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arXiv2026

Optimal Sensor and Actuator Selection for Factored Markov Decision Processes: Complexity, Approximability and Algorithms

Factored Markov Decision Processes (fMDPs) are a class of Markov Decision Processes (MDPs) in which the states (and actions) can be factored into a set of state (and action) variables and can be encoded compactly using a factored representation. In this paper, we consider a setting where the state of the fMDP is not directly observable, and the agent relies on a set of potential sensors to gather information. We formulate the problem of selecting a set of sensors for fMDPs (under a limited budget) to maximize the infinite-horizon discounted return provided by the optimal policy. We show the fundamental result that it is NP-hard to approximate this problem to within a factor of $n^{1-c}$ for any $c > 1$, where $n$ is the number of state variables. Our inapproximability results for sensor selection also extend to a general class of Partially Observable MDPs (POMDPs). We also consider the dual problem of budgeted actuator selection (at design-time) to maximize the expected return under the optimal policy, for which we establish similar inapproximability results. Finally, we consider a simple greedy algorithm and empirically show that, despite the lack of formal theoretical guarantees, it performs effectively in practice, achieving on average over $70\%$ of the optimal solution value across a variety of real-world and randomly generated problem instances.

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arXiv2026

Deep Reinforcement Learning for Reach-Avoid-Stay Problems

Reach-Avoid-Stay (RAS) tasks are essential in applications where systems must safely reach a target set and remain within it under all bounded disturbances. Existing approaches either struggle to compute the maximal robust RAS set, the set of all states from which the RAS task is achievable, or are limited in handling general dynamic systems. To address these challenges, this paper proposes a two-step deep reinforcement learning framework that jointly learns the maximal robust RAS set and the corresponding control policy. The first step identifies the maximal robust control-invariant set within the target set and derives a policy that ensures the system remains within it. The second step computes the maximal robust reach-avoid (RA) set using this invariant set as the target, and it is proven that this RA set is equivalent to the maximal robust RAS set. Leveraging this result, a switching policy is constructed from the two step-wise policies, which constitutes a valid policy guaranteeing completion of the RAS task. Simulation results demonstrate that the proposed framework (1) computes the exact maximal robust RAS set in the absence of training errors, yielding the least restrictive RAS policy, and (2) identifies the RAS set with high accuracy while outperforming baseline methods on RAS tasks.

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arXiv2026

Sample Complexity of Linear Quadratic Regulator Without Initial Stability

Inspired by REINFORCE, we introduce a novel receding-horizon algorithm for the Linear Quadratic Regulator (LQR) problem with unknown dynamics. Unlike prior methods, our algorithm avoids reliance on two-point gradient estimates while maintaining the same order of sample complexity. Furthermore, it eliminates the restrictive requirement of starting with a stable initial policy, broadening its applicability. Beyond these improvements, we introduce a refined analysis of error propagation through the contraction of the Riccati operator under the Riemannian distance. This refinement leads to a better sample complexity and ensures improved convergence guarantees.

math.OC↗

arXiv2026

Robust Closed-Form Control for MIMO Nonlinear Systems under Generalized Conflicting Time-Varying Hard and Soft Constraints (extended version)

This paper introduces a novel robust closed-form control law to handle time-varying hard and soft constraints in uncertain high-relative-degree nonlinear MIMO systems. These constraints represent spatiotemporal specifications in mechanical systems' operational space, with hard constraints ensuring safety-critical requirements and soft constraints encoding performance or task objectives. Initially, all constraints are consolidated into two separate scalar time-varying hard and soft constraint functions, whose positive level sets define feasible regions. A closed-form control law is developed to enforce these constraints using appropriately designed reciprocal barriers and nonlinear transformation functions. When conflicts between hard and soft constraints arise, the control law prioritizes hard constraints by virtually relaxing soft constraints via a dynamic relaxation law. Notably, the proposed control law maintains low complexity, avoiding approximation schemes for system uncertainties. Simulation results confirm the effectiveness of the proposed method.

