Systems and Control
Control Synthesis against LTL Specifications with Long-Run Visit Proportion Objectives
Zhiyuan Huang, Zhao Tong, Jiakai Li et al. (+2 more)
This paper investigates the path-planning problem for systems required to satisfy a linear temporal logic (LTL) specification while achieving a desired long-run visit proportion. For a path represented in prefix-suffix structure, the long-run visit proportion quantifies the asymptotic occurrence proportion of an atomic proposition (AP) sequence of interest in the suffix trace. Such a quantitative requirement generally cannot be expressed by standard LTL specifications. Furthermore, we develop a planning approach that synthesizes an LTL-satisfying path whose long-run visit proportion remains within a prescribed tolerance of a desired value while satisfying an overall cost constraint. By adjusting the desired proportion, the synthesized path can allocate more or less long-run
attention to the atomic proposition sequence of interest, thereby improving the flexibility and efficiency of the task execution. Finally, experiments on a quadruped
robot demonstrate the practical significance of the proposed long-run visit proportion and the effectiveness of the proposed planning approach.
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All authors Zhiyuan Huang, Zhao Tong, Jiakai Li, Chenrui Xiang, Bingzhuo Zhong
Systems and Control
Explicit Second-Order Bounds on the Domain of Validity for Lyapunov-Schmidt Reduction
Pranav Gupta, Ravi Banavar and Anastasia Bizyaeva
Lyapunov-Schmidt reduction is a widely used dimensionality reduction technique for bifurcation analysis in high-dimensional systems. While classical formulations guarantee the local existence of reduced-order equations, they typically lack explicit quantitative estimates on the size of the neighbourhoods in which these representations faithfully capture the full bifurcation structure. In recent work, we have addressed this limitation by deriving bounds on the domain of validity of this reduction using first-order conditions on the vector field together with a quantitative result for the implicit function
theorem. In this article we explore beyond, and adopt second-order conditions that incorporate the Hessians of the vector field to develop these bounds, and obtain a new set of results. We then investigate the applicability of these newly derived bounds to Hopfield-like networked dynamical systems, evaluate these bounds for pitchfork bifurcations on connected regular graphs, and finally examine the relationship between the two certified domains for this class of systems.
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Systems and Control
Offline Reinforcement Learning for Distribution-Grid Protection
Julian Oelhaf, Alexander Luce, Christian Bergler et al. (+2 more)
Data-driven protection may complement conventional relays in distribution grids whose operating conditions vary with distributed generation, switching events, and changing short-
circuit levels. We study line-selective tripping from static trajectories of a realistically simulated CIGRE medium-voltage network using offline reinforcement learning. A convolutional Q-network receives causal voltage-current phasor and apparent-impedance features, optionally together with raw waveforms, and is trained with conservative Q-learning (CQL). A controlled sensitivity study evaluates two observation windows, reward variants, and three CQL weights under a common split and training protocol; one exploratory post-hoc run additionally increases the discount factor from $\gamma$=0.95 to 0.99. On 225 held-out episodes, the best per-timestep result is obtained with combined input and CQL weight $\alpha$=0.9, reaching precision 0.9993, recall 0.9496, and F1-score 0.9738. Because dense per-timestep scores do not encode the terminal semantics of relay operation, we also evaluate the first non-wait action in each episode. The default combined-input
agent selects the correct line-trip action first in 98.13% of 214 fault episodes, but trips in 72.73% of the 11 non-fault episodes. In the post-hoc run, the corresponding rates are 98.60% and 54.55%, respectively. The results show that dense predictive performance and terminal protection behavior can lead to different model rankings. Offline CQL therefore demonstrates strong faulted-line selection on the simulated fault episodes, while the static trajectories, small non-fault set, and single-seed post-hoc design preclude conclusions about practical relay security or deployment readiness.
