrated in comparative case studies as well as a feasible-constraint selection problem, indicating its promise for online feasibility evaluation of optimization-based controllers.

Keywords: Stochastic systems, Optimization algorithms, Optimization
Abstract: In this paper, we study discrete-time feedback optimization in stochastic scenarios. Specifically, we consider a discrete-time stochastic nonlinear system where the goal is to optimize its steady-state performance while simultaneously controlling it. Moreover, in our framework, we deal with packet losses in the communication between the controller and the physical system. To address these challenges, we propose a gradient-based controller embedding sample-and-hold mechanisms to handle packet losses. We analyze the resulting stochastic closed-loop system through the lens of stochastic timescale separation. This perspective allows us to establish the almost sure global asymptotic convergence of the closed-loop system to a set in which first-order optimality conditions of the underlying nonconvex optimization problem are satisfied. Finally, we provide numerical simulations to support our theoretical findings.

Keywords: Optimization, Optimization algorithms
Abstract: Optimization problems involving the minimization of a finite sum of smooth, possibly non-convex functions arise in numerous applications. To achieve a consensus solution over a network, distributed optimization algorithms, such as EXTRA (decentralized exact first-order algorithm), have been proposed to address these challenges. In this paper, we analyze the convergence properties of EXTRA in the context of smooth, non-convex optimization. By interpreting its updates as a nonlinear dynamical system, we show novel insights into its convergence properties. Specifically, i) EXTRA converges to a consensual first-order stationary point of the global objective with a sublinear rate; and ii) EXTRA avoids convergence to consensual strict saddle points, offering second-order guarantees that ensure robustness. These findings provide a deeper understanding of EXTRA in a non-convex context.

Keywords: Optimization, Optimization algorithms
Abstract: Bilevel optimization (BLO) problems find wide-ranging applications in network optimization, transportation, game theory, and machine learning. Recently, there has been significant interest in developing efficient gradient-based algorithms for solving BLO problems, with a particular focus on first-order methods due to their scalability. However, lower-level (LL) constraints introduce challenges for first-order gradient-based methods. To address these challenges, this paper focuses on barrier-reformulated constrained BLO problems, where the LL problem is transformed by incorporating a log barrier into the objective function. We propose a first-order method for barrier-reformulated constrained BLO problems with a non-asymptotic convergence guarantee to an epsilon-stationary point. The convergence rate is near-optimal in terms of dependency on epsilon, though at the cost of a linear dependence on dimension. We also demonstrate the effectiveness of the proposed method through the linear price-setting experiment.

Keywords: Optimization, Machine learning
Abstract: Heterogeneity in federated learning (FL) is a critical and challenging aspect that significantly impacts model performance and convergence. In this paper, we propose a novel framework by formulating heterogeneous FL as a hierarchical optimization problem. This new framework captures both local and global training processes through a bilevel formulation and is capable of the following: (i) addressing client heterogeneity through a personalized learning framework; (ii) capturing the pre-training process on the server side; (iii) updating the global model through nonstandard aggregation; (iv) allowing for nonidentical local steps; and (v) capturing clients' local constraints. We design and analyze an implicit zeroth-order FL method (ZO-HFL), equipped with nonasymptotic convergence guarantees for both the server-agent and the individual client-agents, and asymptotic guarantees for both the server-agent and client-agents in an almost sure sense. Notably, our method does not rely on standard assumptions in heterogeneous FL, such as the bounded gradient dissimilarity condition. We implement our method on image classification tasks and compare with other methods under different heterogeneous settings.

Keywords: Cooperative control, Optimization algorithms, Agents-based systems
Abstract: We consider a class of personalized distributed bilevel optimization (PDBO) problems with smooth but potentially nonconvex objectives over undirected networks. To address this problem, we propose a Hessian-free distributed algorithm with a loopless structure by incorporating Moreau smoothing to enhance convexity and gradient tracking to mitigate heterogeneity, enabling inner- and outer-level dynamics at the same time-scale.By leveraging new proof techniques that combine potential functions with the Moreau envelope, we establish a rate of mathcal{O}(frac{kappa^2}{(1-rho)^2K}) to a stationary point of a value-function-based penalty formulation of the PDBO problem, and a rate of mathcal{O}(frac{kappa^3}{(1-rho)^2K^{1/3}}) to a stationary point of the PDBO problem under Polyak–Łojasiewicz (PL) conditions. These results improve the convergence performance over existing Hessian-free bilevel optimization methods in terms of dependence on the condition number kappa. Numerical experiments further validate the effectiveness of the algorithm.

Keywords: Cooperative control, Agents-based systems, Reinforcement learning
Abstract: In this paper, we consider the distributed control of a team of agents set to solve multiple tasks. We model the assignment of agents to tasks as a multi-agent constrained reinforcement learning problem in which the task specifications are set as constraints involving the global state of the team whose compliance is revealed by a vector of reward signals. We derive a stochastic dual algorithm to solve this feasibility problem in a distributed fashion over a stochastic communication network with intermittent links, with two theoretical innovations with respect to standard dual designs. First, we incorporate the dual variables into the system state to enable a cyclic assignment of agents to tasks for the relevant case in which there are more tasks than agents. And secondly, we introduce a contraction in the dual update to control the aggregate effect of communication errors across the stochastic network links. These modifications to the dual dynamics allow us to establish theoretical feasibility guarantees with probability one, which we further corroborate in a numerical experiment involving the patrolling of multiple areas by a team of robots.

Keywords: Data driven control, Agents-based systems, Formal Verification/Synthesis
Abstract: We address control synthesis of stochastic discrete-time linear multi-agent systems under jointly chance-constrained collaborative signal temporal logic specifications in a distribution-free manner using available disturbance samples, which are partitioned into training and calibration sets. Leveraging linearity, we decompose each agent’s system into deterministic nominal and stochastic error parts, and design disturbance feedback controllers to bound the stochastic errors by solving a tractable optimization problem over the training data. We then quantify prediction regions (PRs) for the aggregate error trajectories corresponding to agent textit{cliques}, involved in collaborative tasks, using conformal prediction and calibration data. This enables us to address the specified joint chance constraint via Lipschitz tightening and the computed PRs, and relax the centralized stochastic optimal control problem to a deterministic one, whose solution provides the feedforward inputs. To enhance scalability, we decompose the deterministic problem into agent-level subproblems solved in an MPC fashion, yielding a distributed control policy. Finally, we present an illustrative example and a comparison with [1].

Keywords: Agents-based systems, Large-scale systems, Sensor networks
Abstract: In this paper, we focus on the distributed quantized average consensus problem in open multi-agent systems consisting of communication links that change dynamically over time. Open multi-agent systems exhibiting the aforementioned characteristic are referred to as open dynamic multi-agent systems in this work. We present a distributed algorithm that enables active nodes in the open dynamic multi-agent system to calculate the quantized average of their initial states. Our algorithm consists of the following advantages: (i) ensures efficient communication by enabling nodes to exchange quantized valued messages, and (ii) exhibits finite time convergence to the desired solution. We establish the correctness of our algorithm and we present necessary and sufficient topological conditions for it to successfully solve the quantized average consensus problem in an open dynamic multi-agent system. Finally, we illustrate the performance of our algorithm with numerical simulations.

Keywords: Agents-based systems, Switched systems, Distributed control
Abstract: This paper focuses on the data-driven consensus problem of switched multi-agent systems (MASs) in data-scarce scenarios. Firstly, a new data-driven switching control approach is proposed to utilize the data to directly design consensus protocol, thus avoiding the subsystem matrix dependency of switched MASs. Subsequently, an online transfer mechanism is developed with data from similar systems. On this basis, the control gain can be updated online using a small amount of real-time data from the switched MASs, breaking through the difficulty of not being able to calculate the gain due to data scarcity. Notably, the effect of noise is considered for both offline and online data collection. Theoretical analysis shows that the switched MASs can realize the asymptotic consensus when the average dwell time satisfies specific conditions. Finally, a numerical experiment is given to verify the effectiveness of the proposed strategy.

Keywords: Agents-based systems, Distributed control, Networked control systems
Abstract: Consensus is a well-studied problem in distributed sensing, computation and control, yet deriving useful and easily computable bounds on the rate of convergence to consensus remains a challenge. This paper discusses the use of seminorms for this goal. A previously suggested family of seminorms is revisited, and an error made in their original presentation is corrected, where it was claimed that the a certain seminorm is equal to the well-known coefficient of ergodicity. Next, a wider family of seminorms is introduced, and it is shown that contraction in any of these seminorms guarantees convergence at an exponential rate of infinite products of matrices, generalizing known results on stochastic matrices to the class of matrices whose row sums are all equal one. Finally, it is shown that such seminorms cannot be used to bound the rate of convergence of classes larger than the well-known class of scrambling matrices.

Keywords: Agents-based systems, Cooperative control, Optimal control
Abstract: We present an algorithm for a multi-agent path planning problem with pattern coordination based on dynamic programming and a Hamilton-Jacobi-Bellman equation. This falls broadly into the class of partial differential equation (PDE) based optimal path planning methods, which give a black-box-free alternative to machine learning hierarchies. Due to the high-dimensional state space of multi-agent planning problems, grid-based methods for PDE which suffer from the curse of dimensionality are infeasible, so we instead develop grid-free numerical methods based on variational Hopf-Lax type representations of solutions to Hamilton-Jacobi Equations. Our formulation is amenable to nonlinear dynamics and heterogeneous agents. We apply our method to synthetic examples wherein agents navigate around obstacles while attempting to maintain a prespecified formation, though with small changes it is likely applicable to much larger classes of problems.

Keywords: Sensor networks, Sensor fusion, Agents-based systems
Abstract: In this paper, we investigate distributed source seeking from a collaborative estimation perspective. To reduce the online sampling and computational burden on each agent, we propose a sensor fusion scheme for comprehensive signal field detection. In our approach, each agent measures only a subset of the signal field’s physical characteristics and relies on an information transmission protocol to achieve sensor fusion. A distributed set-membership estimation scheme is employed to ensure the convergence of our method. Additionally, we provide sufficient conditions for the stability of our approach and validate our results through simulation experiments.

Keywords: Power systems, Smart grid, Optimization
Abstract: This paper presents a new approach to approximate the AC optimal power flow (ACOPF). By eliminating the need to solve the ACOPF every few minutes, the paper showcases how a realtime feedback controller can be utilized in lieu of ACOPF and its variants. By i) forming the grid dynamics as a system of differential-algebraic equations (DAE) that naturally encode the non-convex OPF power flow constraints, ii) utilizing DAE-Lyapunov theory, and iii) designing a feedback controller that captures realtime uncertainty while being uncertainty-unaware, the presented approach demonstrates promises of obtaining solutions that are close to the OPF ones without needing to solve the OPF. The proposed controller responds in realtime to deviations in renewables generation and loads, guaranteeing improvements in system transient stability, while always yielding approximate solutions of the ACOPF with no constraint violations. As the studied approach herein yields slightly more expensive realtime generator controls, the corresponding price of realtime control and regulation is examined. Cost comparisons with the traditional ACOPF are also showcased—all via case studies on standard power networks.