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arXiv2026

Predictive control barrier functions for piecewise affine systems with non-smooth constraints

Obtaining control barrier functions (CBFs) with large safe sets for complex nonlinear systems and constraints is a challenging task. Predictive CBFs address this issue by using an online finite-horizon optimal control problem that implicitly defines a large safe set. The optimal control problem, also known as the predictive safety filter (PSF), involves predicting the system's flow under a given backup control policy. However, for non-smooth systems and constraints, some key elements, such as CBF gradients and the sensitivity of the flow, are not well-defined, making the current methods inadequate for ensuring safety. Additionally, for control-non-affine systems, the PSF is generally nonlinear and non-convex, posing challenges for real-time computation. This paper considers piecewise affine systems, which are usually control-non-affine, under nonlinear state and polyhedral input constraints. We solve the safety issue by incorporating set-valued generalized Clarke derivatives in the PSF design. We show that enforcing CBF constraints across all elements of the generalized Clarke derivatives suffices to guarantee safety. Moreover, to lighten the computational overhead, we propose an explicit approximation of the PSF. The resulting control methods are demonstrated through numerical examples.

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arXiv2026

An Energy-Based Mechanism for Compositional Behavior

Flexible intelligence relies on the ability to reuse previously acquired behaviors and combine them differently as circumstances change. In biological and artificial systems, this ability is often attributed to gating mechanisms that determine how much each available behavior should contribute at a given time. Yet these gating rules, the dynamics that compute them, and the neural circuits that may implement them are usually introduced separately, leaving unclear whether they reflect a common underlying principle. Here, we show that they can all be derived from a single variational principle for behavioral composition. The resulting mechanism naturally gives rise to softmax gating, evolves as an energy-based dynamical system with guaranteed convergence, and admits a recurrent neural network instantiation featuring context-dependent and local interactions. Across collective behavior, human decision-making, and layered control, the same mechanism reproduces characteristic behavioral patterns, provides interpretable accounts of how different behaviors are combined, and matches or outperforms established approaches. These results provide a unified account of how behavioral composition can emerge from a common principle, with implications for understanding flexible behavior in natural systems and for designing artificial agents that can adapt by recombining existing capabilities.

math.OC↗

arXiv2026

Compensating Coarse Quantization in Massive MIMO: Channel Estimation and BER under Imperfect CSI

Low-resolution quantization is essential to reduce implementation cost and power consumption in massive multiple-input multiple-output (MIMO) systems for 5G and 6G. While most existing studies assume perfect channel state information (CSI), we model the impact of coarse quantization noise on both channel estimation and data transmission, yielding a more realistic assessment of system performance under imperfect CSI conditions in the uplink. We develop a tight approximation for the bit-error ratio (BER) of uncoded M-QAM with zero-forcing detection, based on the linear minimum mean-square error (LMMSE) channel estimate. These analytical results enable compensation strategies that jointly optimize quantization resolution, transmit power, and pilot length across different numbers of users and base station antennas. We further demonstrate the applicability of the proposed framework through several design scenarios that highlight its effectiveness in optimizing system parameters and improving energy efficiency under quantization constraints. For example, in a 16-QAM system, extending the pilot sequence by 2.5 times and lowering transmit power by 0.5 dB enables a 3-bit quantized system to match the BER of the full-resolution case. The proposed framework offers a fast and accurate alternative to Monte Carlo simulations, enabling practical system optimization under realistic quantization constraints.

eess.SP↗

arXiv2026

Equivariant Filter Transformations for Consistent and Efficient Visual--Inertial Navigation

This paper presents an equivariant filter (EqF) transformation approach for visual--inertial navigation. By establishing analytical links between EqFs with different symmetries, the proposed approach enables systematic consistency design and efficient implementation. First, we formalize the mapping from the global system state to the local error-state and prove that it induces a nonsingular linear transformation between the error-states of any two EqFs. Second, we derive transformation laws for the associated linearized error-state systems and unobservable subspaces. These results yield a general consistency design principle: for any unobservable system, a consistent EqF with a state-independent unobservable subspace can be synthesized by transforming the local coordinate chart, thereby avoiding ad hoc symmetry analysis. Third, to mitigate the computational burden arising from the non-block-diagonal Jacobians required for consistency, we propose two efficient implementation strategies. These strategies exploit the Jacobians of a simpler EqF with block-diagonal structure to accelerate covariance operations while preserving consistency. Extensive Monte Carlo simulations and real-world experiments validate the proposed approach in terms of both accuracy and runtime.

