Keywords: Biological systems, Biologically-inspired methods, Neural dynamics
Abstract: The intersection of control engineering and neuroscience is rich and growing. The brain, fundamentally, is a dynamical system, and from this perspective, the formalisms of control theory provide vehicles for the processes of analysis and design. Design is where much effort at the control-neuroscience intersection has historically been directed, in applicative contexts such as clinical brain stimulation and related neurotechnology development. Analysis, on the other hand, represents an area of substantial recent momentum, as neuroscientists seek new and improved understanding of the complexities of brain function. In this talk, I will discuss our work bridging dynamics, control, and brain and cognitive science. I will highlight the importance of analysis-design synergy in this context, and the question of defining control objectives for cognitive enhancement. Engaging this question requires us to convert abstract cognitive endpoints (i.e., our ability to perceive, think and reason) into mathematically sound descriptions of neural dynamics. I will describe our efforts in this area, through the development of new methods for whole-brain modeling and system identification, enabling us to formally analyze brain states, dynamics, and their person-to-person variation. I will discuss the insights that this analysis provides regarding the intrinsic mechanisms by which the brain enables key cognitive functions, such as memory and attention, and in turn, how they impact our pursuit of control design for exogenous neuromodulation.

Keywords: Safety-critical control, Quantized systems, Learning-based Control
Abstract: Safety-critical autonomous systems must satisfy hard state constraints under tight computational and sensing budgets, yet learning-based controllers are often far more complex than safe operation requires. To formalize this gap, we study how many distinct control signals are needed to render a compact set forward invariant under sampled-data control, connecting the question to the information-theoretic notion of invariance entropy. We propose a vector-quantized autoencoder that jointly learns a state-space partition and a finite control codebook, and develop an iterative forward certification algorithm that uses Lipschitz-based reachable-set enclosures and sum-of-squares programming. On a 12-dimensional nonlinear quadrotor model, the learned controller achieves a 157times reduction in codebook size over a uniform grid baseline while preserving invariance, and we empirically characterize the minimum sensing resolution compatible with safe operation.

Keywords: Iterative learning control, Data driven control, Adaptive control
Abstract: The study proposes iterative Learning Control (ILC) for single-input, single-output, discrete-time, time invariant linear systems, where system outputs are expressed by the convolution of Markov parameters and historical input data. In the proposed method, the input signals and system parameters are updated in a pointwise manner after every trial. Then, normalization signals are introduced to ensure the boundedness of the magnitude of both the input signals and the estimated parameters. The main feature of the proposed method is the pointwise evaluation of the convergence rate for the input signals to the desired ones. The theoretical analysis is conducted under the assumption that the sign of the initial first Markov parameter estimate is selected to be the same as that of the true value. It should be noted that the convergence of tracking errors could be achieved even when the estimated parameters do not converge to the true values. The feature contrasts with the existing model-based ILC, where the control performance is significantly dependent on the precision of the estimated parameters. Finally, a numerical example is shown that supports the analysis of the proposed method.

Keywords: Optimization, Iterative learning control, Data driven control
Abstract: The performance of iterative learning control (ILC) with basis functions strongly depends on the selection of the feedforward model structure. In particular, the choice of model order introduces a trade-off between tracking accuracy and numerical conditioning. Underparameterized models lack expressiveness, while overparameterized models lead to ill-conditioning and unstable learning. This paper proposes a data-driven approach for automatic model order selection in basis function ILC using Bayesian optimization (BO). The model order is treated as a discrete design variable, and a complexity-aware cost function is introduced to balance tracking performance and numerical robustness. The proposed method, referred to as complexity-aware BO (CABO), integrates ILC for parameter optimization and BO for structure selection, enabling efficient exploration of the discrete model space. Simulation results on a two-mass system demonstrate that CABO successfully identifies an appropriate model structure, improves tracking performance, and remains stable at noise levels where overparameterized models diverge. The results highlight the effectiveness of combining data-driven learning with probabilistic optimization for structure selection in ILC.

Keywords: Data driven control, Output regulation, LMIs
Abstract: This paper proposes a data-driven technique for the design of controllers that solve the output regulation problem for discrete-time, linear time-invariant systems using only a single input–output trajectory. The proposed approach first processes the available measurements through an internal model of the exosystem combined with filtering tools inspired by adaptive control. The effects of the exosystem and the unreachable part of the interconnection are then filtered using a Toeplitz matrix, allowing one to reconstruct the portion of the state that is reachable from the control input. Finally, a controller achieving output regulation is synthesized by solving a linear matrix inequality constructed from the data, yielding the feedback gains without requiring an explicit system model.

Keywords: Data driven control, Constrained control, Linear systems
Abstract: This paper presents a data-driven framework for enforcing constraints on discrete-time linear systems with unknown dynamics, operating under real-time (potentially unsafe) controllers. {Utilizing measured input-output data from the closed-loop system, we first construct a data-driven maximal admissible set (MAS). We introduce a novel reparameterization of the MAS and demonstrate that the projection of this new set onto the recent plant input-output trajectories results in a safe control-invariant set for the underlying open-loop plant.} This set is then used to construct a discrete-time data-driven control barrier function (D3CBF) directly from data, without an explicit model. The resulting D3CBF is embedded within a real-time optimization-based filter that minimally modifies the output of the nominal controller to enforce safety constraints. Numerical simulations demonstrate the effectiveness of the approach.

Keywords: Optimal control, Data driven control
Abstract: Linear programming (LP) formulations offer a conceptually elegant approach to infinite-horizon, model-free nonlinear optimal control in continuous spaces. However, in addition to the curse of dimensionality, their practical use is limited by the difficulty of consistently obtaining bounded solutions. In this work, we use moment-matching techniques to derive sufficient boundedness conditions in terms of the available dataset and the cost vector of the LP. Moreover, we discuss practical design methods for nonlinear systems and polynomial features.

Keywords: Autonomous robots, Learning-based Control, Optimal control
Abstract: Safe navigation of Unmanned Aerial Vehicles (UAVs) in cluttered environments remains a challenging problem in robotics. While Model Predictive Contouring Control (MPCC) offers high-performance trajectory tracking, it often lacks rigorous safety assurances in the presence of complex obstacle geometries. Conversely, Control Barrier Functions (CBFs) can provide these formal guarantees but are restricted to simple dynamic systems. To address these challenges, we propose a High-Order Control Barrier Function (HOCBF) enabled MPCC framework that enforces safety constraints derived from a receding-horizon, swept elliptical safety corridor. To ensure feasibility across diverse obstacle geometries, we employ a Soft Actor-Critic (SAC) policy to dynamically adapt the HOCBF gain parameters at runtime. The approach is validated with extensive simulation and experimental studies on UAV navigation in cluttered environments.

Keywords: Safety-critical control, Data driven control, Distributed control
Abstract: Gaussian process-based control barrier functions (GP-based CBFs) have been shown to be an effective approach in data-driven safety control methods. However, for safety-critical control in multi-agent systems, performing GP regression calculations in a centralized manner is undesirable. Thus, in this letter, we propose a distributed Gaussian process-based CBF, which provides data-driven safety control by using a robust Bayesian committee machine (rBCM) and performs computation in a distributed manner over partitioned datasets. Employing the rBCM alleviates computational complexity associated with GP regression and offers improved computational efficiency in a decentralized manner. The proposed method is evaluated through experiments on multi-agent safe exploration in unknown environments using differential-drive vehicles.

Keywords: Safety-critical control, Estimation
Abstract: This paper studies safety analysis and controller synthesis for partially observable nonlinear control systems. We extend the control barrier--value function (CBVF) framework, which combines Hamilton--Jacobi reachability and control barrier functions, to settings where full state information is not available and control is based on an estimated state. Given an estimator, we apply conformal prediction to the estimation error and obtain an error bound at a user-chosen miscoverage level. We incorporate this bound into the estimator-space safety analysis and define a CBVF-based safety certificate for partially observable systems. We then derive a finite-horizon probabilistic safety guarantee for the true system state. Finally, we propose a QP-based online safety filter for systems affine in the control and disturbance, whose solution enforces the CBVF safety condition in real time against bounded disturbance. The proposed framework is illustrated on a partially observable obstacle-avoidance case study.