Keywords: Power systems, Optimization
Abstract: Most existing generation scheduling models for power systems under demand uncertainty rely on energy-based formulations with a finite number of time periods, which may fail to ensure that power supply and demand are balanced continuously over time. To address this issue, we propose a robust generation scheduling model in a continuous-time framework, employing a decision rule approach. First, for a given set of demand trajectories, we formulate a general robust generation scheduling problem to determine a decision rule that maps these demand trajectories and time points to the power outputs of generators. Subsequently, we derive a surrogate of it as our model by carefully designing a class of decision rules that are affine in the current demand, with coefficients invariant over time and constant terms that are continuous piecewise affine functions of time. As a result, our model can be recast as a finite-dimensional linear program to determine the coefficients and the function values of the constant terms at each breakpoint, solvable via the cutting-plane method. Our model is non-anticipative unlike most existing continuous-time models, which use Bernstein polynomials, making it more practical. We also provide illustrative numerical examples.

Keywords: Power systems, Optimization, Energy systems
Abstract: Many resources in the grid connect to power grids via programmable grid-interfacing inverters that can provide grid services and offer greater control flexibility and faster response times compared to synchronous generators. However, the current through the inverter needs to be limited to protect the semiconductor components. Existing controllers are designed using somewhat ad hoc methods, for example, by adding current limiters to preexisting control loops, which can lead to stability issues or overly conservative operations.

In this paper, we study the geometry of the feasible output region of a current-limited inverter. We show that under a commonly used model, the feasible region is convex. We provide an explicit characterization of this region, which allows us to efficiently find the optimal operating points of the inverter. We demonstrate how knowing the feasible set and its convexity allows us to design safe controllers such that the transient trajectories always remain within the current magnitude limit, whereas standard droop controllers can lead to violations.

Keywords: Power systems, Smart grid, Optimization
Abstract: Managing power grids with the increasing presence of variable renewable energy-based (distributed) generation involves solving high-dimensional optimization tasks at short intervals. Linearizing the AC power flow (PF) constraints is a standard practice to ease the computational burden at the cost of hopefully acceptable inaccuracies. However, the design of these PF linearizations has traditionally been agnostic of the use case. Towards bridging the linearization-application gap, we first model the complete operational sequence needed to implement optimal power flow (OPF) decisions on power systems and characterize the effect of PF linearization on the resulting steady-state system operation. We then propose a novel formulation for obtaining optimal PF constraint linearizations to harness desirable system-operation attributes such as low generation cost and engineering-limit violations. To pursue the optimal PF linearization, we develop a gradient-based approach backed by sensitivity analysis of optimization routines and AC PF equations. Numerical tests on the IEEE 39-bus system demonstrate the capabilities of our approach in traversing the cost-optimality vs operational feasibility trade-off inherent to OPF approximations.

Keywords: Power systems, Neural networks, Optimization
Abstract: When solving decision-making problems with mathematical optimization, some constraints or objectives may lack analytic expressions but can be approximated from data. When an approximation is made by neural networks, the underlying problem becomes optimization over trained neural networks. Despite recent improvements with cutting planes, relaxations, and heuristics, the problem remains difficult to solve in practice. We propose a new solution based on a bilinear problem reformulation that penalizes ReLU constraints in the objective function. This reformulation makes the problem amenable to efficient difference-of-convex algorithms (DCA), for which we propose a principled approach to penalty selection that facilitates convergence to stationary points of the original problem. We apply the DCA to the problem of the least-cost allocation of data center electricity demand in a power grid, reporting significant savings in congested cases.

Keywords: Optimization, Power systems, Control over communications
Abstract: This letter addresses the resilience of cyber-physical systems with fixed connectivity of the physical network and controllable connectivity of the cyber network. We focus on the case where, to ensure effective control, the connected components of both networks should always align. In other words, when some of the physical lines fail, the cyber graph should be reconfigured via link additions or removals. Such a need arises, e.g., in the distributed control of power grids. To ensure the resilience of the system to major disruptions, we aim to design a cyber network that minimizes the number of cyber reconfigurations in the worst case of physical failure. We will call this number incongruity. Our contributions are threefold: (1) an analytical formula for computing incongruity, (2) a proof that an optimally resilient cyber graph can always be found in the form of a tree, and (3) a bi-level MILP formulation of the problem derived from our theoretical results. The latter contribution is of particular importance given the existence of solvers for bi-level MILPs and the fact that the straightforward MILP formulation of the problem would be tri-level.

Keywords: Optimization, Smart grid
Abstract: We consider decision-making problems under decision-dependent uncertainty (DDU), where the distribution of uncertain parameters depends on the decision variables and is only observable through a finite offline dataset. To address this challenge, we formulate a decision-dependent distributionally robust optimization (DD-DRO) problem, and leverage multivariate interpolation techniques along with the Wasserstein metric to construct decision-dependent nominal distributions (thereby decision-dependent ambiguity sets) based on the offline data. We show that the resulting ambiguity sets provide a finite-sample, high-probability guarantee that the true decision-dependent distribution is contained within them. Furthermore, we establish key properties of the DD-DRO framework, including a non-asymptotic out-of-sample performance guarantee, an optimality gap bound, and a tractable reformulation. The practical effectiveness of our approach is demonstrated through numerical experiments on a dynamic pricing problem with nonstationary demand, where the DD-DRO solution produces pricing strategies with guaranteed expected revenue.

Keywords: Energy systems, Optimization algorithms, Control applications
Abstract: Biogas plants represent one of several energy sources that can facilitate the expansion of renewable energy generation. However, the operation of a biogas plant may not yield profits without governmental support. A potential solution to this problem is to enable flexible operation of the biogas plant. This flexible approach allows for enhanced electricity sales during periods of high prices and decreased production when prices are low. However, many biogas plants typically operate constantly, mainly due to the complexities involved in modeling the process and the absence of necessary monitoring sensors. This paper presents a practical strategy for the flexible control of biogas plants. It features a combination of an economic Model Predictive Controller (MPC) and a Model Reference Adaptive Controller (MRAC). The economic MPC formulates the optimal trajectory aimed at profit maximization using the nominal model, while the MRAC addresses the uncertainties in the model, enabling the actual plant to follow the calculated optimal trajectory.

Keywords: Adaptive control, Flight control, Lyapunov methods
Abstract: The control of a Dubins Vehicle when subjected to a loss of control effectiveness in the turning rate is considered. A complex state-space representation is used to model the vehicle dynamics. An adaptive control design is proposed, with the underlying stability analysis guaranteeing closed-loop boundedness and tracking of a desired path. It is shown that a path constructed by waypoints and a minimum turn radius can be specified using a reference model which can be followed by the closed loop system. The control design utilizes the complex state-space representation as well as a PID controller for the nominal closed-loop. How the design can be modified to ensure path following even in the presence input constraints is also discussed. Simulation studies are carried out to complement the theoretical derivations.

Keywords: Adaptive control, Identification, Optimization
Abstract: In this paper, a constrained parameter update law is developed within the framework of adaptive control. The update law is derived using a constrained optimization approach, where a Lagrangian is formulated to incorporate parameter constraints through an inverse barrier function. This constrained update law is then integrated into the design of an adaptive tracking controller. The overall stability of the closed-loop system, including both the adaptive controller and the constrained update mechanism, is established using Lyapunov analysis and the recent results on the stability of constrained primal-dual dynamics. The effectiveness of the proposed method is demonstrated through simulations, which verify its ability to maintain parameter estimates within prescribed bounds while ensuring convergence to the true parameter values.

Keywords: Adaptive control, Lyapunov methods, Time-varying systems
Abstract: This paper proposes a new scheme for the so-called adaptive immersion-and-invariance (I&I) control that requires neither solving partial differential equations nor adding dynamic scaling factors to obtain the static I&I parameter estimation term. By exploiting a specially designed time-varying candidate Lyapunov function, we show that it is sufficient to pass the regressor through a strictly passive filter with a normalization-like output nonlinearity to generate a proxy regressor that forms the static I&I estimate. Closed-loop boundedness and asymptotic stabilization can be guaranteed. Simulation results illustrate the theory.

Keywords: Adaptive systems, Observers for Linear systems
Abstract: We show that constructing an augmented adaptive observer, where the extended state is a mix of the original states and their derivatives, we can enhance the transient performance and obtain robust estimation results for the original state and the unknown parameters. The convergence of the proposed augmented adaptive observer is shown under the persistence of excitation assumption by constructing a Lyapunov function and using the input-to-output stability framework. The performance of the proposed design is illustrated via numerical simulations.

Keywords: Autonomous vehicles, Adaptive control, Control applications
Abstract: This paper studies the trajectory tracking control problem of a quadrotor-slung-payload system with an unknown payload mass. To achieve accurate payload mass estimation, a novel estimator is designed using the immersion and invariance manifold design technique, enabling exponential convergence for the estimated parameter error dynamics. The estimator is then integrated into a cascaded control framework, which guarantees the asymptotic stability of the closed-loop system under the estimator-based controller. Numerical simulations are conducted to evaluate the effectiveness and performance of the proposed estimator.

Keywords: Time-varying systems, Lyapunov methods, Adaptive systems
Abstract: We study stability and robustness for a large class of linear time-varying systems under the assumption that the system possesses some kind of excitation, which is necessary for uniform attractivity of the origin, but not even boundedness of the solutions is assumed a priori. Our main statements provide strict Lyapunov functions, i.e., having a strictly negative-definite derivative, constructed based on an initial candidate whose derivative is sign-undefined. The Lyapunov function that we construct guarantees uniform global asymptotic stability and input-to-state stability with respect to bounded additive inputs. As a byproduct of our main results, we provide a Lyapunov function for a class of systems reminiscent of model-reference adaptive control with non-differentiable regressors.

Keywords: Lyapunov methods, Uncertain systems, Adaptive systems
Abstract: In this paper, we propose a low-frequency learning method with a discrete model reference adaptive control approach for uncertain systems with actuator dynamics. Our control architecture uses a low-pass filter-like version of the uncertainty estimate that is included in the estimation dynamics to attenuate the high-frequency oscillations. Additionally, a hedging term is used for the reference model to account for the existence of actuator dynamics. Lyapunov methods are used to guarantee the stability of the closed-loop system, and a linear matrix inequality (LMI) analysis is performed to guarantee boundedness of the hedging-based reference model trajectories and to prove the asymptotic convergence of the tracking error. Finally, the numerical simulation result is presented to illustrate the effectiveness of the proposed approach.