cs.RO↗

arXiv2026

Hierarchical Control for Continuous-time Systems via General Approximate Alternating Simulation Relations

This paper introduces a general approximate alternating simulation relation (\emph{$\varepsilon$-gAAS relation}) for continuous-time systems, which relaxes existing simulation relations to tolerate larger mismatches between abstract and concrete models. The definition of gAAS for continuous-time systems is first proposed, and its properties are investigated. Then, a control refinement method is developed to enable hierarchical control for the gAAS relation. Finally, case studies demonstrate the effectiveness of the proposed approach, highlighting its advantages over existing methods.

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arXiv2026

Joint Accuracy and Confidentiality in Semantic-Aware Secure Remote Reconstruction

In this paper, we consider remote reconstruction over wireless networks when simultaneous accuracy at the legitimate receiver and confidentiality against eavesdropping are required. These two objectives are often treated separately, even though they arise from the same update process and are marginals of a joint reconstruction event. This paper introduces confidential reconstruction accuracy (CRA), a metric to capture the joint event in which the legitimate receiver reconstructs correctly while the eavesdropper fails. Under randomized stationary policies, we develop a three-dimensional stationary analysis and derive closed-form expressions for the long-term average CRA and the optimal transmission probability. The results show that conventional marginal analysis can misidentify the optimal policy and misestimate the achievable simultaneous accuracy-confidentiality performance. They also reveal nontrivial behaviors: more frequent transmissions or better legitimate channels do not necessarily improve joint accurate and confidential reconstruction, and when the eavesdropping channel is strong, improving the legitimate channel alone may be insufficient. Finally, the framework induces the spatial safety boundary in a geofencing setting for secure remote reconstruction.

cs.IT↗

arXiv2026

Variational Contraction Conditions for Iterative Algorithms in Multi-Population Discrete-Time Regularized Mean-Field Games

In this work, we study the contraction conditions of iterative algorithms for stationary and finite-horizon discrete-time regularized mean-field games (MFGs) with multiple populations, where each population only interacts with the state distributions of the other populations. Due to the high dimensionality caused by the interaction of different populations, contraction rates for these algorithms cannot, in general, be expressed in terms of radicals. By studying the dynamics of these iterative algorithms and assuming that the system components of each population's MFG are Lipschitz continuous, we present explicit (eventual) contraction conditions for each algorithm in any normed space, relying only on these Lipschitz parameters. As a consequence of these contraction conditions, we provide convergence rates of finite-horizon mean-field equilibria to infinite-horizon stationary (and non-stationary) mean-field equilibria (MFEs), under restrictions on a variational characterization of the dynamics of these iterative algorithms. In the single-population case, the restrictions we impose on this variational characterization to obtain these convergence results are less restrictive than previous results in the literature.

math.OC↗

arXiv2026

Reinforcement Learning for Heterogeneous Sensor Selection in Maritime Surveillance

This paper presents an information-gain-guided reinforcement-learning sensor-selection framework for single-vessel tracking in heterogeneous maritime sensor networks. The proposed approach is motivated by information-theoretic sensor management: instead of activating all sensors or repeatedly performing computationally expensive online expected-information-gain evaluation, a learned policy selects one tracking-relevant sensor at each decision epoch. A Bayesian sequential Monte Carlo tracker estimates the vessel state from noisy measurements and provides a belief representation for scheduling under nonlinear and non-Gaussian conditions. A Proximal Policy Optimization agent selects one of five sensors in a georeferenced simulation of the CMMI Smart Marina testbed at Ayia Napa Marina, Cyprus. The policy is trained on the testbed's actual five-sensor configuration. The agent observes belief-state, detection-history, coverage, sensor-geometry, and realized-information-gain features. The reward is defined as a realized-information-gain term gated by an observability mask. Final-test simulations compare the proposed framework with random single-sensor selection, always-on sensing using all sensors simultaneously, and the expected-information-gain sensor-selection baseline proposed in our previous work. Results show that the learned policy achieves tracking performance close to always-on sensing while activating only one sensor per decision time step and avoiding the computationally expensive online entropy search required by expected-information-gain selection. Additional zero-shot evaluation without retraining on ten moderately perturbed versions of actual layout configuration showed broadly stable tracking, with any increase in positional tracking error remaining below 1 meter across all perturbations.