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All authors Julian Oelhaf, Alexander Luce, Christian Bergler, Andreas Maier, Siming Bayer
Systems and Control
Adaptive sliding mode formation control for space interferometer missions
Mauro Mancini, Giulia Alessandra Tataru, Satoshi Satoh et al. (+1 more)
This paper addresses high-precision formation control for spacecraft operating in low Earth orbit, motivated by the requirements of future space interferometry missions such as SILVIA. The proposed approach formulates the relative dynamics within a port-
Hamiltonian framework and introduces an Adaptive Boundary-layer Sliding Mode Control (AB-SMC) law to overcome the limitations of conventional SMC with constant gains. The key innovation lies in a dynamic, error-dependent adjustment of the sliding
manifold, enhancing transient performance while guaranteeing high-precision trajectory tracking. Rigorous Lyapunov-based analysis establishes explicit ultimate bounds on the tracking error and ensures closed-loop stability, while extensive Monte Carlo simulations further validate the proposed AB-SMC compared to standard control approaches. Results show that AB-SMC achieves faster convergence, lower control effort, and sub-millimeter tracking accuracy, demonstrating its practical robustness and implementation feasibility in realistic, uncertain orbital environments while respecting low-thrust constraints.
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All authors Mauro Mancini, Giulia Alessandra Tataru, Satoshi Satoh, Elisa Capello
Systems and Control
Agentic AI Enabling Autonomous, Self-Organizing, and Evolving UAV Networks
Zhaoyang Li, Xingzhi Jin, Zijiu Yang et al. (+2 more)
As low-altitude applications expand across emergency response, intelligent transportation, and autonomous operations, they demand communication networks that can deliver flexible, resilient, and rapidly deployable connectivity. Heterogeneous
UAV networks are a promising solution, as they can dynamically provide sensing, access, relay, and backhaul functions. Yet, most existing approaches assume predefined missions, prior knowledge of user distributions, and manually configured infrastructure, making them ill suited to dynamic and initially unknown environments. Addressing this limitation requires a shift from mission-oriented
UAV deployment to autonomous network formation, in which
UAVs continuously perceive their surroundings, infer evolving service demands, and self-organize network resources. Agentic AI, empowered by large
language models (LLMs), offers a new foundation for this shift by integrating closed-loop perception,
reasoning, planning, and execution across heterogeneous information sources. Unlike conventional optimization and learning methods designed for individual networking tasks, agentic AI can coordinate these capabilities to support sustained, network-level autonomy. In this article, we explore agentic AI for autonomous and self-organizing heterogeneous
UAV networks in low-altitude environments. Our key contribution is an LLM-assisted architecture in which a base-station-hosted
agent conducts global network
reasoning and autonomously reconfigures access and backhaul infrastructure. The proposed system explores unknown environments, discovers users, and deploys
UAVs on demand to provide access and establish end-to-end backhaul connectivity. A case study illustrates how this agentic-AI-driven approach can transform
UAVs from task-specific platforms into a continuously evolving communication network.
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All authors Zhaoyang Li, Xingzhi Jin, Zijiu Yang, Qianqian Yang, Zhiguo Shi
Systems and Control · Cross-listed from cs.DC
Analytical Power-Aware Provisioning for Prefill-Decode Disaggregated AI Inference
Mingyuan Yan, Haiyu Wang, Linxuan Biao et al. (+3 more)
Power availability increasingly constrains the operation of AI inference fleets, creating a need for provisioning methods that jointly consider serving capacity and power consumption. Prefill–decode (PD) disaggregation has emerged as a prevalent architecture for large-scale inference serving. However, determining the appropriate numbers of prefill and decode instances is challenging because serving capacity depends jointly on workload characteristics, hardware constraints, queueing, and KV-cache reservations. Existing approaches largely rely on profiling and simulation, providing limited analytical insight into how provisioning decisions shape the tradeoff between serving capacity and power consumption. This paper develops an analytical framework for power-aware provisioning of PD-disaggregated AI inference. Given an inference workload and hardware, the framework models the serving capacity and average power consumption of a provisioned deployment. The serving-capacity model is derived from the joint distribution of input–output lengths and hardware compute and
memory limits. In particular, it explicitly captures the coupling between prefill and decode induced by KV-cache reservations, as well as the impact of request queueing. On this basis, the power model determines per-instance power consumption as a function of normalized serving throughput. Together, the models determine the serving capacity–power Pareto front among candidate provisioned deployments, enabling the service provider to choose a provisioned deployment as the workload or available power changes.