Keywords: Control of networks, Distributed control, Optimization algorithms
Abstract: In this paper, we propose a weight-balancing algorithm over directed graphs that guarantees fixed-time convergence, regardless of the initial conditions. Under bounded disturbances, we further present a modified fixed-time balancing algorithm and introduce an anchor agent so that the balancing weights remain positive constants. The proposed scheme can be used as an online weight-balancing mechanism for distributed algorithms that require weight-balanced digraphs. As a representative application, we apply it to distributed optimization and illustrate its performance under topology changes through simulations.

Keywords: Autonomous systems, Formal Verification/Synthesis, Control applications
Abstract: We present a communication-aware task decomposition framework for multi-agent systems with collaborative relative configuration objectives specified in Signal Temporal Logic (STL). The framework enables reactive task decomposition under time-varying communication networks and, building on our prior work, allows existing feedback controllers to be used directly for reactive task satisfaction. We address two key challenges: disjunctive STL specifications and time-varying connectivity. Disjunctive specifications are handled through a graph transition system that captures the alternative task sequences induced by logical OR operators. To account for changing connectivity, we introduce a task redistribution mechanism that transfers tasks from disconnected agents to connected ones as the network evolves, while preserving decentralized execution. Numerical studies and experiments with a swarm of Crazyflie drones demonstrate the scalability of the proposed framework with respect to the number of agents, communication connectivity, and specification complexity.

Keywords: Reinforcement learning, Predictive control for nonlinear systems, Stability of nonlinear systems
Abstract: Real-time economic optimization of nonlinear processes must balance profit with strict constraint satisfaction. This paper develops an economic reinforcement learning (RL) control framework that learns an optimization-free feedback policy while enforcing constraints during deployment. The RL policy is trained to maximize an economic stage objective under the constraint-enforced closed-loop dynamics used online, and an economic model predictive controller (EMPC) is used only when a proposed input fails the enforcement checks. The approach is demonstrated on a chemical process example with an economic throughput objective and a material constraint. Simulations show that the learned controller improves the economic performance of EMPC while reducing per-step computation by orders of magnitude and maintaining the prescribed Lyapunov bounds under bounded disturbances.

Keywords: Machine learning and control, Neural networks, Predictive control for nonlinear systems
Abstract: In this paper, we propose multi-step discrete-time physics-informed neural networks (MS-DPINNs) for sample-based model predictive control. Our MS-DPINNs have a novel architecture designed to enable fast future state prediction without sacrificing prediction accuracy. To show the applicability of MS-DPINNs to control problems, we integrate the proposed MS-DPINN based dynamic prediction with model predictive path integral control. The effectiveness of the proposed approach, in terms of computational efficiency and control performance, is demonstrated through physical experiments using a rotary inverted pendulum.

Keywords: Power systems, Stochastic systems, Optimization
Abstract: Optimal scheduling of batteries has significant potential to reduce electricity costs and support the integration of distributed renewable generation. However, effective battery scheduling must account for both physical constraints as well as uncertainties in consumption and renewable generation. Instead of optimizing fixed battery power setpoints, we propose an approach that optimizes battery power intervals, allowing the optimization to explicitly account for uncertain consumption and generation as well as how the battery system should respond to them within its physical limits. Our method is based on mixed random variables, represented as mixtures of discrete and continuous probability distributions. Building on this representation, we develop an analytical stochastic formulation for minimizing electricity costs in a residential setting with load, photovoltaics, and battery storage. We demonstrate its effectiveness across real-world data from 15 residential buildings over five consecutive months. Compared with deterministic and probabilistic benchmark controllers, the proposed interval-based optimization achieves the lowest costs. These results show that mixed random variables are a practical and promising tool for decision-making under uncertainty.

Keywords: Flight control, Learning-based Control, Predictive control for linear systems
Abstract: The powered yaw control of distributed electric propulsion (DEP) aircraft is achieved through differential thrust. However, during differential thrust operation, the associated aerodynamic effects can alter the lift and drag distribution over the wing, thereby inducing additional lateral moments and ultimately affecting the powered yaw control performance. Such aerodynamic effects are difficult to capture accurately in the flight dynamics model and therefore appear as unmodeled aerodynamic effects. To address this issue, this paper proposes a novel model predictive control (MPC) scheme for the powered yaw control of DEP aircraft. In the proposed scheme, a DEP aircraft comprehensive model is established, in which the unmodeled aerodynamic effects are represented by an oracle correction term whose parameters are learned online using a moving horizon estimation (MHE) method. Based on this DEP aircraft comprehensive model, a learning-based MPC (LBMPC) powered yaw controller is developed to compute thrust commands that achieve both optimal differential thrust allocation and effective utilization of the aerodynamic effects. Real-time co-simulation results demonstrate the effectiveness of the proposed scheme.

Keywords: Predictive control for nonlinear systems, Machine learning, Chemical process control
Abstract: Industrial adoption of machine-learning-based model predictive control (ML-MPC) remains limited since directly replacing existing controllers with data-driven ones raises concerns about implementation risk. While plug-and-play (PnP) ML-MPC provides a practical pathway by allowing local controller upgrades without redesigning the entire control architecture, model mismatch and subsystem interactions during PnP operation may lead to state-constraint violations. Motivated by this issue, this work develops a tube-based robust PnP ML-MPC framework and derives sufficient conditions that guarantee both constraint satisfaction and overall closed-loop stability during PnP operation using input-to-state practical stability with the small-gain theorem.

Keywords: Output regulation, Nonlinear systems, Optimization
Abstract: This paper studies the optimal steady-state regulation problem for a class of nonlinear systems. The regulated output is required to track a trajectory that minimizes a steady-state cost depending on both the output and the exosystem.To characterize the desired steady-state behavior, we introduce a generalized regulator equation and develop a two-layer framework. The optimization layer generates the optimal reference online through a steady-state generator combined with gradient-feedback optimization dynamics, while the control layer employs backstepping to stabilize the plant and achieve the desired optimal steady-state regulation. Under suitable immersion and minimum-phase assumptions, global asymptotic stability is established.

Keywords: Machine learning and control, Chemical process control, Modeling
Abstract: In this paper, we consider the data-driven discovery of stable dynamical models with a single equilibrium. The proposed approach uses a basis-function parameterization of the differential equations and the associated Lyapunov function. This modeling approach enables the discovery of both the dynamical model and a Lyapunov function in an interpretable form. The Lyapunov conditions for stability are enforced as constraints on the training data. The resulting learning task is a mixed-integer quadratically constrained optimization problem that can be solved to optimality using current state-of-the-art global optimization solvers. Application to two case studies shows that the proposed approach can discover the true model of the system and the associated Lyapunov function. Moreover, in the presence of noise, the model learned with the proposed approach achieves higher predictive accuracy than models learned with baselines that do not consider Lyapunov-related constraints.

Keywords: Energy systems, Machine learning and control, Power systems
Abstract: Physics-informed machine learning (PIML) surrogates are increasingly explored to accelerate dynamic simulation of generators, converters, and other power grid components. A common practice is to use such models as surrogate components within larger dynamic simulations. The key question is whether the approximation errors they introduce propagate through the simulator and cause an unacceptable deviation in its solutions. This paper formulates that in-simulator use as a verification and validation (V&V) problem. To the best of our knowledge, this is the first power-system verification framework that converts a prescribed complete-simulation accuracy limit into an allowable component-output error for a machine-learning surrogate. The resulting finite-horizon bound accounts for algebraic-coupling sensitivity, dynamic error amplification, and the simulation horizon. Two complementary settings are then studied: model-based verification against a reference component solver, and data-based validation through conformal calibration of the component-output variables exchanged with the simulator. The framework is general, but the case study focuses on PIML surrogates of second-, fourth-, and sixth-order synchronous-machine models. Results show that good stand-alone surrogate accuracy does not by itself guarantee accurate in-simulator behavior. The largest discrepancies concentrate in stressed operating regions, and small equation residuals do not necessarily imply small state-trajectory errors.