cs.AI↗

arXiv2026

Scalable Self-Supervised Learning for Multiphase AC-OPF in Distribution Systems with Topology Reconfiguration

The proliferation of distributed energy resources (DERs) in distribution grids enables the active coordination of these assets to reduce costs and enable cleaner operations. Realizing this potential requires solving multiphase AC optimal power flow (AC-OPF) quickly across varying loads, DER availabilities, and topology reconfigurations, at much greater speed and scale than conventional nonlinear solvers. Learning-based surrogates can offer millisecond inference, yet existing methods target largely balanced transmission systems and do not scale to the multiphase, unbalanced, and reconfigurable nature of distribution feeders at utility scale. We present the Penalty + Sequential Linearized Feasibility Seeking (SLFS) algorithm, a self-supervised learning framework for multiphase distribution AC-OPF under switch-induced topology changes. Penalty+SLFS requires no labeled optimal solutions and trains directly from the AC-OPF objective and constraints through a differentiable fixed-point power flow solver, avoiding expensive label generation and admitting robust training procedures. Topology changes are handled efficiently using Sherman-Morrison-Woodbury updates of the admittance-matrix inverse, while an M-step Jacobian approximation accelerates differentiation through the power flow solver. At inference, SLFS repairs any infeasible predictions, providing feasibility guarantees with low computational overhead. On IEEE feeders ranging from 13 to 8,500 nodes, Penalty+SLFS achieves negligible optimality gaps and near-zero constraint violations, delivers up to three orders of magnitude speedups over IPOPT, and remains robust under large distributional shifts, demonstrating a viable path toward real-time, topology-aware AC-OPF for large-scale distribution grids.

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arXiv2026

Lightweight CFR-Based Modulation Adaptation in a Real-Time MIMO-OFDM SDR Testbed

Conventional link adaptation typically relies on scalar link-quality indicators such as signal-to-noise ratio (SNR), while richer channel state information (CSI) can improve adaptation at the cost of higher processing complexity. This paper investigates a compact alternative for modulation selection in a real-time multiple-input multiple-output orthogonal frequency-division multiplexing (MIMO-OFDM) system using channel frequency response (CFR) magnitude descriptors. A dataset of 87,817 over-the-air (OTA) samples is collected using a USRP-based testbed, with CFR measurements extracted at the base station (BS) from received uplink pilots. Decision tree (DT), random forest (RF), and k-nearest neighbours (KNN) classifiers are evaluated using BS-side SNR, CFR features, and their combination. SNR-only classifiers achieve 35%-42% test accuracy, whereas CFR-only features achieve 73.6%, 81.4%, and 80.0% for DT, RF, and KNN, respectively. CFR-based performance is maintained near the 10% BLER reliability thresholds, with RF reaching 82.8%. A depth-7 DT with 123 leaves is further integrated into the LabVIEW C Node for real-time inference. The results show that compact BS-side CFR descriptors provide more discriminative information than the available scalar BS-side SNR while remaining suitable for lightweight SDR implementation.

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arXiv2026

Dimension-Reduced ADP for Real-Time Microgrid Operation with Massive Air-Conditioning Loads under Multiple Uncertainties

This paper proposes a dimension-reduced approximate dynamic programming (ADP) method for real-time microgrid operation with massive air-conditioning loads under multiple uncertainties. The operation problem is formulated as a multi-stage Markov decision process, and a post-decision value function is introduced to characterize the impact of current decisions on future operating costs. To address the curse of dimensionality caused by massive air-conditioning loads, a consistency-based value function projection is developed to map the high-dimensional state space at each node into a tractable aggregated state space. Based on the reduced states, piecewise linear approximation is further employed for efficient value function training. Case studies on 33-bus and 123-bus systems show that the proposed method achieves near-optimal operation performance with low computational cost and good scalability under both deterministic and stochastic conditions.