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All authors Mingyuan Yan, Haiyu Wang, Linxuan Biao, H. Jonathan Chao, Sai Qian Zhang, Wenqi Cui
Systems and Control
Multi-Period Repetitive Control Design in a Time Delay Framework with Application to an Active Vibration Isolation System
Xiaoran Han, Sil Spanjer and Wouter B.J. Hakvoort
Multi-period Repetitive Control (MPRC) can lead to amplification at non-repetitive frequencies due to the multiplication of multi-period repetitive control in their closed-loop sensitivity functions, which leads to closed-to imaginary poles. We propose a MPRC structure that eliminates such interaction. The scheme can be equivalently converted into a disturbance observer to improve robustness to frequency uncertainties. We derive an upper bound on the sensitivity function that can be optimized at either repetitive or non-repetitive frequencies. Experimental results on an active vibration isolation system show superior performance over existing robust MPRC schemes, and the capability to suppress unknown time-varying periodic disturbances.
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Systems and Control
Optimal Allocation of Grid-Forming Frequency Shaping Control
Zhaomin Lyu, Ding Zhang and Yan Jiang
Various inverter-based control strategies have been proposed to improve frequency security for power systems with high renewable penetration. Among them, the grid-forming frequency shaping control is particularly promising due to its ability to shape the post-contingency aggregate system frequency dynamics into first-order with prescribed rate of change of frequency (RoCoF) and steady-state frequency deviation. Moreover, the shaped aggregate dynamics depends on the harmonic sum of all inverter transfer functions rather than on their distribution. In light of this, here we explore how to allocate shaping control resources to minimize the transient control effort needed to achieve ideal coherent dynamics. We formulate it as a constrained optimization problem by tackling two main difficulties. First, we make the squared $\mathcal{H}_2$ norm legitimate quantification of transient control cost under step power imbalances through a system transformation. Second, we simplify the $s$-domain constraint for Nadir elimination into a standard constraint that is easy to implement in optimization. The resulting non-convex optimization problem can be solved by existing successive convexification method. The effectiveness of the allocation has been verified on the modified Icelandic Power Network test case.
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Systems and Control · Cross-listed from cs.RO
FoldQuantVLA: Native Low-Bit Quantization of Vision-Language-Action Models via Consistent Folding
Hung T. Ho, Khanh D. Nguyen, Quang D. Nguyen et al. (+5 more)
Low-bit
vision-
language-action inference must reduce observation-to-action latency while preserving
robot behavior. We present FoldQuantVLA, a post-training quantization framework that carries a consistent activation representation through calibration, weight rounding, and native integer execution. It combines channel scaling and block Hadamard transforms with dynamic per-
token quantization, without policy retraining. Custom TensorRT plugins execute projections in both the
language backbone and iterative action expert with four-bit weights and activations (W4A4) on Ada GPUs and Jetson AGX Orin. Evaluation spans LIBERO, SimplerEnv, and two
robot platforms. Across three GR00T checkpoints and $\pi_{0.5}$, W4A4 achieves $1.20$ to $1.33\times$ speedups over floating-point TensorRT on Orin and $1.25$ to $1.52\times$ on desktop. Retaining
language attention-output and feed-forward down projections at eight bits (W8A8) improves held-out action fidelity on all four checkpoints. Across four real-
robot tasks, this configuration raises observed GR00T N1.7 success from $80.0\%$ with uniform W4A4 to $92.5\%$ over 80 trials per configuration, with a measured additional Orin latency of 1 ms.