Keywords: Reinforcement learning, Power systems, Lyapunov methods
Abstract: Wide-area damping controllers (WADCs) rely on phasor measurement unit (PMU) data transmitted over communication networks, making them inherently vulnerable to cyber attacks. This paper proposes a model-free mathcal{H}_infty wide-area damping controller designed via reinforcement learning (RL) that is simultaneously robust to physical disturbances and resilient to false data injection (FDI) attacks. The power system is modeled as a nonlinear differential-algebraic equation (NDAE) with higher-order generator dynamics, power electronics-based renewable models, and composite load dynamics. We introduce the effective adversarial signal mdelta = m K_d m a, representing the controller-amplified attack, which enters the plant through the fixed channel -tilde{m B}. This yields a consistent composite adversarial input m d = [m w^top ;; mdelta^top]^top with fixed input matrix tilde{m B}_d = [tilde{m B}_w ;; -tilde{m B}], enabling a standard game-algebraic Riccati equation (GARE) formulation and capturing the performance-security tradeoff: a more aggressive controller improves nominal damping but amplifies the effective disturbance energy for a given raw attack. The controller is computed entirely from data via policy iteration whose convergence to the GARE solution is formally proved, and we establish DAE stability and per-channel attenuation guarantees. Case studies on a modified IEEE 9-bus system with {sim}63% renewable generation validate the theoretical results.

Keywords: Fault detection, Fault diagnosis, Machine learning and control
Abstract: This paper presents a novel approach for fault classification in rotating machinery by integrating physics-informed neural networks (PINNs) with machine learning techniques. Our method employs an inverse PINN to estimate speed-dependent dynamic parameters—specifically damping and stiffness coefficients—from cycle-segmented vibration data. By embedding the governing differential equations of rotor dynamics directly into the neural network training, the proposed framework ensures physical consistency and improves the estimated parameters' interpretability. These parameters are subsequently used as discriminative features in a random forest classifier to distinguish between normal operation and misalignment faults. Simulations on a rotary machine dataset demonstrate that the estimated parameters capture meaningful variations across different operating conditions, and the classifier achieves highly robust fault diagnosis, even when subjected to minor variations in misalignment severity.

Keywords: Agents-based systems, Robotics, Biologically-inspired methods
Abstract: This letter investigates a planar tracking problem between a leader and follower agent. We propose a novel feedback speed control law, paired with a constant bearing steering strategy, to maintain an abreast formation between the two agents. We prove that the proposed control yields asymptotic stability of the closed-loop system when the steering of the leader is known. For the case when the leader’s steering is unavailable to the follower, we show that the system is still input-to-state stable with respect to the leader’s steering viewed as an input. Furthermore, we demonstrate that if the leader’s steering is periodic, the follower will asymptotically converge to a periodic orbit with the same period. We validate these results through numerical simulations and experimental implementations on mobile robots. Finally, we demonstrate the scalability of the proposed approach by extending the two-agent control law to an N-agent chain network, illustrating its implications for directional information propagation in biological and engineered flocks.

Keywords: Robotics, Optimal control, Nonlinear systems
Abstract: This paper presents an analytical framework to study the geometry arising when a soft continuum arm grasps a planar object. Both the arm centerline and the object boundary are modeled as smooth curves. The grasping problem is formulated as a kinematic boundary following problem, in which the object boundary acts as the arm's 'shadow curve'. This formulation leads to a set of reduced kinematic equations expressed in terms of relative geometric shape variables, with the arm curvature serving as the control input. An optimal control problem is formulated to determine feasible arm shapes that achieve optimal grasping configurations, and its solution is obtained using Pontryagin’s Maximum Principle. Based on the resulting optimal grasp kinematics, a class of continuum grasp quality metrics is proposed using the algebraic properties of the associated continuum grasp map. Feedback control aspects in the dynamic setting are also discussed. The proposed methodology is illustrated through systematic numerical simulations.

Keywords: Predictive control for nonlinear systems, Algebraic/geometric methods, Robotics
Abstract: Accurate trajectory tracking for robotic systems requires balancing geometric consistency with real-time computational efficiency. The state of many of those systems evolves on manifolds with Lie group symmetries that can be exploited for control design. This paper introduces an extended symmetry group that captures the full second-order dynamics of an underactuated quadrotor, enabling a minimal, almost globally valid invariant error representation. Using equivariant linearization, we derive a convex model predictive control formulation with quadratic program complexity and reference-frame invariance, termed Equivariant MPC (EQ-MPC). Numerical simulations demonstrate recovery from large initial pose errors and aggressive trajectory tracking. Compared with state of the art MPC approaches, the proposed method achieves comparable tracking accuracy with significantly reduced control jitter and improved computational efficiency.

Keywords: Mechatronics, Optimal control, Robotics
Abstract: In this paper, we analyse the time-optimal synthesis problem for braking a variable stiffness actuator under motor velocity and joint stiffness constraints. More specifically, we derive closed-form expressions for a parameterized family of broken extremals terminating at the origin. The expressions define both the time-t-controllable sets to the origin and the switching locus. Moreover, when all extremals are boundary trajectories and mutually non-intersecting, except possibly after their last control switch, the controllable sets are separated by the switching locus into different regions. In each region, the optimal motor velocity and joint stiffness are constant and take their minimum or maximum values. In general, the relation between the optimal controls and switching locus is more complex, but the optimal trajectory can still be numerically determined by exploiting the properties of the minimum braking time from zero-deflection and the derived switching patterns.

Keywords: Agents-based systems, Distributed control, Adaptive systems
Abstract: Symbiotic control has recently been introduced as a novel framework that synergistically integrates fixed-gain control and adaptive learning to achieve predictable closed-loop behavior in the presence of system uncertainties, without requiring prior knowledge of their bounds. Building upon this foundation, the overarching contribution of this paper is to make the first attempt in generalizing the concept of symbiotic control to multiagent systems operating over undirected and connected graph topologies. In the proposed distributed symbiotic control framework, each agent employs a nominal control, a fixed-gain control, and an adaptive learning component, where the nominal control governs the ideal closed-loop behavior under nominal conditions, and both the fixed-gain and adaptive learning components suppress the adverse effects of agent-wise system uncertainties. Specifically, while the fixed-gain control alone is capable of mitigating such uncertainties, it typically requires prior knowledge of their upper bounds. To this end, the fixed-gain control is augmented with an adaptive learning component to remove the need for bound information while simultaneously achieving predictable suppression of the remaining system uncertainties. In addition to the presented system-theoretical results, an illustrative numerical example is also given to demonstrate the efficacy of the proposed distributed symbiotic control framework.

Keywords: AI/LLM and control, Optimal control, Stochastic systems
Abstract: Foundation models can improve their outputs through a self-refinement process driven by external feedback. In this process, the model is embedded in an iterative loop where it generates outputs, receives feedback from verifiers, and refines its responses through in-context learning. Following a novel approach, we formalize this process as an optimal stopping problem where the number of refinement iterations is decided based on expected improvement relative to cost. We derive optimal stopping policies and show that they can be efficiently computed through stochastic approximation. To evaluate our approach experimentally, we apply it to a coding benchmark for foundation models. The empirical results show that our stopping policies are significantly more cost-efficient than stopping policies proposed in prior work.

Keywords: Power systems, Distributed control, Optimization
Abstract: This paper studies distributed secondary frequency regulation for power networks with communication delays under system-wide power-balance constraints, scheduled inter-area ex- change constraints, and transmission-line congestion constraints. Existing delay-independent designs are able to accommodate the first two terms, but incorporating line congestion is nontrivial since congestion constraints are imposed in the edge space, which introduces line-level states, cross-layer couplings, and additional delayed communication channels. To address this challenge, we explicitly realize the congestion-related inequality feedback as a distributed line-layer dynamic subsystem, so that line congestion is no longer merely denoted as a compact optimization con- straint, but becomes an implementable closed-loop component with well-defined states, boundaries, and information flow. We then integrate this line-layer subsystem with the original node- layer dynamics into a unified passive interconnection framework, where the additional communication and delay effects are ab- sorbed into the same stability-analysis chain. A relative-entropy- type storage covers active and inactive line inequalities, with its boundary supply rates integrated into the node-line scattering channels. This yields a closed-loop distributed implementation together with a rigorous convergence proof. Simulations on the IEEE 9-bus system demonstrate the effectiveness of the proposed method.