Keywords: Energy systems, Optimal control, Adaptive control
Abstract: In order to solve the maximum power point tracking (MPPT) problem of photovoltaic (PV) systems under partial shading and dynamic environments, this paper proposes a MPPT method based on the fractional order (FO) Newton-based extremum seeking control (ESC) algorithm, which employs a FO approach to enhance the search of the ESC algorithm for local maxima, and introduces a multi-peak mechanism to enhance the global search capability of the ESC algorithm to ensure that it can find the global power maximum point (GMPP) . The results of the experiment showed that the proposed method can adapt well to the changes of irradiance and temperature, and can accurately locate the GMPP in the case of multiple peaks. Compared with the integer order method, the algorithm has higher convergence speed and tracking accuracy, and can adapt the PV system to more complex operating environments.

Keywords: Nonlinear systems, Nonlinear output feedback, Feedback linearization
Abstract: In a paper of Liberzon in the early 2000s, it was shown that if a MIMO nonlinear system is uniformly invertible and weakly uniformly 0-state detectable, the system can be globally stabilized by static state-feedback. In this paper, it is shown that, if the system satisfies a weakened version of the sufficient conditions established by Hirschorn in his earlier work on invertibility, the method of Liberzon can be cast in a format that makes a recent method of Wu et al. for robust stabilization by dynamic output-feedback applicable.

Keywords: Nonlinear systems, Optimal control, Formal Verification/Synthesis
Abstract: Motivated by the latest research on feasible space monitoring of multiple control barrier functions (CBFs) as well as polytopic collision avoidance, this paper studies the Polytope Volume Monitoring (PVM) problem, whose goal is to design a control law for inputs of nonlinear systems to prevent the volume of some state-dependent polytope from decreasing to zero. Recent studies have explored the idea of applying Chebyshev ball method in optimization theory to solve the case study of PVM; however, the underlying difficulties caused by nonsmoothness have not been addressed. This paper continues the study on this topic, where our main contribution is to establish the relationship between nonsmooth CBF and parametric optimization theory through directional derivatives for the first time, to solve PVM problems more conveniently. In detail, inspired by Chebyshev ball approach, a parametric linear program based nonsmooth barrier function candidate is established for PVM, and then, sufficient conditions for it to be a nonsmooth CBF are proposed, based on which a feasibility-guaranteed quadratic program based safety filter is proposed to address PVM problems. Finally, numerical simulations are given to show the efficiency of the proposed safety filter.

Keywords: Iterative learning control, Nonlinear systems
Abstract: Nonlinear iterative learning control (ILC) and nonlinear repetitive control (RC) approaches introduce additional design freedom compared to linear time-invariant (LTI) approaches. Since the actual performance improvements depend on the parameters used in the nonlinearity, the aim of this paper is to optimize these parameters during the learning process. With optimal parameters, the nonlinear algorithms can outperform their LTI counterparts, for example by achieving fast attenuation of repeating disturbances without amplifying non-repeating disturbances. In this paper, we present the algorithm for the automatic learning/tuning process and validate it using simulations of an industrial flatbed printer.

Keywords: Constrained control, Lyapunov methods
Abstract: Control barrier functions (CBFs) are a powerful tool for the constrained control of nonlinear systems; however, the majority of results in the literature focus on systems subject to a single CBF constraint, making it challenging to synthesize provably safe controllers that handle multiple state constraints. This paper presents a framework for constrained control of nonlinear systems subject to box constraints on the systems' vector-valued outputs using multiple CBFs. Our results illustrate that when the output has a vector relative degree, the CBF constraints encoding these box constraints are compatible, and the resulting optimization-based controller is locally Lipschitz continuous and admits a closed-form expression. Additional results are presented to characterize the degradation of nominal tracking objectives in the presence of safety constraints. Simulations of a planar quadrotor are presented to demonstrate the efficacy of the proposed framework.

Keywords: Constrained control, Feedback linearization, Lyapunov methods
Abstract: In this paper we address the problem of control Lyapunov-barrier function (CLBF)-based safe stabilization for a class of nonlinear control-affine systems. A difficulty may arise for the case when a constraint has the relative degree larger than 1, at which computing a proper CLBF is not straightforward. Instead of adding an (possibly non-existent) control barrier function (CBF) to a control Lyapunov function (CLF), our key idea is to simply scale the value of the CLF on the unsafe set, by utilizing a sigmoid function as a scaling factor. We provide a systematic design method for the CLBF, with a detailed condition for the parameters of the sigmoid function to satisfy. It is also seen that the proposed approach to the CLBF design can be applied to the problem of task-space control for a planar robot manipulator with guaranteed safety, for which a safe feedback linearization-based controller is presented.

Keywords: Maritime control, Lyapunov methods, Nonlinear systems
Abstract: This paper reconsiders the trajectory tracking problem for a class of underactuated torpedo-type underwater vehicles using a Lagrangian method. Given the vehicle's 5-DOF kinematics, its nonlinear dynamics is derived via the Euler-Lagrangian equation. The resulting dynamics is then transformed into a three-input, three-output feedback form through a spherical coordinate transformation in the body-fixed frame. Based on this reduced-order model, where certain traditional dynamic properties of underwater vehicles no longer hold, this paper proposes a novel control scheme which can partially revive the vehicle's dynamic properties while minimizing the control efforts. Numerical simulations are conducted to validate the effectiveness of the proposed scheme.

Keywords: Iterative learning control, Switched systems, Nonlinear systems
Abstract: This paper develops a multiple model switched iterative learning control (ILC) framework for a general class of nonlinear plant dynamics. Given a set of candidate plant models chosen by the designer as possible representations of the true plant, the switching framework converges to a bounded tracking error whose norm is proportional to the (modified) gap metric between the true plant and the closest model in the candidate model set. This is the first multiple model switched ILC framework to provide guaranteed tracking performance for non-linear systems using a general class of ILC update (including Newton, norm-optimal, and gradient types) subject to unstructured model uncertainty. The transparent design framework is illustrated through application of the framework to a simulation example which demonstrates precise tracking error in the presence of arbitrarily large plant uncertainty.

Keywords: Stability of nonlinear systems, Lyapunov methods, Switched systems
Abstract: When global asymptotic stability under zero input becomes a stringent condition, it may be replaced by some practical variant which ensures convergence to some bounded ball instead of a point. This leads to the property of input-to-state practical stability, sufficient conditions for which exist for systems with different types of evolutions. For time-varying impulsive systems, however, results for establishing input-to-state practical stability are scarce. In this paper, sufficient conditions for input-to-state practical stability of time-varying impulsive systems are provided, based on Lyapunov-type functions. A first contribution is to reduce the analysis to the practical stability of a comparison system, which is scalar and has no inputs. The second contribution is to provide sufficient conditions for the comparison system to have the corresponding practical stability property when the Lyapunov-type functions have linear (time-varying, affine) rates.

Keywords: Robust control, Stochastic optimal control, Optimal control
Abstract: This paper introduces a method for constructing control policies robust to adversarial disturbance distributions that relate to a provided empirical distribution. The character of the adversary is shaped by a regularization term comprising a weighted sum of (i) the cross-entropy between the empirical and the adversarial distributions, and (ii) the entropy of the adversarial distribution itself. The regularization weights are interpreted as the likelihood factor and the temperature respectively. The proposed framework leads to an efficient dynamic programming algorithm --- referred to as the minsoftmax algorithm --- to obtain the optimal control policy, where the disturbances follow an analytical softmax distribution in terms of the empirical distribution, temperature, and likelihood factor. It admits a number of control-theoretic interpretations and can thus be understood as a flexible tool for integrating complementary features of related control frameworks. In particular, in the linear model quadratic cost setting, with a Gaussian empirical distribution, we draw connections to the well-known mathcal{H}_{infty}-control. We illustrate our results through a numerical example.

Keywords: Robust control, Numerical algorithms
Abstract: In this paper, a successive radial basis function (RBF) approximation approach is proposed to solve the Hamilton-Jacobi-Isaacs (HJI) partial differential equation (PDE) associated with finite-horizon nonlinear H∞ control problems. Unlike conventional discretization techniques such as finite difference or Galerkin methods, the successive radial basis function approximation strategy reformulates the nonlinear HJI PDE into a series of easily solvable initial value problems. By iteratively refining the solution through successive point sampling, numerical integration, and RBF interpolation, the method circumvents the need for exhaustive domain discretization. Numerical simulations confirm the effectiveness and accuracy of the proposed method in solving the finite-horizon nonlinear H∞ control problem.

Keywords: Robust control, Predictive control for nonlinear systems, Optimal control
Abstract: Ellipsoidal tube-based model predictive control methods effectively account for the propagation of the reachable set, typically employing linear feedback policies. In contrast, scenario-based approaches offer more flexibility in the feedback structure by considering different control actions for different branches of a scenario tree. However, they face challenges in ensuring rigorous guarantees. This work aims to integrate the strengths of both methodologies by enhancing ellipsoidal tube-based MPC with a scenario tree formulation. The uncertainty ellipsoids are partitioned by halfspaces such that each partitioned set can be controlled independently. The proposed ellipsoidal multi-stage approach is demonstrated in a human-robot system, highlighting its advantages in handling uncertainty while maintaining computational tractability.

Keywords: Robust control, Nonlinear systems, Neural networks
Abstract: This paper proposes a novel control scheme integrating a robust controller with an Echo State Network (ESN)-based control law to stabilize uncertain nonlinear systems under non-vanishing disturbances. First, the robust controller ensures the input-to-state stability (ISS) of the closed-loop system. Then, an ESN-based controller, offline trained and combined with the robust controller via Lyapunov redesign, generates a residual term to mitigate disturbance effects on the system output while preserving closed-loop stability. Numerical simulations demonstrate the strategy’s efficacy, significantly reducing disturbances compared to the standalone robust controller.

Keywords: Nonlinear output feedback, Robust control, Flight control
Abstract: This paper introduces a robust controller for multi-rotor systems that can effectively handle aggressive and high-magnitude disturbances, both in the orientation and position subsystems. Our control design uses only position and angular position vector information and comprises two primary algorithms: a state feedback controller and an extended high-gain observer. Moreover, the proposed controller provides asymptotic stability while satisfying user-imposed constraints on the position, velocity, and angular position error states. To achieve this goal, we introduce a barrier Lyapunov function, which guarantees that the tracking error trajectories of the system remain within the constraints. We evaluate the performance of our proposed control through numerical simulations and a comparison with a state-of-the-art popular controller. The results illustrate the effectiveness of our approach in coping with high-magnitude disturbances, especially in the positioning subsystem of the multi-rotor system.