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All authors Hung T. Ho, Khanh D. Nguyen, Quang D. Nguyen, Thanh Q. Duong, Ngan Le, Meng Guo, Vien A. Ngo, An T. Le
Systems and Control · Cross-listed from math.OC
Benign Geometry and Distributional Robustness of $\mathcal{H}_2$ Synthesis
Arman Sharifi Kolarijani, Peyman Mohajerin Esfahani, Tamás Keviczky et al. (+1 more)
In this paper, we study standard and distributionally robust $\mathcal{H}_2$ synthesis problem of a stabilizing state-feedback controller for discrete-time linear time-invariant systems. Without requiring a nonsingular disturbance controllability Gramian or a positive-definite control penalty, we establish that stationarity of a stabilizing gain in standard $\mathcal{H}_2$ synthesis is equivalent to global optimality and derive an exact Pythagorean identity for the performance difference. We then generalize the $\mathcal{H}_2$ synthesis problem by considering i.i.d. disturbances with zero mean and uniformly bounded second moments, and extend the stationarity-optimality equivalence to the corresponding distributionally robust $\mathcal{H}_2$ synthesis. Moreover, we show that every standard $\mathcal{H}_2$-optimal gain is simultaneously optimal for every such distributionally robust problem. Finally, we specialize the framework to Frobenius, Kullback–Leibler, and Wasserstein-2 ambiguity sets and obtain explicit characterizations of their worst-case covariances, which, in turn, provide performance certificates for a common optimal controller.
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All authors Arman Sharifi Kolarijani, Peyman Mohajerin Esfahani, Tamás Keviczky, Mohamad Amin Sharifi Kolarijani
Systems and Control · Cross-listed from cs.RO
Multi-Agent Transportation of Free-Flyers in Microgravity Via Pushing Interaction Under Human-in-the-Loop Control
Gregorio Marchesini, Nicola De Carli, Sihyun Cho et al. (+5 more)
We propose a safety-critical framework for the cooperative transportation of passive targets in microgravity, where a team of chaser
robots acts through unilateral pushing contacts to track a human-provided desired twist while ensuring safe target motion. The pushing-only nature of the interaction introduces sparse, configuration-dependent actuation constraints requiring chasers to physically relocate on the target body when the desired pushing allocation changes. To address these challenges, we formulate a delay-aware feedback control architecture leveraging Control Lyapunov Function (CLF) and Control Barrier Function (CBF) constraints within a mixed-integer thrust allocation program to enforce stability and safety of the target, respectively. The proposed framework enables reference tracking while guaranteeing obstacle avoidance with a circular obstacle despite intermittent control authority, providing a foundation for human-supervised cooperative transportation of free-flyers in space environments. The proposed framework is validated through Gazebo simulations.
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All authors Gregorio Marchesini, Nicola De Carli, Sihyun Cho, Youngkyoung Kong, Elias Krantz, Mani Hemanth Dhullipalla, Dimos V. Dimarogonas, H. Jin Kim
Systems and Control
Assessment of the N-1 voltage security of a future Nordic energy system
Luis Kuhrmann, Peiyuan Chen, Lisa Göransson et al. (+1 more)
Capacity Expansion - Energy System Models (CE-ESMs) have been widely used to optimize the decarbonization of future energy systems on national and continental scales. To capture the limitations in electricity trade between different parts of the system investigated, CE-ESMs often include a representation of the transmission grid. However, CE-ESMs usually only include linearized representations of the grid and omit or strongly simplify grid stability requirements. In this work, we evaluate the N-1 voltage security of the electricity system results obtained from a CE-ESM of a decarbonized Nordic energy system in Year 2050, and analyze the effects of different grid code requirements and shunt capacitor and reactor automation on voltage security. For comparison, we evaluate a Year 2022 system based on ENTSO-E data.We show that the CE-ESM results for the Nordic countries are not N-1 voltage-secure and that, depending on the grid code and shunt automation requirements, the contingencies with voltage violations range from 1.1% to 17.4%. Furthermore, the results indicate that both Power Park Module voltage control and shunt extreme voltage automation have strong positive effects on voltage security in the modeled future system. Grid regions with low levels generation, and thus little dynamic reactive power from generators, are found to be the most at risk of being voltage-insecure.