Keywords: Networked control systems, Sensor networks, Optimization algorithms
Abstract: Non-smooth and non-convex optimization problems are pervasive in machine learning, control, and signal processing, due to the need for sparse solutions and the inherently non-convex nature of many objective functions. In this paper, we study non-smooth and non-convex distributed optimization problems. We propose a novel bi-level Consensus Alternating Direction Method of Multipliers (ADMM) algorithm, termed CADMM-Prox. The proposed algorithm integrates classical Consensus ADMM with a proximal mechanism by introducing a sufficiently large proximal term associated with an outer-level variable. Under the mild assumption that the local objective functions are semi-convex, CADMM-Prox is guaranteed to converge globally to a neighborhood of a generalized stationary point. Numerical experiments on a phase retrieval problem demonstrate that our proposed method exhibits more stable convergence behavior compared with baseline algorithm.

Keywords: Game theory, Distributed control, Optimization algorithms
Abstract: This paper investigates the distributed global Nash equilibrium (NE) seeking problem for noncooperative composite games over strongly connected unbalanced graphs, addressing an extensive class of compositionally induced non-convex cost functions, where the inner mapping is no longer restricted to the classical quadratic form. To tackle the possible non-convexity induced by the composite structure and ensure global optimality, the canonical duality theory is employed to reformulate the composite game into a tractable complementary dual problem with favorable convex-concave properties. Subsequently, a distributed continuous-time algorithm is developed. By incorporating a local estimation mechanism, the design effectively bypasses centralized coordination, while leveraging Bregman damping and mirror descent to handle the compact set constraints. Through rigorous Lyapunov stability analysis, the exponential convergence of the generated trajectories to the exact global NE is theoretically established under unbalanced topologies. Finally, the theoretical findings and the effectiveness of the strategy over a classical projection-based scheme are validated through a sensor network localization problem.

Keywords: Cooperative control, Optimal control, Predictive control for nonlinear systems
Abstract: This work presents a distributed denoising diffusion model predictive control (D³MPC) framework for nonlinear multi-agent systems with coupled objective and constraints. The proposed approach reformulates distributed MPC as sampling from an unnormalized Boltzmann distribution, whose modes correspond to optimal multi-agent plans, and performs a diffusion-guided search over joint control sequences. A variance-exploding diffusion process is designed in the control space, and its reverse process is computed online by estimating agent-wise block scores via Metropolis-Hastings sampling. At each diffusion level, the agents perform a distributed sequential scan over control blocks that acts as a soft negotiation mechanism, enabling coordinated constraint satisfaction and guidance toward lower-energy joint plans. We show that this sequential coordinated sampling scheme preserves the exact centralized posterior distribution, is uniformly geometrically ergodic, and, together with the diffusion mechanism, provides a global-to-local search capability for tackling nonlinear and nonconvex control problems.

Keywords: Optimization, Decentralized control
Abstract: Decentralized optimization has emerged as a critical paradigm for distributed learning, enabling scalable training while preserving data privacy through peer-to-peer collaboration. However, existing methods often suffer from communication bottlenecks due to frequent synchronization between nodes. We present Overlapping Local Decentralized SGD (OLDSGD), a novel approach to accelerate decentralized training by computation-communication overlapping, significantly reducing network idle time. With a deliberately designed update, OLDSGD preserves the same average update as Local SGD while avoiding communication-induced stalls. Theoretically, we establish non-asymptotic convergence rates for smooth non-convex objectives, showing that OLDSGD retains the same iteration complexity as standard Local Decentralized SGD while improving per-iteration runtime. Empirical results demonstrate OLDSGD's consistent improvements in wall-clock time convergence under different levels of communication delays. With minimal modifications to existing frameworks, OLDSGD offers a practical solution for faster decentralized learning without sacrificing theoretical guarantees.

Keywords: Learning-based Control, Multi-agent learning, Robust control
Abstract: This paper investigates the dynamic regret minimization problem for general distributed uncertain systems. In the context of robust control, regret minimization aims to design causal controllers that minimize the worst-case gap between the achieved closed-loop performance and that of the best noncausal disturbance-dependent benchmark, thereby quantifying robustness against uncertainty and adversarial disturbances. We establish three main results. First, we formulate the distributed regret control problem, and prove it mathematically reduces to a collection of decoupled subproblems. Second, for systems with at least one pole on the unit circle and full-state measurements, we show that the optimal regret performance index gamma must be strictly greater than unity. Third, we construct an augmented state-space model that transforms the regret minimization problem into a standard H-infinity control problem, enabling the synthesis of the optimal causal controller.

Keywords: Model Validation, Estimation, Machine learning and control
Abstract: This paper theoretically analyzes how system model mismatch displaces finite-horizon maximum a posteriori (MAP) initial-state estimates in controlled dynamical systems under partial observation. From pathwise sensitivity analysis, the initial-state nominal-oracle displacement called MAP shift is decomposed into a model-side mismatch injection and an estimator-side curvature resistance to identify a sensor-dependent information-curvature margin as the amplification bottleneck. The margin is governed by the weakest posterior-curvature direction, so that sensor configurations that maximize aggregate information can still be fragile to mismatches. We connect the margin to nominal Gauss-Newton curvature and to the Bayesian Fisher information matrix, distinguishing instance-wise mismatch robustness from design-time inferability. The margin admits a computable nominal proxy in nonlinear systems, becomes explicit in the linear time-invariant case, and is validated through two numerical examples.

Keywords: Estimation, Sensor networks, Uncertain systems
Abstract: In this paper, we study anchor selection for range-based localization under unknown-but-bounded measurement errors. We start from the convex localization set X=XdcapHset recently introduced in cite{CalafioreSIAM}, where Xd is a polyhedron obtained from pairwise differences of squared-range equations between the unknown location x and the anchors, and Hset is the intersection of upper-range hyperspheres. Our first goal is emph{offline} design: we derive geometry-only E- and D-type scores from the centered scatter matrix S(A)=AQ_mAtran, where A collects the anchor coordinates and Q_m=I_m-frac{1}{m}oneonetran is the centering projector, showing that lambda_{min}(S(A)) controls worst-direction and diameter surrogates for the polyhedral certificate Xd, while det S(A) controls principal-axis volume surrogates. Our second goal is emph{online} uncertainty assessment for a selected subset of anchors: exploiting the special structure X=XdcapHset, we derive a simplex-aggregated enclosing ball for Hset and an exact support-function formula for Hset, which lead to finite hybrid bounds for the actual localization set X, even when the polyhedral certificate deteriorates. Numerical experiments are performed in two dimensions, showing that geometry-based subset selection is close to an oracle combinatorial search, that the D-score slightly dominates the E-score for the area-oriented metric considered here, and that the new Hset-aware certificates track the realized size of the selected localization set closely.

Keywords: Reinforcement learning, Data driven control, Safety-critical control
Abstract: This paper considers the problem of zero-shot safety guarantees for cascade dynamical systems. These are systems where a subset of the states (the inner states) affects the dynamics of the remaining states (the outer states) but not vice-versa. We define safety as remaining on a set deemed safe for all times with high probability. We propose to train a safe RL policy on a reduced-order model, which ignores the dynamics of the inner states, but it treats it as an action that influences the outer state. Thus, reducing the complexity of the training. When deployed in the full system the trained policy is combined with a low-level controller whose task is to track the reference provided by the RL policy. Our main theoretical contribution is a bound on the safe probability in the full-order system. In particular, we establish the interplay between the probability of remaining safe after the zero-shot deployment and the quality of the tracking of the inner states. We validate our theoretical findings on a quadrotor navigation task, demonstrating that the preservation of the safety guarantees is tied to the bandwidth and tracking capabilities of the low-level controller.

Keywords: Learning in Game theory, Multi-agent learning
Abstract: We study long-run equilibrium selection in 2-by-2 coordination games under risk-sensitive evolutionary learning dynamics. Agents' risk attitudes enter through the entropic risk measure, which evaluates opponent-induced payoff uncertainty and feeds into two standard revision protocols: best response with mutations and logit choice. We analyze the resulting risk-sensitive evolutionary dynamics in both single-population symmetric and two-population asymmetric settings. In the single-population setting, unlike the risk-neutral case where the dynamics typically favor the risk-dominant equilibrium, risk sensitivity can change the stochastically stable outcome: a greater risk-seeking attitude favors the payoff-dominant equilibrium, while a greater risk-averse attitude favors the maximin equilibrium. Thus, the population's risk attitude may act as a control knob for long-run equilibrium selection. In both population settings, we also identify a robust regime: any super-dominant equilibrium is stochastically stable for all risk attitudes under both protocols. This shows that long-run equilibrium selection in this case is robust to risk preferences.