Keywords: Robust adaptive control, Nonlinear systems, Optimal control
Abstract: This paper proposes a general incremental policy iteration adaptive dynamic programming (ADP) algorithm for model-free robust optimal control of unknown nonlinear systems. The approach integrates recursive least squares estimation with linear ADP principles, which greatly simplifies the implementation while preserving adaptive learning capabilities. In particular, we develop a sufficient condition for selecting a discount factor such that it allows learning the optimal policy starting with an initial policy that is not necessarily stabilizing. Moreover, we characterize the robust stability of the closed-loop system and the near-optimality of iterative policies. Finally, we perform numerical simulations to demonstrate the effectiveness of the proposed method.

Keywords: Robust control, Lyapunov methods, Game theory
Abstract: This letter presents a density function based safe control synthesis framework for the pursuit-evasion problem. We extend safety analysis to dynamic unsafe sets by formulating a reach-avoid type pursuit-evasion differential game as a robust safe control problem. Using density functions and semi-algebraic sets, we derive sufficient conditions for weak eventuality and evasion, reformulating the problem into a convex sum-of-squares program solvable via standard semidefinite programming solvers. This approach avoids the computational complexity of solving the Hamilton-Jacobi-Isaacs partial differential equation, offering a scalable and efficient framework. Numerical simulations demonstrate the efficacy of the proposed method.

Keywords: Robust control, Robotics, Constrained control
Abstract: In this paper, we propose a robust quadratic programming-based control (QPC) for uncertain Euler-Lagrange systems. The key idea of introducing robustness to a QPC is to adopt the disturbance observer (DOB) technique in the QP formulation: that is, an estimate for the lumped disturbance is computed in a least-square sense as the optimal solution of a QP, which is then compensated through the input channel to enhance robustness. Moreover, the input redundancy of the system is additionally utilized for stabilizing null-space motion, but with little sacrifice of task-space tracking performance. We theoretically prove via the singular perturbation theory that task-space dynamics is robustly stable in the presence of model uncertainty, where the concept of the inertially decoupling dynamics is applied. A simulation for twolink robot manipulator is conducted to verity the validity of the proposed controller.

Keywords: Linear systems
Abstract: Finding a positive state-space realization with the minimum dimension for a given transfer function is an open problem in control theory. In this paper, we focus on positive realizations in Markov form and propose a linear programming approach that computes them with a minimum dimension. Such minimum dimension of positive Markov realizations is an upper bound of the minimal positive realization dimension. However, we show that these two dimensions are equal for certain systems.

Keywords: Linear systems, Identification, Modeling
Abstract: We consider the problem of identifying partially observed, marginally stable, stochastic linear time-invariant (LTI) systems from a single input-output trajectory. Classical identification methods typically assume system stability or rely on multiple independent trajectories, which limits their applicability to real-world scenarios where only a single rollout is available. In this paper, we propose a simple and efficient online algorithm for system identification based on a novel autoregressive with exogenous input (ARX) formulation derived using the Cayley-Hamilton theorem. This transformation allows us to express the outputs as a linear function of a fixed number of past inputs and outputs, leading to a bounded-noise regression problem regardless of the trajectory length. Our method enables recursive parameter identification using instrumental variable approach and avoids the unbounded noise growth common in existing Markov-parameter-based methods. We provide a theoretical analysis of the model structure and validate its effectiveness through numerical simulations. Compared to recent methods such as prefiltered least squares and multi-rollout ordinary least squares, our approach achieves significantly lower estimation error, particularly in the marginally stable regimes.

Keywords: Linear systems, Robust control, Uncertain systems
Abstract: A problem of modal state-feedback controller synthesis for a linear system with interval parameters is considered. It is proposed to use the concept of relative intervality of the state matrix norm to design the control law. The obtained control algorithm allows to ensure desired quality indices of the closed-loop system in transient and steady state performance, and also its phase stability margin.

Keywords: Observers for Linear systems, Uncertain systems, Linear systems
Abstract: This paper presents novel polytopic and interval observer designs for uncertain linear continuous-time (CT) and discrete-time (DT) systems subjected to bounded disturbances and noise. Our approach guarantees enclosure of the true state and input-to-state stability (ISS) of the polytopic and interval set estimates. Notably, our approach applies to all detectable systems that are stabilized by any optimal observer design, utilizing a potentially non-square (lifted) time-invariant coordinate transformation based on polyhedral Lyapunov functions and mixed-monotone embedding systems that do not impose any positivity constraints, enabling feasible and optimal observer designs, even in cases where previous methods fail. The effectiveness of our approach is demonstrated through several examples of uncertain linear CT and DT systems.

Keywords: Observers for Linear systems, Hybrid systems, Switched systems
Abstract: A new switched-gain observer for linear systems subject to bounded disturbances is proposed. Specifically, we formulate the problem of constructing bimodal switched-gain observers within a hybrid systems framework, and establish novel conditions based on max/min Lyapunov functions to ensure positive invariance of the estimation error. The invariant sets are described by sublevel sets of such Lyapunov functions, which can be found by solving conditions given in terms of bilinear matrix inequalities. The observer design stems from solving such conditions by using grid search methods based on linear matrix inequalities. Numerical results are reported to show improvements with respect to previous design methods.

Keywords: Markov processes, Stability of linear systems
Abstract: This extended abstract presents the findings of our paper [1], which proposes a polyhedral approximation approach for improving the use of partially known transition and sojourn information in the stability analysis and control of discrete-time semi-Markov jump linear systems. By integrating both known and approximated probabilistic data, the proposed method reduces conservatism in the analysis, as demonstrated through case studies [1].

[1] Z. Ning, P. Colaneri, and X. Yin, “Stability analysis and stabilization of semi-Markov jump linear systems with improved efficiency of probabilistic information utilization,” IEEE Trans. Autom. Control, vol. 70, no. 3, pp. 1835–1850, 2025.

Keywords: Hybrid systems, Linear systems, Uncertain systems
Abstract: We consider linear systems with additive exogenous signals, whose range is state-dependent and is constrained in a polytope in the state-disturbance space. We observe that these systems are equivalent (i) to a linear inclusion defined as projection of a polytopic set on the state space, and (ii) to piecewise polytopic affine dynamics, which is convex on the support of the disturbance set. We use these descriptions to characterise the reachable sets and consequently characterise the minimal Robust Positively Invariant (mRPI) set. Our results can be used in a variety of applications.

Keywords: Formal Verification/Synthesis, Linear systems, Numerical algorithms
Abstract: We present a method to approximate output reachable sets at time points, for continuous-time LTI systems, where the initial state lies in a compact convex uncertainty set and the input signal takes values in a zonotopic uncertainty set at each point in time. Our focus is on over-approximations. We present an interval over-approximation margin and derive bounds on the approximation error that improve upon our previous work, in part through the use of a posteriori information. The error exhibits second-order convergence with respect to a discretization parameter. Our method significantly outperforms existing approaches across a wide range of approximation accuracies, as demonstrated on several examples.

Keywords: Optimal control, Predictive control for nonlinear systems, Optimization algorithms
Abstract: Singular arcs emerge in the solutions of Optimal Control Problems (OCPs) when the optimal inputs on some finite time intervals cannot be directly obtained via the optimality conditions. Solving OCPs with singular arcs often requires tailored treatments, suitable for offline trajectory optimization. This approach can become increasingly impractical for online closed-loop implementations, especially for large-scale engineering problems. Recent development of Integrated Residual Methods (IRMs) have indicated their suitability for handling singular arcs; the convergence of error measures in IRM automatically suppresses singular arc-induced fluctuations and leads to non-fluctuating solutions more suitable for practical problems. Through several examples, we demonstrate the advantages of solving OCPs with singular arcs using {IRM} under an economic model predictive control framework. In particular, the following observations are made: i) IRM does not require special treatment for singular arcs, ii) it solves the OCPs reliably with singular arc fluctuation suppressed, and iii) the closed-loop results closely match the analytic optimal solutions.

Keywords: Optimal control, Nonlinear systems, Control applications
Abstract: Hamilton-Jacobi Reachability (HJR) analysis has been successfully used in many robotics and control tasks, and is especially effective in computing reach-avoid sets and control laws that enable an agent to reach a goal while satisfying state constraints. However, the original HJR formulation provides no guarantees of safety after a) the prescribed time horizon, or b) goal satisfaction. The reach-avoid-stabilize (RAS) problem has therefore gained a lot of focus: find the set of initial states (the RAS set), such that the trajectory can reach the target, and stabilize to some point of interest (POI) while avoiding obstacles. Solving RAS problems using HJR usually requires defining a new value function, whose zero sub-level set is the RAS set. The existing methods do not consider the problem when there are a series of targets to reach and/or obstacles to avoid. We propose a method that uses the idea of admissible control sets; we guarantee that the system will reach each target while avoiding obstacles as prescribed by the given time series. Moreover, we guarantee that the trajectory ultimately stabilizes to the POI. The proposed method provides an under-approximation of the RAS set, guaranteeing safety. Numerical examples are provided to validate the theory.

Keywords: Optimal control, Stability of nonlinear systems, LMIs
Abstract: Analogous to H-infinity-methods for LTI systems, L2-gain is an important input-output characterization of robustness for nonlinear systems. The HJI can be used to establish L2-gain if an appropriate storage function can be identified. Continuous piecewise affine storage functions for small-signal L2-stability analysis of nonlinear systems have previously been applied to open-loop analysis. Here, they are used to develop a suboptimal controller synthesis method for nonlinear systems that minimizes the local, closed-loop small-signal L2-gain. The method selects a piecewise affine state feedback controller using convex optimization.

Keywords: Optimal control, Neural networks, Aerospace
Abstract: This paper proposes a first-order optimization framework for nonlinear optimal control problems, efficiently handling complex dynamics via projection onto a lifted, approximately linear constraint manifold constructed using a physics-informed deep Koopman operator. By circumventing repeated convex programming and avoiding penalty-based refinements, the algorithm mitigates sensitivity to hyperparameters and reduces reliance on domain-specific knowledge and manual modeling. A physics-informed loss function preserves physical consistency when mapping back to the original space, enabling fast convergence to near-optimal solutions. Experiments demonstrate improved computational efficiency and stability over established sequential programming approaches.

Keywords: Optimal control, Neural networks, Algebraic/geometric methods
Abstract: In this work, we propose a novel approach to periodic orbit stabilization using the periodic Linear Quadratic Regulator (LQR) framework. While conventional methods rely on transverse coordinates for control design and controller implementation, our approach transforms the optimal feedback back to the original coordinates, enabling seamless application. By leveraging the symplectic geometric structure of the control problem, we approximate the value function, which defines the Lagrangian submanifold representing the optimal feedback in a coordinate independent way, using a neural network. This eliminates the need for explicit online transverse coordinate computation. The method is demonstrated on two nonlinear systems in two and five dimensions.