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All authors Luis Kuhrmann, Peiyuan Chen, Lisa Göransson, Filip Johnsson
Systems and Control
An Algebraic Observer for State-Affine Systems
Romeo Ortega, Alexey Bobtsov, Anton Pyrkin et al. (+1 more)
We present a new systematic method to design an algebraic swapping lemma observer for nonlinear systems which are affine in the state. Four are the main features of the new observer: (i) Far superior transient performance compared to standard asymptotically convergent observers; (ii) structural simplicity - its construction relies solely on basic linear filtering and a single
matrix inversion; (iii) applicability to non-uniformly-completely-observable systems, for which classical methods are not applicable; (iv) straightforward extension to the cases of unknown time-varying parameters and measurement delay. The core idea exploited in the paper is to combine the construction of a generalized parameter estimation-based observer with a simple filtering technique to derive the algebraic observer. The resulting design is shown to apply to a class of state-affine systems satisfying a weak generic condition. Moreover, it is established that for time-invariant systems, this condition is always satisfied globally.
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All authors Romeo Ortega, Alexey Bobtsov, Anton Pyrkin, Olga Zarina
Systems and Control
Nonlinear Dynamic Modeling and Receding-Horizon NMPC of an Electric Unicycle on a Tensioned Cable
Yousef Sweiti and Jasem Tamimi
Traversing flexible slender structures involves strong bidirectional coupling between vehicle motion and structural vibration caused by a moving contact point. This paper presents a nonlinear modeling-and-control framework for an electric unicycle traversing a tensioned flexible cable. The cable is modeled using a tension-dominated finite-element formulation retaining vertical and lateral transverse dynamics, and is coupled to the unicycle roll and pitch dynamics through moving-contact kinematics. A modal truncation yields a control-oriented reduced-order model that preserves the nonlinear vehicle–cable coupling. Based on this model, a constrained nonlinear model predictive controller is formulated to regulate traversal, balance, actuator limits, and cable-span constraints. To reduce the computational burden associated with moving-contact interpolation, a frozen spatial contact-point interpolation strategy is introduced for the NMPC prediction model. Numerical studies under nominal, disturbed, constrained, and model-mismatch scenarios show accurate traversal, roll and pitch stabilization, attenuation of cable vibrations, and constraint-consistent closed-loop behavior. The frozen-interpolation formulation reduces and regularizes NMPC computation times relative to the non-frozen formulation, supporting its use as a computationally tractable approach for finite-element-based moving-contact vehicle–structure interaction systems.
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Systems and Control · Cross-listed from cs.RO
vla.simd: Efficient CPU Inference for Language-Conditioned Manipulation
Khanh D. Nguyen, Hoang M. Truong and An T. Le
Deploying
language-conditioned manipulation without a dedicated GPU requires efficient inference and action chunks that cover the delay between policy queries. We present vla.simd, a CPU inference engine that combines shared SIMD micro-kernels, reusable computation, and target-specific optimization. We relate query latency and execution horizon to action availability under lagged and time-aligned execution, distinguishing action supply from feedback frequency. Across six policies and four CPUs, vla.simd achieves approximately $1.4\times$ median speedup over compiled PyTorch references while preserving fp32 numerical fidelity. We also introduce IMPACT, an ACT-based policy with cached text representations and
language-modulated visual features. IMPACT is the only
language-conditioned policy in our evaluated set that supplies at least 30 actions/s on the Raspberry Pi 5: after a 90 s thermal soak, it supplies 33.5 actions/s in fp32 and 81.2 with int8. Separate GPU evaluations yield $76.4\%$ mean success across four LIBERO suites without
robot pretraining; instruction-shuffling tests demonstrate selection among familiar goals. Trials with IMPACT on an SO-101 arm and SmolVLA on a UR10e with a Robotiq gripper demonstrate CPU deployment on two
robot embodiments.
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Systems and Control
Equivalent Modeling of Load-Side Systems With Distributed Renewable Generation Considering Fault Responses and Nodal Voltage Coherence
Yuqi Cao, Chen Shen, Shaowei Huang et al. (+2 more)
Operating conditions and fault severity change both the initial states and control modes of active distribution networks. Direct capacity aggregation can therefore lose the power responses required for transmission-system dynamic analysis. This paper develops a procedure for generating low-order physical electromagnetic transient equivalents from a small set of representative operating conditions. Device power, ride-through states, load mechanical states, and local sequence voltages are combined with electrical distance to form response families. Response reconstruction and terminal simulation errors determine the retained architecture, after which bounded sensitivity calculations determine effective dynamic coefficients. The architecture and coefficients are then fixed. For a new operating condition, capacity and power balances, voltage-dependent load relations, and an initialization correction generate the model parameters from static inputs and power-flow results. A representative severe fault establishes a template for each fault type, which is reused across fault depths. Aggregation and switching-time bounds explain the roles of voltage coherence and state separation. Comparisons with direct aggregation show improved terminal responses across operating conditions and several fault types, with the largest gains under severe unbalanced faults. The method provides a reusable physical equivalent for operating-condition studies and fault-depth screening.