Keywords: Safety-critical control, Constrained control, Robust control
Abstract: Tunable input-to-state safety (TISSf) generalizes input-to-state safety (ISSf) by incorporating a tuning function that regulates safety conservatism while preserving robustness against perturbations. However, the tuning function is often designed without explicitly incorporating actuator limits, which can lead to incompatibility with input constraints. To address this issue, this paper proposes a framework that integrates general compact input constraints into the tuning function design. Using a geometric perspective, we characterize the TISSf condition as a state-dependent half-space constraint and derive a verifiable compatibility certificate using support functions. This yields an explicit lower bound on the tuning function and characterizes the admissible tunings under input constraints. The results are specialized to norm-bounded, polyhedral, and box constraints, yielding tractable design conditions. Combined with tuning function monotonicity, these conditions guarantee input compatibility and pointwise feasibility of the resulting quadratic program (QP)-based safety filter. An offline covering-based sampling strategy further upgrades the pointwise compatibility condition to a finite-dimensional linear program (LP) for parameter selection. A connected cruise control (CCC) application demonstrates robust safety under TISSf while enforcing input constraints.

Keywords: Safety-critical control, Control system architecture, Control over communications
Abstract: Ensuring safe behavior is critical for modern autonomous cyber-physical systems. Control barrier functions (CBFs) are widely used to enforce safety in autonomous systems, yet their placement within networked control architectures remains largely unexplored. In this work, we investigate where to enforce safety in a networked control system in which a remote model predictive controller (MPC) communicates with the plant over a delayed network. We compare two safety strategies: i) a local myopic CBF filter applied at the plant and ii) predictive CBF constraints embedded in the remote MPC. For both architectures, we derive state-dependent disturbance tolerance bounds and show that safety placement induces a fundamental trade-off: local CBFs provide higher disturbance tolerance due to access to fresh state measurements, whereas MPC-CBF enables improved performance through anticipatory behavior but yields stricter admissible disturbance levels. Motivated by this insight, we propose a combined architecture that integrates predictive and local safety mechanisms. The theoretical findings are illustrated in simulations on a planar three-degree-of-freedom robot performing a collision-avoidance task.

Keywords: Robust adaptive control, Reinforcement learning, Adaptive control
Abstract: This work investigates the robust integration of reinforcement learning (RL) and adaptive control (AC). The need for robustness arises from the lack of guarantees for an AC-based loop to match the reference dynamics obtained from RL-based offline training, possibly leading to instability. We attain robustness by incorporating a state-dependent leakage in the adaptive law: we prove that such adaptation mechanism can handle the unmatchable terms between the AC-based and the RL-based loops. Numerical experiments on the Mountain Car benchmark are presented to validate the proposed ideas.

Keywords: Cooperative control, Autonomous vehicles, Distributed control
Abstract: A typical approach to design platooning strategies for vehicles with heterogeneous characteristics is to compensate for their heterogeneities by selecting a common reference behavior to which all vehicles should converge. In this work, we enhance this approach by letting the platoon elect and dynamically update the reference behavior based on the characteristics of the vehicles composing the platoon. In particular, we consider dynamic election in the presence of heterogeneous vehicle dynamics and heterogeneous actuation limits. Stability of the proposed dynamic election mechanism is analyzed in the framework of slowly time-varying parameters with infrequent discontinuities, which can even capture discontinuities caused by vehicles with different characteristics leaving and joining the platoon. Numerical validations on a SUMO-Veins platform show the effectiveness of dynamic election.

Keywords: Constrained control, Safety-critical control, Learning-based Control
Abstract: Designing feedback controllers that satisfy predefined performance specifications while enforcing hard input constraints is a challenging task. Our work is motivated by the idea that state trajectory data, e.g., obtained from an expert controller, often implicitly encode feasible performance attributes and input limitations. We propose an optimization-based framework that uses state trajectory data to jointly learn: (i) a performance funnel that mimics the transient and steady-state behavior encoded within the observed trajectories, and (ii) a feedback controller that enforces the learned performance specifications under hard input constraints. Unlike imitation learning methods, the proposed approach does not rely on control input data and does not reconstruct an expert policy. Instead, it synthesizes a prescribed performance controller by combining nominal model compensation with a learned state-dependent feedback gain. The resulting synthesis problem is nonconvex, for which we develop a feasibility-driven active-set synthesis procedure. Finally, we establish two complementary guarantees: a semi-global conservative actuator-authority-based certificate for prescribed performance and input satisfaction, and a local data-driven certificate ensuring these properties near sufficiently dense demonstrated trajectories.

Keywords: Optimization, Aerospace, Uncertain systems
Abstract: Commercial launch cadence depends on tightly coupled terrestrial networks spanning suppliers, assembly, testing, propellant support, and launch sites, yet launch readiness is typically modeled as an isolated pad-level problem. We instead model readiness as the output of this multi-echelon system. We develop a deterministic multi-period launch-fulfillment model with lead time and payload assignment, then extend it to two-stage stochastic models capturing demand and lead-time uncertainty. First-stage decisions activate transportation lanes and reserve launch capacity. Second-stage operations then adapt to realized scenarios. Computational studies show payload-arrival timing shifts congestion between launch-site queues and the upstream readiness chain. Stochastic planning yields modest gains under demand uncertainty, mainly via launch-slot reallocation, but substantially larger gains under lead-time uncertainty, where serial bottlenecks propagate disruptions across tiers and can require additional upstream lanes. These results underscore the value of uncertainty-aware supply-chain coordination for high-cadence launch-readiness planning.

Keywords: Decentralized control, Networked control systems, Optimization algorithms
Abstract: We study decentralized constrained optimization over Hadamard manifolds. Existing decentralized Riemannian methods typically require a projection onto the constraint set at every iteration, which may incur a high computational cost. We propose a distributed penalized Riemannian Frank-Wolfe algorithm (PRFW), a projection-free method that combines a fixed consensus penalty with local Riemannian linear minimization oracles. At each iteration, each agent communicates only with its neighbors, solves a local Riemannian linear minimization oracle, and performs a geodesic update step. Under assumptions of geodesic convexity and smoothness, PRFW achieves an mathcal{O}(1/K) convergence rate for the penalized suboptimality with a fixed penalty. When the fixed penalty is selected as rho=cK^{2/3} for a prescribed iteration budget K, the original objective gap at any agent satisfies an mathcal{O}(K^{-1/3}) bound. Numerical experiments on constrained Fr'echet mean problems over symmetric positive-definite (SPD) manifolds compare objective accuracy and running time with projected decentralized methods.

Keywords: Power systems, Optimization, Linear systems
Abstract: This paper studies unreachability screening for power systems, focusing on the inadequate control authority that arises under stressed grid conditions. Its main result is an infeasibility margin for linearized differential algebraic equation models that quantifies how far a prescribed terminal target lies from the reachable set in finite time. The paper specifically develops a conic benchmark method together with two first order methods based on projected subgradients and bundle updates for scalably repeated screening. Studies on IEEE benchmark networks show reduced terminal reachability under stressed conditions and tighter actuation limits, while first order methods remain accurate and substantially faster on large systems. Comparisons with standard reachability methods such as CORA further demonstrate the usefulness and scalability of the proposed infeasibility margins. All results and codes are included in a Github repository.