Keywords: Optimal control, Nonlinear systems, Linear systems
Abstract: The infinite-horizon optimal control problem is studied in the linear setting with the objective of revisiting the role of the underlying Algebraic Riccati Equation. It is shown that this may be interpreted in terms of a triangularizing change of coordinates for the Hamiltonian dynamics associated to the optimal control problem. Such a perspective leads to a few implications, including the observation that duality between the Riccati equations arising in various contexts is simply related to a choice of coordinates for the Hamiltonian dynamics. Similar arguments are then extended to the nonlinear setting. It is shown that, by relying on such alternative view point, the computational complexity associated to the solution of nonlinear optimal control problems over an infinite horizon tantamounts to the solution of an Algebraic Riccati Equation, for the linearized problem, and a quasi-linear partial differential equation.

Keywords: Optimal control, Nonlinear systems, Reinforcement learning
Abstract: We introduce magnitude and direction (MAD) policies, a policy parameterization for reinforcement learning (RL) that preserves lp closed-loop stability for nonlinear dynamical systems. Despite their completeness in describing all stabilizing controllers, methods based on nonlinear Youla and system-level synthesis are significantly impacted by the difficulty of parametrizing lp-stable operators. In contrast, MAD policies introduce explicit feedback on state-dependent features – a key element behind the success of reinforcement learning pipelines – without jeopardizing closed-loop stability. This is achieved by letting the magnitude of the control input be described by a disturbance-feedback lp-stable operator, while selecting its direction based on state-dependent features through a universal function approximator. We further characterize the robust stability properties of MAD policies under model mismatch. Unlike existing disturbance-feedback policy parametrizations, MAD policies introduce state-feedback components compatible with model-free RL pipelines, ensuring closed-loop stability with no model information beyond assuming open-loop stability. Numerical experiments show that MAD policies trained with deep deterministic policy gradient (DDPG) methods generalize to unseen scenarios – matching the performance of standard neural network policies while guaranteeing closed-loop stability by design.

Keywords: Aerospace
Abstract: Ensuring a safe and fuel-efficient precision soft landing on planetary surfaces containing hazardous terrain is a critical challenge in space exploration missions. Traditional fixed-final-time guidance laws either prolong the descent unnecessarily or require aggressive thrusting, leading to excessive fuel consumption. To this end, this paper presents a two-stage strategy for the development of guidance commands for terrain-avoided precision soft landing while also satisfying the thrust constraints. First, hazardous regions are modeled using simple piecewise linear barrier functions covering the terrain. Then, a closed-form sub-optimal guidance law is derived under a fixed-final-time set-up using optimal control principles, explicitly guaranteeing terrain avoidance via an exponential penalty function based on distance to barriers. This guidance structure is next embedded into an outer-loop free-final-time optimization framework with a performance index of fuel consumption to derive a free-final-time sub-optimal guidance. The final time for near-fuel-optimal precision soft landing is obtained through a fast derivative-free one-dimensional optimization that minimizes fuel usage. Extensive simulation studies under thrust constraints and uncertainties are performed to validate the effectiveness of the developed guidance law in achieving precision soft landing while also successfully avoiding hazardous terrain and maintaining fuel efficiency.

Keywords: Behavioural systems, Nonlinear systems, Modeling
Abstract: Negative conductance elements are key in shaping the input-output behavior at the terminals of a network through localized positive feedback amplification. The balance of positive and negative differential conductances creates singularities at which rich, intrinsically nonlinear, and ultrasensitive terminal behaviors emerge. Motivated by neuromorphic engineering applications, in this note we extend a recently introduced nonlinear network graphical modeling framework to include negative conductance elements. We use this extended framework to define the class of singular networks and to characterize their ultrasensitive input-output behaviors at given terminals. Our results are grounded in the Lyapunov-Schmidt reduction method, which is shown to fully characterize the singularities and bifurcations of the input-output behavior at the network terminals, including when the underlying input-output relation is not explicitly computable through other reduction methods.

Keywords: Modeling, Uncertain systems, Optimization
Abstract: Neuromorphic control is receiving growing attention due to advantages it brings over more classical control approaches, including: sparse and on-demand sensing, information transmission, and actuation; energy-efficient designs and realizations in neuromorphic hardware; event-based signal processing and control signal computation. In this note, we suggest a possible path toward formalizing neuromorphic control systems. We apply the proposed framework to a rhythmic control case study and apply mature control theoretical approaches like describing function analysis, fast-slow analysis, discrete and hybrid systems, and robust optimization.

Keywords: Large-scale systems, Modeling, Biologically-inspired methods
Abstract: This paper proposes a variable metric splitting algorithm to solve the electrical behavior of neuromorphic circuits made of capacitors, memristive elements, and batteries. The gradient property of the memristive elements is exploited to split the current-to-voltage operator as the sum of a derivative operator, a Riemannian gradient operator, and a nonlinear residual operator that is linearized at each step of the algorithm. The diagonal structure of the three operators makes the variable metric forward-backward splitting algorithm scalable and amenable to the simulation of large-scale neuromorphic circuits.

Keywords: Biological systems
Abstract: A quantitative understanding of interneuronal communication is imperative for elucidating the information-processing mechanisms in the brain. Action potential (AP)-triggered transmitter release is a hallmark of interneuronal communication and is inherently stochastic. This process is orchestrated by transmitter-filled synaptic vesicles (SVs) docking at sites in the axon terminal, and probabilistically fusing to release the transmitter upon AP arrival, impacting the activity of the postsynaptic neuron. Expanding previous stochastic models, we consider feedback regulation, where the released neurotransmitters affect the rate of SV replenishment at docking sites or the probability of SV fusion. While in many regimes negative feedback provides effective buffering of stochastic fluctuations, counterintuitively, our analysis reveals that for certain physiological parameter spaces, positive feedback loops can reduce noise levels in both the number of docked SVs and neurotransmitters in the cleft. We further extend these presynaptic feedback models to investigate stochasticity in postsynaptic AP generation.

Keywords: Biological systems, Stability of nonlinear systems, Optimal control
Abstract: A defining property of excitable systems is the existence of a threshold, that is, a sharp distinction between subthreshold and suprathreshold trajectories. Quantifying this distinction calls for a mathematical definition of threshold, which has remained an elusive question in the literature. In this paper, we introduce a novel, energy-based threshold definition for excitable circuits. The definition is grounded in dissipativity theory and uses the classical concept of required supply. We illustrate and validate the proposed definition through analytical and numerical studies of three examples: RC circuits, the FitzHugh–Nagumo circuit, and the canonical conductance-based model of excitability, derived by Hodgkin and Huxley.

Keywords: Network analysis and control, Nonlinear systems, Information technology systems
Abstract: The slowing of Moore's law and the increasing energy demands of machine learning present critical challenges for both the hardware and machine learning communities, and drive the development of novel computing paradigms. Of particular interest is the challenge of incorporating memory efficiently into the learning process. Inspired by how human brains store and retrieve information, associative memory mechanisms provide a class of computational methods that can store and retrieve patterns in a robust, energy-efficient manner. Existing associative memory architectures, such as the celebrated Hopfield model and oscillatory associative memory networks, store patterns as stable equilibria of network dynamics. However, their capacity (i.e., the number of patterns that a network can memorize normalized by their number of nodes) has been shown to decrease with the size of the network, making them impractical for large-scale, real-world applications. In this paper, we propose a novel associative memory architecture based on Kuramoto oscillators. We show that the capacity of our associative memory network increases exponentially with network size, and features no spurious memories. In addition, we present algorithms and numerical experiments to support these theoretical findings, providing guidelines for the hardware implementation of the proposed associative memory networks.

Keywords: Nonlinear systems, Biologically-inspired methods, Stability of nonlinear systems
Abstract: Spiking Nonlinear Opinion Dynamics (S-NOD) is an excitable decision-making model inspired by the spiking dynamics of neurons. S-NOD enables the design of agile decision-making that can rapidly switch between decision options in response to a changing environment. In S-NOD, decisions are represented by discrete opinion spikes that evolve in continuous time. Here, we extend previous analysis of S-NOD and explore its potential as a nonlinear controller with a tunable balance between robustness and responsiveness to input. We identify and provide necessary conditions for the bifurcation that determines the onset of periodic opinion spiking. We leverage this analysis to characterize the tunability of the input-output threshold for opinion spiking as a function of the model basal sensitivity and the tunable dependence of opinion spiking frequency on input magnitude above the threshold. We conclude with a discussion of S-NOD as a new neuromorphic control block and its extension to distributed spiking controllers.

Keywords: Network analysis and control, Nonlinear systems, Optimization
Abstract: Oscillator Ising machines (OIMs) are networks of coupled oscillators that seek the minimum energy state of an Ising model. Since many NP-hard problems are equivalent to the minimization of an Ising Hamiltonian, OIMs have emerged as a promising computing paradigm for solving complex optimization problems that are intractable on existing digital computers. However, their performance is sensitive to the choice of tunable parameters, and convergence guarantees are mostly lacking. Here, we show that lower energy states are more likely to be stable, and that convergence to the global minimizer is often improved by introducing random heterogeneities in the regularization parameters. Our analysis relates the stability properties of Ising configurations to the spectral properties of a signed graph Laplacian. By examining the spectra of random ensembles of these graphs, we show that the probability of an equilibrium being asymptotically stable depends inversely on the value of the Ising Hamiltonian, biasing the system toward low-energy states. Our numerical results confirm our findings and demonstrate that heterogeneously designed OIMs efficiently converge to globally optimal solutions with high probability.

Keywords: Predictive control for nonlinear systems, Optimal control, Optimization
Abstract: Model predictive path integral (MPPI) control has recently received a lot of attention, especially in the robotics and reinforcement learning communities. This letter aims to make the MPPI control framework more accessible to the optimal control community. We present three classes of optimal control problems and their solutions by MPPI. Further, we investigate the suboptimality of MPPI to general deterministic nonlinear discrete-time systems. Here, suboptimality is defined as the deviation between the control provided by MPPI and the optimal solution to the deterministic optimal control problem. Our findings are that in a smooth and unconstrained setting, the growth of suboptimality in the control input trajectory is second-order with the scaling of uncertainty. The results indicate that the suboptimality of the MPPI solution can be modulated by appropriately tuning the hyperparameters. We illustrate our findings using numerical examples.