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All authors Yuqi Cao, Chen Shen, Shaowei Huang, Ying Chen, Hongyi Zhu
Systems and Control · Cross-listed from math.OC
Global Exponential Stabilization of a 3D Nonholonomic Vehicle in Spherical Coordinates
Kwang Hak Kim, Velimir Todorovski and Miroslav Krstic
Many spatial (3D) vehicles, including AUVs and fixed-wing aircraft, are effectively nonholonomic and subject to limited actuation, such that continuous time-invariant stabilization is fundamentally obstructed by Brockett's necessary condition. To overcome this obstruction, we exploit the
geometric singularity of spherical coordinates to design a backstepping continuous, time-invariant feedback law that exponentially stabilizes a 3D nonholonomic vehicle actuated solely by forward surge velocity, pitch rate, and yaw rate. The resulting closed-loop region of attraction excludes only the coordinate singularity, codimension-two, measure-zero set of initial conditions in which the vehicle lies on the line through the target orthogonal to the target plane, thereby covering the largest possible domain. We further construct a strict control Lyapunov function to prove global exponential stability of the origin on this domain with a user-specified decay rate, while simultaneously preventing the system from approaching the singular set. Finally, we show that the closed-loop system is exponentially attractive to the origin in Cartesian coordinates. Numerical simulation examples in both spherical and Cartesian coordinates illustrate the effectiveness of the control law.
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Systems and Control
Remote State Estimation with Unreliable Communication: Information Asymmetry and Belief Structure
Ioannis Tzortzis and Themistoklis Charalambous
In this paper, we study remote state estimation under unreliable forward and feedback communication between a smart sensor and a remote
estimator. When the sensor cannot perfectly reconstruct the filtering state maintained by the remote
estimator, an information asymmetry arises between the two sides of the network. To analyze this asymmetry, we first characterize the internal state maintained by the remote
estimator and its
evolution under the packet reception process. The sensor's uncertainty about this state is then captured through a belief conditioned on its information set, and we derive a recursive update under noisy acknowledgment feedback. Finally, we show that the resulting belief admits a finite Gaussian mixture representation whose number of components grows at most linearly over time, ensuring computational tractability. Simulation results illustrate the impact of information asymmetry on the estimation performance and demonstrate the effectiveness of the proposed framework.
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Systems and Control · Cross-listed from eess.AS
Performance Analysis and Design of an Optomechanical Microphone Using an Integrated Photonic Waveguide Interferometer
Xiaoyu Niu, Yuqi Meng, Zihuan Liu et al. (+2 more)
We present an optomechanical microphone based on a diaphragm-integrated photonic waveguide Mach-Zehnder interferometer. Acoustic pressure deforms the MEMS diaphragm, inducing strain in the sensing waveguide and changing its optical path length. We analytically evaluate the optical and mechanical transduction mechanisms and key figures of merit, including signal-to-noise ratio, dynamic range, acoustic overload pressure, and minimum detectable pressure. Two design cases are considered: a MEMS microphone and a measurement microphone. The results indicate competitive performance but no substantial overall advantage over state-of-the-art microphones in conventional applications. The architecture may nevertheless offer advantages for high-temperature and other harsh-environment sensing applications.