Keywords: Linear systems, Healthcare and medical systems, Power systems
Abstract: Many incentive design problems must contend with information asymmetries due to non-observation of efficiency (adverse selection) or non-observation of effort (moral hazard). Although a growing body of literature considers incentive design in control systems, the problem of designing incentives for control systems under information asymmetries has been less studied. This paper considers a model of moral hazard within control systems. In our model, the control system is described by an (affine) linear time-invariant (LTI) system with process noise. There is an agent who gets to choose (from between two choices) a linear state-feedback controller to apply to the LTI system, with one of the state-feedback controllers having a higher quadratic cost on the control inputs than the other. Our goal is to design a payment scheme that incentivizes the agent to choose the state-feedback controller that minimizes a quadratic cost on system states plus the time-discounted payment amount, subject to the understanding that the agent bears the control cost while being risk-averse with respect to their time-discounted payment. We formulate the problem as a constrained optimization, and prove that for a payment given after a fixed (but optimizable) time horizon the optimal payment scheme chooses the payment amount using a likelihood ratio hypothesis test. We numerically demonstrate our results by applying the derived optimal payment scheme to two examples: load frequency control (LFC) in power systems and wellness interventions for body weight loss.

Keywords: Identification, Estimation, Stochastic systems
Abstract: In numerous network system identification prob- lems, such as social media, the nodal signals are point processes. Of particular interest are network information flows which throw light on network function. We compare three recent approaches to assessing Granger causality in a small point process network. One is based on a likelihood ratio test; the second, nonparametric, uses cumulants and the third, which is new, uses model-based directed mutual information (DMI). We establish a relation between the first and third methods. We compare the three in a simulation. The guaranteed positivity of DMI makes it superior to the second method which has positivity problems. Furthermore, DMI outperforms the nonparametric approach.

Keywords: Linear systems, Control of networks, Network analysis and control
Abstract: This letter revisits the classical PBH test through the lens of finite-horizon reachability. By casting state transfer as a minimum energy, primal optimization problem, we show that unreachable state-space maneuvers admit dual infeasibility certificates. These certificates are computable without forming the controllability matrix meaning that uncontrollability can be efficiently certified. We prove that any such certificate is a linear combination of uncontrollable generalized eigenvectors, thereby providing a spectral interpretation without a global eigendecomposition. We also devise algorithms based on Krylov subspace methods that extract some of the uncontrollable PBH modes from a certificate and demonstrate favorable scaling on large dynamic networks with thousands of nodes.

Keywords: Finance, Control of networks, Optimization
Abstract: In the context of containment of default contagion in financial networks, we here study a regulator that allocates pre-shock capital or liquidity buffers across banks connected by interbank liabilities and common external asset exposures. The regulator chooses a nonnegative buffer vector under a linear budget before asset-price shocks realize. Shocks are modeled as belonging to either an ell_{infty} or an ell_{1} uncertainty set, and the design objective is either to enlarge the certified no-default/no- insolvency region or to minimize worst-case clearing losses at a prescribed stress radius. Four exact synthesis results are derived. The buffer that maximizes the default resilience margin is obtained from a linear program and admits a closed-form minimal-budget certificate for any target margin. The buffer that maximizes the insolvency resilience margin is computed by a single linear program. At a fixed radius, minimizing the worst-case systemic loss is again a linear program under ell_{infty} uncertainty and a linear program with one scenario block per asset under ell_{1} uncertainty. Crucially, under ell_{1} uncertainty, exact robustness adds only one LP block per asset, ensuring that the computational complexity grows linearly with the number of assets. A corollary identifies the exact budget at which the optimized worst-case loss becomes zero.

Numerical experiments on the 8-bank benchmark of cite{Calafiore2025}, on a synthetic core-periphery network, and on a data-backed 107-bank calibration built from the 2025 EBA transparency exercise show large gains over uniform and exposure-proportional allocations. The empirical results also indicate that resilience-maximizing and loss-minimizing interventions nearly coincide under diffuse ell_infty shocks, but diverge under concentrated ell_1 shocks.

Keywords: Game theory, Optimal control
Abstract: We study the design of functional incentive mechanisms for dynamical systems, in which a leader parametrizes a fixed incentive function to motivate a self-interested follower to actuate the system beneficially over an extended horizon, without real-time revision of the incentive. This stands in contrast to the adaptive paradigm, in which the incentive is itself a continuously updated control variable. We formalize the problem as a discrete-time bi-level optimal control problem and derive analytical results for the linear-quadratic case with bilinear incentives and a myopic follower. Specifically, we establish a necessary and sufficient stability condition for the induced closed-loop system, derive a closed-form expression for the gradient of the expected leader cost with respect to the incentive parameter matrix, and obtain a fully closed-form cost expression in the scalar setting. Based on the latter, explicit characterizations of the optimal incentive parameter are provided in two asymptotic regimes: the infinite-horizon limit and the limit of high follower cost. For long horizons, the optimal incentive is shown to become independent of the follower's private cost parameter, with direct implications for robust mechanism design under private information.

Keywords: Aerospace, Flight control, Constrained control
Abstract: This paper presents a nonlinear direct control allocation framework for Innovative Control Effector (ICE) aircraft whose actuators exhibit strongly nonlinear, state-dependent, and cross-coupled authority characteristics. Such behavior invalidates standard linear allocation methods with gain scheduling. The allocation problem is formulated as polynomial equations in actuator deflections and solved in real time using precomputed Gröbner-basis multiplication matrices and online eigendecomposition. Actuator limits are handled through spherical mapping of desired body-rate accelerations and direction-dependent magnitude lookup tables. High-fidelity simulations on the ICE platform demonstrate accurate steady-state allocation, improved decoupling between controlled axes, and superior overall performance compared to state-of-the-art Incremental Nonlinear Control Allocation (INCA) in highly nonlinear flight regimes.

Keywords: Game theory, Uncertain systems, Optimal control
Abstract: This work presents a comprehensive analysis and design of global sensitivity-based input shapers for a 3D Unmanned Aerial Vehicle-payload system, emphasizing robustness against uncertainties in payload mass and rope length. The proposed approach also leverages the Shapley value concept in controller design to systematically account for uncertainties, thereby reducing the controller’s sensitivity to unknown parameters. To validate the effectiveness of the methodology, numerical simulations are conducted, comparing the proposed controller against non-robust, robust, and minimax designs. The results demonstrate that the standard global sensitivity or Shapley-based input shapers improve performance and offer a promising framework for uncertainty-aware control in aerial payload transport.

Keywords: Stochastic systems, Lyapunov methods, Markov processes
Abstract: In this paper, we establish a stochastic analogue to the classical Krasovskii-LaSalle invariant set stability theorem. Specifically, we develop a stochastic invariant set principle involving the existence, and convergence of the probability distribution of the stochastic process, to an invariant set of probability measures. Furthermore, we present extensions of Lyapunov’s direct method for asserting local and global asymptotic stability in probability of stochastic dynamical systems whose Lyapunov function infinitesimal generators are only negative semidefinite. Several classical examples adopted into a stochastic setting are presented to show the efficacy of the proposed Lyapunov stability theorem extensions.

Keywords: Stochastic optimal control, Machine learning and control, Optimization
Abstract: There is a growing literature adopting a stochastic optimal control (SOC) perspective to fine-tune diffusion models and related generative policies. A prominent class of methods, known as iterative diffusion optimization, solves the SOC problem by simulating the diffusion process, evaluating a loss function, and applying stochastic optimization algorithms, with adjoint matching emerging as a state-of-the-art approach. However, the adjoint process used in these methods is not adapted to the forward diffusion filtration, which can lead to unstable or high-variance gradient estimates. In this paper, we revisit gradient estimation in diffusion models through the lens of backward stochastic differential equations (BSDEs). We propose an alternative estimator based on a time-reversed BSDE formulation introduced in our prior work, which produces an adjoint process adapted to the underlying filtration. This adapted structure leads to more stable gradient estimates with potentially lower variance. We analyze the accuracy of the proposed estimator and compare it with adjoint matching. Numerical experiments on fine-tuning toy diffusion models demonstrate improved gradient stability and competitive performance.

Keywords: Boolean control networks and logic networks, Stochastic systems, Stability of nonlinear systems
Abstract: This paper investigates a class of semi-Markovian jump Boolean networks (S-MJBNs) in which the active mode remains constant over a random dwell interval. By defining an augmented random variable as the product of state variable, switching signal and dwell time memory information, the Markov property of S-MJBNs is restored. Subsequently, a criterion for asymptotic set stability of S-MJBNs is established, and the affine dependence of the augmented transition matrix on the dwell time distribution together with its effect on transient behavior is investigated. Finally, an illustrative example is provided to validate the theoretical results.