Keywords: Optimal control, Constrained control, Optimization
Abstract: Inverse optimal control (IOC) is a promising paradigm for learning and mimicking optimal control strategies from capable demonstrators, or gaining a deeper understanding of their intentions, by estimating an unknown objective function from one or more corresponding optimal control sequences. When computing estimates from demonstrations in environments with safety-preserving inequality constraints, acknowledging their presence in the chosen IOC method is crucial given their strong influence on the final control strategy. However, solution strategies capable of considering inequality constraints, such as the inverse Karush-Kuhn-Tucker approach, rely on their correct activation and fulfillment; a restrictive assumption when dealing with noisy demonstrations. To overcome this problem, we leverage the concept of exact penalty functions for IOC and show preservation of estimation accuracy. Considering noisy demonstrations, we then illustrate how the usage of penalty functions reduces the number of unknown variables and how their approximations enhance the estimation method’s capacity to account for wrong constraint activations within a polytopic-constrained environment. The proposed method is evaluated for three systems in simulation, outperforming traditional relaxation approaches for noisy demonstrations.

Keywords: Iterative learning control, Data driven control, Adaptive control
Abstract: The dual control problem, first introduced by Feldbaum in the 1960s, is recognized as encapsulating the ``exploration versus exploitation'' dilemma, central to online learning and control. Numerous heuristic-based exploration methods have been developed to facilitate active learning. However, the theoretically optimal solution provided by dynamic programming (DP) remains computationally intractable for most problems due to the curse of dimensionality. In this paper, we revisit the DP framework within the context of regret minimization for a simple real-time optimization problem, aiming to identify valuable insights and uncover new avenues for simplified DP-based exploration strategies. By deriving the two-horizon DP solution in our simple setting, we observe that the optimal input is obtained by solving a closed-form optimization problem composed of two distinct components representing exploration and exploitation separately, clearly highlighting their inherent trade-off. For longer horizons, receding and cyclic horizon control based on the iterative application of the two-horizon DP provide possible approximations, reducing computational complexity while yielding useful suboptimal control policies. A key advantage of the DP-based exploration method is its ability to automatically adjust the exploration based on the current exploitation and system uncertainty. The proposed method is studied numerically through comparative evaluations against classical heuristic exploration methods from the literature.

Keywords: Optimal control, Data driven control, Optimization algorithms
Abstract: In this paper, we propose EXPRONTO, a data-driven approach for nonlinear optimal control problems with unknown dynamics. Our method combines the numerical stability benefits of feedback-based optimal control methods with the computational efficiency and minimal information requirements of extremum-seeking algorithms. More in detail, in our approach, the system is run in closed loop, thanks to an available feedback policy, to collect values of the cost function along a perturbed trajectory estimate. The gathered cost values are then used to update the trajectory estimate by relying on a mechanism based on extremum seeking. We theoretically guarantee local convergence of EXPRONTO in an arbitrarily small neighborhood of an isolated optimal trajectory. Specifically, by using system theory tools based on averaging theory, combined with ideas from nonlinear optimal control, we show local practical exponential stability properties for the algorithm evolution. We numerically test the effectiveness of our method.

Keywords: Predictive control for linear systems
Abstract: A novel Model Predictive Control (MPC) framework called disturbance-learning MPC (DL-MPC) for constrained LTI systems subject to bounded disturbances is proposed. The primary objective is to improve the disturbance rejection performance of the tube-based MPC (tube-MPC) law, especially focusing on periodic disturbance signals. Based on convex optimization, the method uses real-time measurements to learn a model of the disturbance, to predict its future behavior. By including this model in the MPC, the latter can proactively counteract the disturbance, significantly improving closed-loop performance. The presented technique includes the disturbance model while preserving robust recursive feasibility and constraint satisfaction. The effectiveness of DL-MPC is demonstrated through simulation of a multivariable nonlinear system, a Continuous-flow Stirred Tank Reactor, subject to periodic disturbances. The results clearly show enhanced tracking accuracy compared to nominal MPC and tube-MPC methods.

Keywords: Data driven control, Predictive control for nonlinear systems
Abstract: Data-enabled Predictive Control (DeePC) has recently gained the spotlight as an easy-to-use control technique that allows for constraint handling while relying on raw data only. Initially proposed for linear time-invariant systems, several DeePC extensions are now available to cope with nonlinear systems. Nonetheless, these solutions mainly focus on ensuring the controller's effectiveness, overlooking the explainability of the final result. In this paper, we focus on analyzing the explainability of the outcome for the earliest and simplest DeePC approach, which utilizes Lasso regularization to cope with nonlinearities in the controlled system. Our theoretical analysis reveals that the decisions made by DeePC with Lasso regularization are unexplainable, as control actions are determined by data incoherent with the system's local behavior. This result is true even when the available input/output samples are grouped according to the different operating conditions explored during data collection. Our numerical study confirms these findings, highlighting the benefits of data grouping in terms of performance while showing that explainability remains a challenge in control design via DeePC.

Keywords: Data driven control, Predictive control for nonlinear systems, Robust control
Abstract: We propose a data-driven min-max model predictive control (MPC) scheme to control unknown discrete-time bilinear systems. Based on a sequence of noisy input-state data, we state a set-membership representation for the unknown system dynamics. Then, we derive a sum-of-squares (SOS) program that minimizes an upper bound on the worst-case cost over all bilinear systems consistent with the data. As a crucial technical ingredient, the SOS program involves a rational controller parameterization to improve feasibility and tractability. We prove that the resulting data-driven MPC scheme ensures closed-loop stability and constraint satisfaction for the unknown bilinear system. We demonstrate the practicality of the proposed scheme in a numerical example.

Keywords: Reinforcement learning, Predictive control for nonlinear systems, Uncertain systems
Abstract: The reinforcement learning (RL) and model predictive control (MPC) communities have developed vast ecosystems of theoretical approaches and computational tools for solving optimal control problems. Given their conceptual similarities but differing strengths, there has been increasing interest in synergizing RL and MPC. However, existing approaches tend to be limited for various reasons, including computational cost of MPC in an RL algorithm and software hurdles towards seamless integration of MPC and RL tools. These challenges often result in the use of ``simple'' MPC schemes or RL algorithms, neglecting the state-of-the-art in both areas. This paper presents MPCritic, a machine learning-friendly architecture that interfaces seamlessly with MPC tools. MPCritic utilizes the loss landscape defined by a parameterized MPC problem, focusing on ``soft'' optimization over batched training steps; thereby updating the MPC parameters while avoiding costly minimization and parametric sensitivities. Since the MPC structure is preserved during training, an MPC agent can be readily used for online deployment, where robust constraint satisfaction is paramount. We demonstrate the versatility of MPCritic, in terms of MPC architectures and RL algorithms that it can accommodate, on classic control benchmarks.

Keywords: Distributed parameter systems, Uncertain systems, Biomedical
Abstract: The process of heat transfer in biological tissues is described by a parabolic partial differential equation, known as the Pennes’ bio-heat equation, which has the form a heat equation with an affine reaction term. Handling adequately such equation is of paramount importance for the effectiveness of minimally invasive thermal therapies like, e.g., superficial hyperthermia. The control and estimation for the bio-heat equation are practically challenging due to the presence of uncertain diffusion and reaction coefficients, and to the fact that, typically, one can rely on pointwise measurements only. In this paper we address the problem by proposing an adaptive framework based on multiple-models building on a family of PDE observers together with a set of dynamic weights. The proposed techniques are general enough to be extended to other parabolic PDEs with unknown coefficients, thus going beyond the motivating setup of the bio-heat equation. Simulation examples illustrate and support the theoretical findings.

Keywords: Distributed parameter systems, Flexible structures, Nonlinear systems
Abstract: This paper investigates the preservation of uniform stability for a spatial semi-discrete finite difference scheme applied to a one-dimensional wave equation with nonlinear internal damping. The discretization process employs the order reduction method. Unlike previous studies, this systemfocuses on a nonlinear system, with absolute stability being a special case. Due to the nonlinearity, the system may not always exhibit exponential stability, but it can be polynomially stable in some cases. After semi-discretization, the system transforms into an infinitely large number of lumped parameter nonlinear systems. Achieving uniform polynomial stability, is a challenging endeavor. We demonstrate that when the nonlinear function satisfies certain conditions at the origin and infinity, the system possesses polynomial stability. These properties are preserved during the semi-discretization process. The mathematical proofs are similar to those for the continuous counterpart in many ways.

Keywords: Distributed parameter systems, Backstepping, Differential-algebraic systems
Abstract: This paper considers the backstepping control for a class of general linear infinite-dimensional descriptor systems. By assuming constant matrices in the system description, a decoupling of the descriptor system is possible using the Weierstraß normal form for a matrix pencil with index 1. With this, well-posedness and consistent initial conditions are verified. The resulting decoupled system is a fully actuated hyperbolic-elliptic PDE, where the elliptic PDE can be eliminated by state feedback control. This allows to apply backstepping for the stabilization of a general heterodirectional hyperbolic system with several zero speed states. For the resulting closed-loop system exponential stability is shown. The results of the paper are demonstrated for an unstable infinite-dimensional descriptor system with 6 distributed descriptor variables.

Keywords: Distributed parameter systems, Uncertain systems
Abstract: In a series of papers, the authors developed and refined a cascading-type approximate regulation methodology for symptotic tracking. This method is rooted in the well known geometric theory and involves regularizing the regulator equations with an iterative scheme that generates a sequence of increasingly accurate control laws. One of the main advantages of this method is that no exo-system is required, allowing very general reference and disturbance signals.

Although this earlier approach provided precise tracking and disturbance rejection for complex control systems, similar to the classical regulator method, it was not equipped to handle systems with parameter uncertainties. In this paper, we present a modification of that basic method that ensures accurate tracking and is applicable to a wide range of uncertain systems. The main assumptions include the standard stability condition for both the nominal and perturbed plants and the availability of the tracking error for the uncertain system to the controller. Examples illustrate the theoretical results and demonstrate the method’s effectiveness. Although this paper primarily focuses on distributed parameter systems, the results equally apply to lumped parameter systems.

Keywords: Distributed control, Distributed parameter systems, Large-scale systems
Abstract: In this paper, we develop a distributed control framework for a class of spatially invariant systems (SISs) that arise from certain partial differential equations (PDEs). Our focus is on designing optimal H^2 spatially distributed controllers, achieved through a spatially invariant version of the Youla parametrization. This formulation allows us to cast the control design problem within a Hilbert space setting and solve it using tools from optimization theory. The solution relies on expansions in specific bases and the use of orthogonal projectors, with Parseval’s theorem playing a central role. The overall approach is closely related to Wiener–Hopf theory and serves as a complement to existing state-space methods, which typically require solving families of parametrized Riccati equations.

Keywords: Distributed parameter systems, Lyapunov methods, Nonlinear systems
Abstract: We propose a novel framework for stabilization, with an estimate of the region of attraction, of quasilinear parabolic partial differential equations (PDEs) that exhibit finite-time blow-up phenomena when null boundary inputs are imposed. Using Neumann-type boundary controllers, which are cubic polynomials in boundary outputs, we ensure L2 exponential stability of the origin with an estimate of the region of attraction, boundedness and exponential decay towards zero of the state’s max norm, well-posedness, as well as positivity of solutions starting from positive initial conditions. Unlike existing methods, our approach handles nonlinear state-dependent diffusion, convection, and reaction terms. In many cases, our estimate of the size of the region of attraction is shown to expand unboundedly as diffusion increases. Our controllers can be implemented as Neumann, Dirichlet, or mixed-type boundary conditions. Numerical simulations validate the effectiveness of our approach in preventing finite-time blow up.