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arXiv2026

Efficient Sensor Fusion Through Covariance-Constrained Observation Decimation (CCOD)

Observation decimation is frequently employed in state estimation to reduce sensing, communication, and computational requirements, but decreasing the measurement assimilation frequency increases estimation uncertainty. Selecting an appropriate observation decimation factor therefore requires accurately predicting the resulting estimator performance. While the discrete algebraic Riccati equation (DARE) provides the steady-state estimation-error covariance for standard linear time-invariant Kalman filters, it is not directly applicable to estimators employing decimated measurement updates. Existing approaches address this limitation through lifted system representations or periodic Riccati equation formulations, both of which incur additional computational complexity. This paper presents a covariance-constrained observation decimation (CCOD) framework that reformulates the DARE inputs using equivalent decimated system and process-noise matrices that capture covariance growth between measurement updates. The proposed reformulation enables direct prediction of the steady-state estimation-error covariance through a single DARE evaluation without increasing the system dimension or solving coupled periodic Riccati equations. The resulting covariance prediction is used to determine the maximum observation decimation factor that satisfies a prescribed estimation uncertainty bound. Validation using a high dimensional linear time-invariant system and a space object tracking application demonstrates that the proposed approach accurately predicts steady-state estimator performance while reducing the measurement assimilation frequency required to satisfy specified covariance constraints.

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arXiv2026

Seed-Anchored Budget-Bounded Graph Rendering for Question Answering on Industry-Standard Power-Grid Information and Exchange Models

Large language model question answering over power-grid models must respect a fixed context budget. We introduce seed-anchored graph rendering, a deterministic method that prioritizes query-local graph evidence without adding method-specific tuned or learned parameters beyond the shared hop bound and context budget. The method provides a checkable condition under which predefined seed-local answer-bearing render units are preserved in a greedy bounded-context prefix. We evaluate the approach on Common Information Model (CIM) network models exchanged through the Common Grid Model Exchange Standard (CGMES). On two budget-binding CGMES encodings, naive descriptions-first rendering retains local evidence for every single-hop item but only 0.12 and 0.00 of multi-hop items, whereas seed-anchored rendering retains all such evidence. On a preregistered fresh 100-item bank from the SmallGrid topology family, accuracy rises from 0.450 to 0.970 under a fixed 8,000-character context budget. Under a common retrieval and rendering pipeline, the standards-native seed-anchored graph matches or exceeds extracted graph representations produced by LightRAG, Microsoft GraphRAG, and HippoRAG, while avoiding LLM graph-construction tokens. The results are specific to the evaluated CIM/CGMES models, reader, and context budget; they concern budget-bounded retrieval rather than general question answering.

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arXiv2026

Turnpike properties in nonlinear system identification

We analyze the problem of learning general discrete-time nonlinear state-space models using the simulation error minimization (SEM) method. In this setting, model parameters are typically learned by minimizing the mismatch between simulated and measured outputs over a training dataset, or shorter subsequences extracted from it. Specifically, we study the cumulative output turnpike property of the underlying SEM optimization problem, which requires optimal output sequences emanating from a fixed initial state to approach and remain close to an optimal output sequence of the corresponding SEM problem with free initial state. In the presence of non-unique optimal output sequences---as may arise, for instance, in fully black-box system identification using neural networks---the property is formulated with respect to the closest such sequence. Turnpike behavior is generally desirable in practice, as it provides a theoretical justification for employing computationally more tractable SEM formulations with fixed initial states while ensuring that their optimal output sequences remain close to unconstrained optimal ones. Under a mild reachability condition, we establish equivalence between the cumulative turnpike property, coercivity of the value function, and a tailored notion of strict dissipativity. We additionally introduce a cardinality turnpike property and show that it is strictly weaker than the cumulative notion. Finally, we establish sufficient conditions for turnpike behavior based on incremental output stability, convexity of the stage cost, and a suitable optimality condition, and illustrate the theory by means of a numerical example.

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