Keywords: Event-triggered/resource-aware control, Variable-structure/sliding-mode control, Linear systems
Abstract: This paper investigates the convergence of multivariable super-twisting sliding mode control systems under the event-triggered mechanism. Unlike existing studies that rely on component-wise sign functions, a norm-based multivariable super-twisting algorithm is employed. By exploiting the properties of the event-triggering condition, uniform ultimate boundedness of the closed-loop system is established via Lyapunov analysis. Notably, the obtained bound is independent of the states at the triggering instants, thereby addressing a common limitation in the existing literature. Moreover, the Zeno behavior is rigorously excluded. Numerical simulations illustrate the effectiveness of the theoretical findings.

Keywords: Networked control systems, AI/LLM and control
Abstract: Self-triggered control is a control method in which both the control input and the next sampling time are determined. In this paper, a new method of self-triggered control for nonlinear systems is proposed using a Transformer, which is a powerful deep learning model. The proposed method consists of offline and online phases. In the offline phase, after a dataset is generated by simulations, a Transformer is trained. In the online phase, both the control input and the next sampling time are determined based on the trained Transformer. Similar to self-triggered model predictive control, the control input may vary depending on the next sampling time. The effectiveness of the proposed method is demonstrated through a numerical example.

Keywords: Linear systems, Robust control, Data driven control
Abstract: Graphical methods for system analysis have played a central role in control theory. The Scaled Relative Graph (SRG) has recently emerged as a useful tool for stability analysis of feedback interconnections. In this paper, we further extend its applicability by showing how the SRG of a discrete-time linear-time-invariant (LTI) system can be computed exactly from its state-space representation using linear matrix inequalities. We additionally propose a fully data-driven approach where we demonstrate how to compute the SRG exclusively from input-output data. Furthermore, we introduce a robust version of the SRG, which can be computed from noisy data trajectories and contains the SRG of the actual system.

Keywords: Distributed control, Control over communications, Numerical algorithms
Abstract: This paper investigates the distributed least-squares (LS) problem for a multi-agent system. Unlike conventional distributed frameworks where data is partitioned row-wise or column-wise, we consider a summation-based formulation where the global coefficient matrix and supply vector are the sums of local submatrices and subvectors, respectively. Each agent possesses only its local pair of data, necessitating a decentralized approach. Leveraging a recent tuning-free discretization method studied in [1], we develop a novel discrete-time distributed algorithm that does not require manual step-size tuning--a common bottleneck in existing methods. Rigorous convergence analysis demonstrates that, under a mild condition on the single design parameter--independent of the problem data--the algorithm converges exponentially to a LS solution of the linear algebraic equation with sum-separable data.

Keywords: Distributed control, Algebraic/geometric methods, Neural networks
Abstract: Graph neural networks (GNNs) are a well-regarded tool for learned control of networked dynamical systems due to their ability to be deployed in a distributed manner. However, current distributed GNN architectures assume that all nodes in the network collect geometric observations in compatible bases, which limits the usefulness of such controllers in GPS-denied and compass-denied environments. This paper presents a GNN parametrization that is globally invariant to choice of local basis. 2D geometric features and transformations between bases are expressed in the complex domain. Inside each GNN layer, complex-valued linear layers with phase-equivariant activation functions are used. When viewed from a fixed global frame, all policies learned by this architecture are strictly invariant to choice of local frames. This architecture is shown to increase the data efficiency, tracking performance, and generalization of learned control when compared to a real-valued baseline on an imitation learning flocking task.

Keywords: Estimation, Sensor networks, Distributed control
Abstract: This paper studies distributed state estimation for linear systems over double-layered networks. We consider a state-partitioned architecture in which each agent estimates only a local sub-state, thereby reducing the per-agent computational and storage burden compared with conventional full-state observers. To address the dimension mismatch and dynamic coupling induced by the state partition, we develop a distributed observer that combines a dynamic average tracking mechanism with a projection-based inter-cluster coupling scheme. We show that the estimation error system is input-to-state stable with respect to the perturbation caused by the tracking mismatch, which decays as O(1/gamma) in the tracking gain gamma. Consequently, the estimation error admits an arbitrarily small ultimate bound, which reveals a trade-off between scalability and estimation accuracy. The theoretical results are illustrated by a numerical example.

Keywords: Distributed control, Network analysis and control, Optimal control
Abstract: We consider the linear plant with multiple pairs of input and output channels, and solve the problem of designing a stabilizing controller consisting of a set of control stations, one for each channel pair, connected with an arbitrarily fixed network topology and communication dynamics. It is shown that such stabilizing distributed controller exists if and only if the fixed modes of the plant, augmented with the network communication, are stable; this leverages and extends the classical fixed mode result for decentralized control. Moreover, a condition is given to reveal exactly what connections are needed between control stations to achieve stabilizability via a distributed control. Thus, the feasibility of optimal distributed control synthesis can readily be checked or enforced before applying computationally expensive optimization methods. Stabilizing distributed controllers, if feasible, can be designed using decentralized control theories.

Keywords: Machine learning and control, Neural networks, Markov processes
Abstract: This paper provides a rigorous optimal control-theoretic approach to Transformer training. Our formulation respects key operational and structural constraints such as (i) realized-input-independence during execution, (ii) the ensemble control nature of the problem, and (iii) positional dependence. We establish the existence of globally optimal policies under mild assumptions of compactness. We further prove that closed-loop policies in the lifted is equivalent to an initial-distribution dependent open-loop policy, which are realized-input-independent and compatible with standard Transformer training. To train a Transformer, we propose a triply quantized training procedure for the lifted MDP by quantizing the state space, the space of probability measures, and the action space, and show that any optimal policy for the triply quantized model is near-optimal for the original training problem. Finally, we study the generalization problem and establish stability and empirical consistency properties of the lifted model by showing that the value function is continuous with respect to the perturbations of the initial empirical measures and convergence of policies as the data size increases. This approach provides a globally optimal and robust alternative to gradient-based training without requiring smoothness or convexity.

Keywords: Game theory, Biological systems
Abstract: We present a new solution concept called evolutionarily stable Stackelberg equilibrium (SESS). We study the Stackelberg evolutionary game setting in which there is a single leading player and a symmetric population of followers. The leader selects an optimal mixed strategy, anticipating that the follower population plays an evolutionarily stable strategy (ESS) in the induced subgame and may satisfy additional ecological conditions. We consider both leader-optimal and leader-pessimal selection among ESSs, which arise as special cases of our framework. Prior approaches to Stackelberg evolutionary games either define the follower response via evolutionary dynamics or assume rational best-response behavior, without explicitly enforcing stability against invasion by mutations. We present algorithms for computing SESS in discrete and continuous games, and validate the latter empirically. Our model applies naturally to biological settings; for example, in cancer treatment the leader represents the physician and the followers correspond to competing cancer cell phenotypes.

Keywords: Game theory, Optimization
Abstract: Ensuring the security of complex systems involves the strategic allocation of defensive resources to prevent various types of attacks from succeeding. A defender often has multiple types of defensive assets at its disposal, where it must decide how to optimally deploy their heterogeneous capabilities across different attack types. In this paper, we formulate a multi-resource allocation problem in the form of a General Lotto game where a defender possesses various types of resources. A feature that we introduce is that their individual effectiveness against different types of attacks is characterized by a network weight matrix. In our analysis, we derive upper and lower bounds on the performance of the defender, and provide numerical evidence suggesting that they are tight. For the case of two attack types, we analytically prove that the bounds coincide, establishing an exact equilibrium characterization. We then numerically compare our proposed networked multi-resource architecture to an independent-defense benchmark from the existing literature. These results highlight fundamental and tractable structures underlying multi-attack-type defense problems.