Keywords: Distributed parameter systems, Observers for Linear systems, Stability of linear systems
Abstract: This paper proposes an output-feedback controller design strategy for a certain class of dynamically coupled systems of linear ordinary differential equations (ODEs) and homodirectional hyperbolic partial differential equations (PDEs), specifically transport equations. Assuming that a combination of lumped and distributed states can be measured, the developed approach permits reconstructing the dynamics of the whole ODE-PDE interconnection. This allows the design of a control law that suppresses the coupling between the ODE and PDE states. In particular, the technique investigated in this paper exploits the stabilizability and detectability of the ODE and PDE subsystems in isolation, and relies on the inversion of the (stabilized) PDE (error) dynamics in the Laplace domain, thus avoiding infinite-dimensional coordinate transformations. The results advocated in this paper are essentially novel in the literature, and complement the existing methods available for hyperbolic ODE-PDEs.

Keywords: Distributed parameter systems, Robust control, LMIs
Abstract: This paper investigates the stability of a coupled system consisting of a finite-dimensional ordinary differential equation (ODE) and a partial differential equation (PDE), with a focus on incorporating boundary condition derivatives into the stability analysis. Building on a combination of projection methods and Integral Quadratic Constraints (IQCs), we develop a novel approach that generates stability conditions through Linear Matrix Inequalities (LMIs). The IQC framework rigorously accounts for the interconnection structure and dissipation mechanisms at the boundaries, providing a more comprehensive analysis of coupled finite and infinite-dimensional systems while explicitly considering boundary condition dynamics and their impact on stability.

Keywords: Data driven control, Robust control, Machine learning
Abstract: Model agnostic controller learning, for instance by direct policy optimization, has been the object of renewed attention lately, since it avoids a computationally expensive system identification step. Indeed, direct policy search has been empirically shown to lead to optimal controllers in a number of cases of practical importance. However, to date, these empirical results have not been backed up with a comprehensive theoretical analysis for general problems. In this paper we use a simple example to show that direct policy optimization is not directly generalizable to other seemingly simple problems. In such cases, direct optimization of a performance index can lead to unstable pole/zero cancellations, resulting in the loss of internal stability and unbounded outputs in response to arbitrarily small perturbations. We conclude the paper by analyzing several alternatives to avoid this phenomenon, suggesting some new directions in direct control policy optimization.

Keywords: Machine learning, Stochastic systems
Abstract: Recent advancements in generative models have made their output often indistinguishable from human generated data. As a result, training large language models (LLMs) exclusively on human generated data is becoming infeasible; not only due to the difficulty of determining the data provenance but also due to the cost of curating the large amounts of data required to meet the demands of ever-larger models. Although several works have empirically demonstrated the dangers of training models on AI-generated data, these studies often overlook a broader phenomenon: LLMs are not merely passive products of internet data but active agents that shape its contents.

In this paper we study the interaction between LLMs and humans when the latter are influenced by LLM-generated data or have immutable opinions. We prove that if a sufficient proportion of content is produced by stubborn humans, the limit set of the opinion dynamics inflates, preventing total model collapse. However, we note that such outcome can also be interpreted as stubborn humans driving the opinion dynamics thereby shaping and controlling online discourse.

Keywords: Extremum seeking, Delay systems, Learning
Abstract: We study prescribed-time extremum seeking (PT-ES) for scalar maps in the presence of time delay. The PT-ES problem has been solved by Yilmaz and Krstic in 2023 using chirpy probing and time-varying singular gains. To alleviate the gain singularity, we present an alternative approach, employing delays with bounded time-periodic gains, for achieving prescribed-time convergence to the extremum. Our results are not extensions or refinements but a new methodological direction- applicable even when the map has no delay. Our main contribution compensates for the map's delay while relying on perturbation-based techniques and a Newton-like (as opposed to gradient-based) strategy. Leveraging averaging theory in infinite dimensions—specifically for Retarded Functional Differential Equations (RFDEs)—we analyze the prescribed-time convergence of a carefully constructed, perturbation-averaged target ES system that incorporates both time-periodic gains and feedback delays. We further extend our method to multi-variable static maps and illustrate our results through numerical simulations.

Keywords: Machine learning, Nonlinear systems
Abstract: The use of synthetic data in the training of generative models is a common approach to address the lack of large amounts of high quality training data. It has been reported in the literature that using synthetic data can lead to model degeneration, i.e., the model stops producing useful outputs. In this paper we propose a very simple strategy to combine synthetic data and human-generated data so as to prevent model degeneration. At the technical level we show that the evolution of a generative model, caused by re-training, can be described by a differential equation and provide conditions on the ratio of synthetic and human-generated data to ensure the existence of an asymptotically stable equilibrium.

Keywords: Optimization algorithms, Machine learning, Neural networks
Abstract: Many theoretical studies on neural networks attribute their excellent empirical performance to the implicit bias or regularization induced by first-order optimization algorithms when training networks under certain initialization assumptions. One example is the incremental learning phenomenon in gradient flow (GF) on an overparamerterized matrix factorization problem with small initialization: GF learns a target matrix by sequentially learning its singular values in decreasing order of magnitude over time. In this paper, we develop a quantitative understanding of this incremental learning behavior for GF on the symmetric matrix factorization problem, using its closed-form solution obtained by solving a Riccati-like matrix differential equation. We show that incremental learning emerges from some time-scale separation among dynamics corresponding to learning different components in the target matrix. By decreasing the initialization scale, these time-scale separations become more prominent, allowing one to find low-rank approximations of the target matrix. Lastly, we discuss the possible avenues for extending this analysis to asymmetric matrix factorization problems.

Keywords: Nonlinear systems, Robust control, Neural networks
Abstract: We study the invertibility of nonlinear dynamical systems from the perspective of contraction and incremental stability analysis and propose a new invertible recurrent neural model: the BiLipREN. In particular, we consider a nonlinear state space model to be robustly invertible if an inverse exists with a state space realisation, and both the forward model and its inverse are contracting, i.e. incrementally exponentially stable, and Lipschitz, i.e. have bounded incremental gain. This property of bi-Lipschitzness implies both robustness in the sense of sensitivity to input perturbations, as well as robust distinguishability of different inputs from their corresponding outputs, i.e. the inverse model robustly reconstructs the input sequence despite small perturbations to the initial conditions and measured output. Building on this foundation, we propose a parameterization of neural dynamic models: bi-Lipschitz recurrent equilibrium networks (biLipREN), which are robustly invertible by construction. Moreover, biLipRENs can be composed with orthogonal linear systems to construct more general bi-Lipschitz dynamic models, e.g., a nonlinear analogue of minimum-phase/all-pass (inner/outer) factorization. We illustrate the utility of our proposed approach with numerical examples.

Keywords: Neural networks, Machine learning, Stability of nonlinear systems
Abstract: We study the local stability of nonlinear systems in the Lur’e form with static nonlinear feedback realized by feedforward neural networks (FFNNs). By leveraging positivity system constraints, we employ a localized variant of the Aizerman conjecture, which provides sufficient conditions for exponential stability of trajectories confined to a compact set. Using this foundation, we develop two distinct methods for estimating the Region of Attraction (ROA): (i) a less conservative Lyapunov-based approach that constructs invariant sublevel sets of a quadratic function satisfying a linear matrix inequality (LMI), and (ii) a novel technique for computing tight local sector bounds for FFNNs via layer-wise propagation of linear relaxations. These bounds are integrated into the localized Aizerman framework to certify local exponential stability. Numerical results demonstrate substantial improvements over existing integral quadratic constraint-based approaches in both ROA size and scalability.

Keywords: Optimization, Nonlinear systems, Reinforcement learning
Abstract: This work explores generalizations of the Polyak-Łojasiewicz inequality (PŁI) and their implications for the convergence behavior of gradient flows in optimization problems. Motivated by the continuous-time linear quadratic regulator (CT-LQR) policy optimization problem – where only a weaker version of the PŁI is characterized in the literature – this work shows that while weaker conditions guarantee global convergence of gradient flows and optimality at the critical points of the cost function, the trajectory “profile” of the solutions may differ considerably depending on which “flavor” of inequality the cost satisfies. After a general theoretical analysis, we focus on fitting the CT-LQR policy optimization problem to the proposed framework, showing that, in fact, it can never satisfy a PŁI in its strongest form. We finish our analysis with a brief discussion on the difference between continuous- and discrete-time LQR policy optimization, proposing some intuition to explain why one satisfy a PŁI while the other does not.

Keywords: Transportation networks, Power systems, Game theory
Abstract: This paper proposes an integrated equilibrium model to characterize the complex interactions between electrified logistics systems and electric power delivery systems. The model consists of two major players: an electrified logistics operator (ELO) and a power system operator (PSO). The ELO aims to maximize its profit by strategically scheduling and routing its electric delivery vehicles (e-trucks) for deliveries and charging, in response to the locational marginal price (LMP) set by the PSO. The routing, delivery, and charging behaviors of e-trucks are modeled by a perturbed utility Markov decision process (PU-MDP) while their collective operations are optimized to achieve the ELO's objective by designing rewards in the PU-MDP. On the other hand, PSO optimizes the energy price by considering both the spatiotemporal e-truck charging demand and the base electricity load. The equilibrium of the integrated system is formulated as a fixed point, proved to exist under mild assumptions, and solved for a case study on the Hawaii network via Anderson's fixed-point acceleration algorithm. Along with these numerical results, this paper provides both theoretical insights and practical guidelines to achieve sustainable and efficient operations in modern electrified logistics and power systems.

Keywords: Transportation networks, Traffic control, Lyapunov methods
Abstract: In this paper, we propose a Cooperative Compliance Control framework for mixed traffic routing, where a Social Planner optimizes vehicle routes for system-wide optimality while a compliance controller incentivizes human drivers to align their behavior with route guidance from the Social Planner through a “refundable toll” scheme. A key challenge arises from the heterogeneous and unknown response models of different human driver types to these tolls, making it difficult to design a proper controller and achieve desired compliance probabilities over the traffic network. To address this challenge, we employ Control Lyapunov Functions to adaptively correct crucial components of our compliance probability model online, construct data-driven feedback controllers, and demonstrate that we can achieve the desired compliance probability for HDVs, thereby contributing to the social optimality of the traffic network.