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All authors Xiaoyu Niu, Yuqi Meng, Zihuan Liu, Ehsan Vatankhah, Neal Hall
Systems and Control
The Operational Value of Spatial Dependence in Renewable Forecast Scenarios for Single-Period Economic Dispatch: A Controlled Ablation Study
Jayakumar Manoharan
Renewable forecasts are evaluated by statistical skill (e.g., CRPS), but grid operators pay for realized dispatch cost. We diagnose what drives dispatch value in a single-period newsvendor-style economic dispatch using real public data from two European transmission systems (CWE, DE-4TSO). Spatial coherence across forecast sites falls below the pre-specified 1% practical-significance threshold: a controlled ablation holding per-zone marginal forecasts bit-identical and varying only cross-zone dependence (10 configurations, 3 seeds, paired-bootstrap confidence intervals) shows a coherence gain of at most 0.64% of dispatch cost, indistinguishable from zero in 3 of 10 configurations, reached only under an unrealistic 8-fold forecast-error stress test. Decision-focused training, an established paradigm in this venue, delivers a robust 2.82-5.19% gain. A parametric Gaussian-copula approximation matches the empirical copula at realistic error magnitudes but performs worse than no dependence under extreme stress. A single-seed sweep shows that a 12% energy-score gain changes cost by less than 0.1%. Results characterize this single-period dispatch class; a lightweight four-period extension supports the same conclusion. For this dispatch class, spatially-correlated scenario generation provides limited operational value on its own; grid operators and forecast vendors should instead evaluate dependence models by downstream decision value and prioritize decision-focused training.
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Systems and Control
Sufficient and Necessary Smooth Barrier-like Conditions for Continuous-Time Stochastic Reach-Avoid Verification
Bai Xue
In this paper, we study infinite-horizon reach-avoid verification for continuous-time
stochastic systems modeled by
stochastic differential equations (SDEs). We formulate this problem within a barrier-function-based framework, which transforms the verification problem into an existence problem for barrier functions satisfying barrier-like conditions expressed as functional inequalities. We provide sufficient and necessary barrier-like conditions in terms of
polynomial barrier functions for infinite-horizon reach-avoid verification under suitable regularity and uniform ellipticity assumptions. We first construct a discounted value function that characterizes lower bounds on the reach-avoid probability. We then show that it is the unique classical solution of an associated elliptic Dirichlet problem. Based on this characterization, we further show that the barrier-like condition proposed in our previous work on finite-horizon reach-avoid verification is not only sufficient for infinite-horizon reach-avoid verification but also necessary whenever the reach-avoid probability is strictly larger than the specified threshold. In particular, whenever the reach-avoid probability is strictly larger than the specified threshold fro every state in the initial set,
polynomial barrier functions satisfying this barrier-like condition exist. Furthermore, when the system dynamics are
polynomial, we formulate the problem of finding
polynomial barrier functions satisfying this barrier-like condition as sum-of-squares (SOS) programs, which are shown to be sound and complete. Finally, we demonstrate the theoretical results on two numerical examples.
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Systems and Control
Sufficient and Necessary Continuous Barrier-like Conditions for Discrete-Time Stochastic Reach-Avoid Verification
Bai Xue
This paper develops necessary and sufficient barrier-like characterizations using continuous barrier functions for infinite-horizon reach-avoid verification of discrete-time
stochastic systems. Existing results establish necessary and sufficient conditions in terms of functional inequalities involving measurable or lower semicontinuous barrier functions. However, the limited regularity of such functions may hinder their numerical approximation and computational synthesis. Building on our previous barrier-like condition for finite-horizon reach-avoid verification, we show that this condition can also be used for infinite-horizon reach-avoid verification and, under a uniform absolute continuity condition on the transition kernels, admits a continuous barrier function whenever the exact reach-avoid probability is strictly larger than the prescribed threshold for every state in the initial set. We further show that the resulting continuous barrier function can be uniformly approximated by a
polynomial one while preserving the required barrier-like conditions. For
polynomial systems, we formulate these conditions as
polynomial positivity constraints over compact basic semialgebraic sets. Putinar's Positivstellensatz then converts the positivity conditions into sum-of-squares (SOS) certificates, yielding semidefinite programming (SDP) formulations for synthesizing
polynomial barrier functions. We establish both soundness and completeness of the resulting SOS-based procedure. Finally, two numerical examples illustrate the theoretical results and demonstrate the resulting SDP approach.
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