Keywords: Nonlinear systems, Game theory, Learning
Abstract: We use evolutionary game theory to investigate the problem of encouraging rational agents to select desirable actions. Most past studies explore solutions to this problem under the assumption that agents are simple, imitative decision makers. However, with the proliferation of information in the modern age (e.g., AI, GPS, internet, etc.), decision making is often a process rooted in the rational appraisal of information. Inspired by the likes of information campaigns and advertisements, we explore ways of encouraging desirable behaviors by influencing rational agents' effective rationality, i.e., their ability to accurately assess information. Using the logit dynamics---a model for the population dynamics of boundedly-rational decision makers---and focusing on two-player, two-strategy, symmetric, dominant-strategy games, we approach this problem as a set point regulation problem. First, we extend the logit dynamics to include an external input of effective rationality; then we demonstrate that a unique input stabilizes almost all set points in the state space---i.e., guarantees that rational agents choose desired actions. In doing so, we find that, intuitively, misinformation is necessary to guarantee certain outcomes. Finally, we design and numerically assess a feedback law for the extended logit dynamics that requires little information of the underlying system parameters.

Keywords: Network analysis and control, Large-scale systems, Control of networks
Abstract: This paper studies hierarchical networks, such as those in large organisations and Command and Control environments, as a discrete-time averaging system, using the convergence rate to reach a consensus as an index of performance. We focus on a two-layer network, with a single node in the upper layer and a general structure in the lower layer ---certain constraints are placed on the intra-layer weights. First, we show how one can model the presence of two different communication rates in how information is transmitted upwards and downwards. Next, we prove that having two communication rates can both increase and decrease the convergence speed when compared to a single communication rate across the entire network, depending on the coupling strengths between the layers. Finally, we consider a constant external input at the top layer, capturing e.g. external orders received by a commander to be passed to the lower layer. We show that i) convergence is always slower when there is an input compared to without, and ii) when there is input, having two communication rates slows down convergence with respect to having one communication rate.

Keywords: Systems biology, Markov processes, Stochastic optimal control
Abstract: Multiplex tissue imaging (MTI) enables high- dimensional, spatially resolved measurements of the tumor microenvironment (TME), but most clinical datasets are tempo- rally undersampled and longitudinally limited, restricting direct inference of underlying spatiotemporal dynamics and effective intervention timing. Agent-based models (ABMs) provide mechanistic, stochastic simulators of TME evolution; yet their high-dimensional state space and uncertain parameterization make direct control design challenging. This work presents a reduced-order, simulation-driven framework for therapeutic strategydesign using ABM-derived trajectory ensembles. Starting from a nominal ABM, we systematically perturb biologically plausible parameters to generate a set of simulated trajectories and construct a low-dimensional trajectory landscape describing TME evolution. From time series of spatial summary statistics extracted from the simulations, we identify a switched Markov State Model (MSM) that captures metastable states and the transitions between them, and whose modes are indexed by the parameter regimes most predictive of terminal-state outcome within the sampled ensemble. To connect simulation dynamics with clinical observations, we map patient MTI snapshots onto the landscape and assess concordance with observed spatial phenotypes and clinical outcomes. We further show that conditioning the MSM on the most predictive parameters yields group-specific transition models to formulate a finite-horizon Markov Decision Process (MDP) and use it for reachability analysis and finite-horizon intervention design. The resulting framework enables simulation-grounded therapeutic policy design for partially observed biological systems without requiring longitudinal patient measurements, taking a step towards adaptive, state-aware therapeutic strategies in oncology.

Keywords: Biological systems, Markov processes, Stochastic systems
Abstract: The quantitative assessment of tumour eradication under therapy is a key problem in mathematical oncology, since stochastic fluctuations become particularly relevant when the tumour burden is low and may ultimately determine whether extinction occurs. In this work we propose a method to estimate the probability of tumour eradication and the corresponding mean eradication time in stochastic models of tumour growth under treatment. The modelling framework is based on the Chemical Reaction Network (CRN) formalism, which allows tumour dynamics to be represented as a Continuous-Time Markov Chain. By exploiting a quasi-steady-state approximation (QSSA), the original multi-dimensional stochastic model is reduced to a one-dimensional birth–death process governing the proliferating tumour cell population. Within this reduced framework, explicit expressions for the eradication probability and, when meaningful, for the mean eradication time are derived as functions of the model propensities. Unlike previous approaches, the proposed method does not require linearity assumptions on the reduced propensities and relaxes restrictive steady-state hypotheses on the remaining model variables. The effectiveness of the approach is illustrated through simulations on a tumour growth model from the literature, showing how the quasi-steady-state reduction captures qualitative behaviours that may be missed by earlier steady-state approximations.

Keywords: Stochastic optimal control, Optimization algorithms, Biological systems
Abstract: In Real-Time, Feedback-Driven Single Particle Tracking, measurements of the emission intensity from a fluorescently-labeled, nanometer-scale particle are used in a feedback loop to track the motion of the particle as it moves inside its native environment, including within living cells. In this work, we take advantage of Point Spread Function (PSF) engineering techniques that encode the axial position of the particle into the shape of the PSF in the focal plane to eliminate the need for out-of-focal-plane measurements, reducing the complexity of implementation and decreasing the overall measurement time of the control loop. Specifically, we used the Double Helix PSF (DH-PSF) in which a single fluorescent source gives rise to two lobes in the image plane with the lobes rotating in the plane as the particle moves along the optical axis. This is combined with a dual-stage approach to decouple the time scale of measurement acquisition from that of tracking. We explored the efficacy of the approach through simulation studies based on physically relevant physical parameters, demonstrating tracking of fast-moving particles (with diffusion coefficients up to 1 mu m^2/s) over long time periods (with tracking times of multiple seconds).

Keywords: Quantum information and control
Abstract: Hamiltonian estimation is an effective approach in studying the structure and dynamical evolution of quantum systems. The difficulty in estimating the Hamiltonian is that an N-qubit Hamiltonian has 4^N − 1 unknown parameters, requiring exponentially many equations for information extraction. In this paper we develop a method based on compressed sensing to estimate the Hamiltonian of a multi-qubit system. We identify a problem where as N increases, the common sufficient condition (Restricted Isometry Property) for compressed sensing often fails, obstructing the application of compressed sensing in (N ≥ 3)-qubit Hamiltonian estimation. To solve this problem, we propose a “scale transformation” technique to restore RIP and ensure a compressive estimation of a k-sparse Hamiltonian using only O(k log(4^N/k)) equations. In the numerical examples, we estimate the Hamiltonian of a 30-qubit system, demonstrating the effectiveness of the method.

Keywords: Quantum information and control, Robust control
Abstract: Measurement-based feedback control would introduce disturbance to the evolution of quantum states due to quantum measurement. To avoid this issue, a coherent feedback controller is designed for a cavity system disturbed by quantum Lorentzian noise in this paper. Since quantum colored noise generally induces complicated dynamics of the mode in the cavity, we adopt an augmented system approach to describe the system dynamics. Based on the augmented system model, a coherent controller is designed using an H^infty approach, where the physical realizability of the controller can be satisfied. The simulation results demonstrate the effectiveness of our method.

Keywords: Stochastic systems, Safety-critical control, Robotics
Abstract: We generalize our previous work [1], [2] and establish two concentration inequalities for nonlinear stochastic systems with time-dependent contraction rates and contraction metrics. The key to our approach is a function termed Averaged Moment Generating Function (AMGF). By combining it with incremental stability analysis, we develop a concentration inequality that bounds the deviation between the stochastic system state and its deterministic counterpart. As this inequality is restricted to single time instance, we further combine AMGF with martingale-based methods to derive a concentration inequality that bounds the fluctuation of the entire stochastic trajectory. Additionally, by synthesizing the two results, we significantly improve the trajectory-level concentration inequality for strongly contractive systems. Given the probability level 1-delta, the derived inequalities ensure an mathcal{O}(sqrt{log(1/delta)}) bound on the deviation of stochastic trajectories, which is tight under our assumptions. Our results are exemplified through a case study on stochastic safe control.

Keywords: Stability of nonlinear systems, Stability of hybrid systems, Autonomous systems
Abstract: We introduce local Input-to-State Stability to time scale systems and provide a Lyapunov result to analyze this property. Furthermore we show that Input-to-State Stability of non-linear systems is robust to small distortions of time scales, in the sense that if a dynamic equation is Input-to-State Stable in continuous time then the equation is locally Input-to-State Stable on any time scale where the graininess is small enough. We provide some examples to apply the main result and give an idea to further generalize this framework by considering a metric space of time scales.