Keywords: Transportation networks, Optimization
Abstract: This paper presents a dynamic routing guidance system that optimizes route recommendations for individual vehicles in an emerging transportation system while enhancing travelers' trip equity. We develop a framework to quantify trip quality and equity in dynamic travel environments, providing new insights into how routing guidance influences equity in road transportation. Our approach enables real-time routing by incorporating both monitored and anticipated traffic congestion. We provide conditions that ensure perfect trip equity for all travelers in a free-flow network. Simulation studies on 1,000 vehicles traversing an urban road network in Boston demonstrate that our method improves trip equity by approximately 11.4% compared to the shortest-route strategy. In addition, the results reveal that our approach redistributes travel costs across vehicle types through route optimization, contributing to a more equitable transportation system.

Keywords: Traffic control, Transportation networks, Cooperative control
Abstract: This paper proposes a novel control algorithm which guarantees global stability of the Nash equilibrium set in a discrete-time, mixed-autonomy routing game. We frame the network routing process as a population game, where each population corresponds to a unique combination of origin-destination (OD) pair and vehicle type (regular/RV or autonomous/AV). Populations update their strategies based on the payoff discrepancies between routes. The strategy revision process is modeled by impartial pairwise comparison (IPC) evolutionary dynamic models (EDMs) derived from a backward Euler discretization. We establish that the EDM satisfies a discrete notion of delta-dissipativity, and we leverage this property to design the control scheme. Our key result is a dynamic payoff mechanism which governs AV populations, while RV populations update strategies according to the travel time payoff. Critically, our controller exhibits payoff equity, meaning that both RV and AV populations converge to paths of minimum travel time. This avoids the altruistic scenario in which AVs are routed to paths with higher travel time. Our control is amenable to non-monotone payoff functions, capturing the case in which travel time variations due to AV-induced capacity changes depend on the proportion of AVs as well as the vehicle type being followed.

Keywords: Estimation, Traffic control, Emerging control applications
Abstract: This paper proposes a deep learning-based Kazantzis–Kravaris–Luenberger (KKL) observer design to estimate position and speed in mixed-autonomy traffic environments. The approach relies on position measurements of vehicles surrounding the autonomous vehicle (AV), obtained through remote sensing, resulting in a subsequent time delay due to communication latency. The proposed deep learning KKL observer is designed to compensate for this delay and to ensure global asymptotic convergence of the estimation of position and speed by using a chain of sub-observers. We employ an unsupervised learning-based approach to identify the nonlinear injective map involved in the KKL observer design, as well as its left inverse. Based on the obtained mappings, a chain of observers is designed in the latent space, ensuring global asymptotic convergence in both coordinates. The performance of the proposed deep learning-based KKL chain of observer estimation approach is evaluated through numerical simulations and validated using experimental data. Our findings underscore the importance of the KKL-based chain of observers in compensating for output-delayed measurements, thereby establishing a relationship between delay bounds and the number of sub-observers while ensuring stable performance in mixed-autonomy traffic environments.

Keywords: Game theory, Transportation networks, Agents-based systems
Abstract: To steer the behavior of selfish, resource-sharing agents in a socio-technical system towards the direction of higher efficiency, the system designer requires accurate models of both agent behaviors and the underlying system infrastructure. For instance, traffic controllers often use road latency models to design tolls whose deployment can effectively mitigate traffic congestion. However, misspecifications of system parameters may severely restrict a system designer's ability to influence collective behavior toward efficient outcomes. In this work, we study the impact of system misspecifications on toll design for atomic congestion games. We prove that tolls designed under sufficiently minor system misspecifications, when deployed, do not introduce new Nash equilibria in atomic congestion games compared to tolls designed in the noise-free setting, implying a form of local robustness. We then upper bound the degree to which the worst-case equilibrium system performance could decrease when tolls designed under a given level of system misspecification are deployed. We validate our theoretical results via Monte-Carlo simulations on modeled traffic networks as well as realizations of our worst-case guarantees.

Keywords: Game theory, Transportation networks, Traffic control
Abstract: In the context of network routing games, the “revelation principle,” a cornerstone of information design, suggests that messages can take the form of itinerary recommendations and that the probability distribution underlying these recommendations is contingent on the network’s state. This dependency is usually tacitly assumed deterministic. Our study contends that this neglects the possibility that the probability distributions are mere stochastic functions of the state, and illustrates, via a minimal example of an incomplete information nonatomic routing game, how this oversight leads to suboptimal congestion mitigation.

Keywords: Game theory, Cooperative control, Learning
Abstract: Autonomous vehicles envision a future where congestion games are played between cooperative rather than selfish players. We consider N cooperative players engaged in a congestion game on a graph G, where they all share the same source and destination nodes. The goal of the team of players is to minimize the sum of their trip times (costs). This model captures the interaction between a fleet of autonomous vehicles that constitutes all the traffic in a given area. We propose a communication-free distributed algorithm that enables players to learn the action profile (i.e., routing decisions) that minimizes the sum of their trip times. Our algorithm only requires each player to observe its own trip times for each edge it travels (i.e., bandit feedback). The delay functions of the edges, which map the loads to trip times, are unknown to all players and are assumed to be polynomials. We prove an expected regret bound for our algorithm that shows polynomial dependence on N and the size of G. We conduct numerical experiments that demonstrate the effectiveness of our algorithm.

Keywords: Supervisory control, Discrete event systems, Control Systems Privacy
Abstract: We study the control problem of distributed discrete event systems with a privacy aspect. Each component of a system may synchronise with one or more groups of components through different sets of shared events. For each group a component belongs to, its behaviour in terms of its nonshared events (with respect to that group) should remain private. To synthesise decentralised supervisors local to each component, we propose a contract-based negotiation method. A contract describes an agreement among the members of each group. This allows cooperation in disabling shared events, which might not be controllable by all components, in order to guarantee the specifications are met. This work extends our previous results, where only two subsystems with local specifications were considered, to allow more complex architectures and nonlocal specifications. We identify cases where there is no need for coordinators nor the communication of nonshared events, respecting privacy both during the synthesis and the execution of the supervisors, even if for some systems that comes at the cost of maximal permissiveness.

Keywords: Supervisory control, Discrete event systems, Automata
Abstract: This paper addresses a novel optimal supervi- sory control problem for reachability tasks in partially-known discrete-event systems (DES). We consider a setting where the supervisor lacks prior knowledge of feasible events in certain states and must discover this information by visiting them. To assess performance in this context, we introduce regret as a metric that quantifies the difference between the actual cost incurred and the optimal cost achievable with full knowledge. We formalize this problem and propose an efficient algorithm to compute an optimal supervisor that guarantees reachability while minimizing regret. Our results demonstrate that regret serves as a meaningful performance measure for supervisory control in partially-known DES, and our method is both correct and effective in practice.

Keywords: Discrete event systems, Supervisory control, Resilient Control Systems
Abstract: Critical real-world applications strongly rely on Cyber-physical systems (CPS), but their dependence on communication networks introduces significant security risks, as attackers can exploit vulnerabilities to compromise their integrity and availability.This work explores the topic of cybersecurity in the context of CPS modeled as discrete event systems (DES), focusing on recovery strategies following the detection of cyberattacks. Specifically, we address actuator enablement attacks and propose a method that preserves the system's full valid behavior under normal conditions. Upon detecting an attack, our proposed solution aims to guide the system toward a restricted yet robust behavior, ensuring operational continuity and resilience. Additionally, we introduce a property termed AE-robust recoverability, which characterizes the necessary and sufficient conditions for recovering a system from attacks while preventing further vulnerabilities. Finally, we showcase the proposed solution through a case study based on a manufacturing system.

Keywords: Fault diagnosis, Discrete event systems, Petri nets
Abstract: In this paper, a novel approach for detecting and isolating faults in discrete manufacturing systems using two models is proposed. By considering the model of the control algorithm and the model of the fault-free behavior of the plant, sensor faults and actuator faults can be detected and isolated. The controller is modeled by a signal interpreted Petri net (SIPN) and the plant is modeled by a time SIPN. Based on the observed sensor signals, the controller model can be used to calculate the control inputs of the plant. The plant model is then used to determine expected sensor outputs and their time of occurrence. By comparing the expected sensor signals to the observed sensor signals while considering the elapsed time since the last event observations, faults can be detected and isolated. The plant model is also used to determine actuator signals justifying a change in the sensor outputs, which can be compared to the calculated actuator signals to isolate faulty actuators. Compared with the existing fault diagnosis approaches in the literature, the use of complementary models can increase the fault detection rate. Moreover, in terms of fault isolation, the proposed approach does not need the model of the plant under different fault scenarios, which significantly reduces the modeling efforts. The main results are illustrated with a heated mixing tank example.

Keywords: Discrete event systems, Automata, Supervisory control
Abstract: With the advancement of communication and network technologies, multiple intruders can collaborate to infer asystem’s confidential information. Without formal models of the system, synthesizing a supervisor to enforce opacity becomes particularly challenging. To address the problem of ensuring joint current-state opacity under cooperative attacks by multiple intruders, this paper proposes a deep reinforcement learning-based algorithm for synthesizing supervisory control policies. A deep Q-network is trained to control the system. Experimental evaluations conducted on a flexible manufacturing system and an automated guided vehicle system demonstrate the effectiveness of the proposed approach.

Keywords: Discrete event systems, Petri nets
Abstract: This paper deals with the synthesis of controllers for (max,+) linear systems. The objective of the controllers is to guarantee that the state trajectories are maintained within a sub-semi-module. Among the possible controllers, the greatest is calculated in order to achieve an output as close as possible to that of the unconstrained system.

Keywords: Discrete event systems, Supervisory control, Automata
Abstract: In active cyberattacks, an intruder can alter the nominal system behavior to cause damage to devices and/or users. Although many works in the literature propose techniques to mitigate active attacks from the perspective of the discrete event supervisory control system, there is limited discussion on the recovery of the system's nominal behavior after an attack is detected and isolated by a cyberdefense mechanism. In this letter, we formulate a recovery structure and define a recoverability property, based on which we propose a method for the synthesis of a nonblocking supervisory control that drives the discrete event system from a state estimate after an extinguished attack back to its nominal closed-loop behavior in a finite number of observations while avoiding unsafe states.

Keywords: Fault diagnosis, Discrete event systems, Automata
Abstract: Diagnosability verification is crucial for ensuring faults can be reliably detected and for enabling effective diagnostic systems. While polynomial-time methods exist for untimed Discrete Event Systems (DES), verifying diagnosability in timed DES remains computationally challenging. In this paper we propose a novel algorithm for time-interval diagnosability verification based on the search for strongly connected components, which is proven to be more efficient than the search for cycles. The algorithm constructs a verifier automaton to compute the intersection between non-faulty and faulty behaviors. Additionally, we provide a detailed computational complexity analysis and demonstrate the results through an illustrative example.