Systems and Control
Predefined-Time Leaderless Consensus Under Denial-of-Service Attacks
Lohitvel Gopikannan, Shashi Ranjan Kumar and Abhinav Sinha
This paper addresses predefined-time resilient consensus of leaderless second-order nonlinear multi-
agent systems under denial-of-service (DoS) attacks, motivated by coordination requirements in safety-critical applications. The
agents are subject to bounded external disturbances and communicate over a strongly connected directed graph whose links are simultaneously disabled during attacks. We develop a switching sliding-mode protocol with the objective of reaching an invariant
manifold of position and velocity agreement. The protocol uses relative position and velocity information during attack-free intervals and local velocity feedback during communication blackouts. A time-scaling function remains constant during each blackout and resumes evolving when communication is restored, accounting for the time available for consensus. Under bounds on attack duration and frequency, we derive sufficient gain conditions through a Lyapunov analysis. We show that, despite bounded disturbances, the
agents achieve position and velocity consensus by a realistic settling time equal to a prescribed convergence duration plus the cumulative attack duration up to the realistic settling time. The prescribed convergence duration is independent of the initial conditions, and the realistic settling time reduces to that duration in the absence of attacks.
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Systems and Control
Construction of Control Lyapunov-Barrier Functions from CLF-CBF Pairs
Bo Wang and Miroslav Krstic
This paper studies the construction of control Lyapunov-barrier functions (CLBFs) from a given control Lyapunov function (CLF) $V$ and control barrier function (CBF) $h$. We consider functions of the form $W=F(V,h)$ that increase with the CLF value and do not increase with the barrier value, and show that the CLBF decrease condition is completely characterized by a nonnegative scalar weight that governs the relative contributions of the CLF and CBF. Because this weight depends only on $(V,h)$, the same value must satisfy the decrease condition at all states sharing the same CLF and CBF values, which leads to a joint-level-set admissibility condition. We then construct CLBFs from admissible weights through a first-order partial differential equation (PDE) and obtain explicit multiplicative and power-type families as special cases. We further identify an integrability obstruction showing that admissibility alone does not guarantee properness. Two nonlinear examples illustrate the constructions and demonstrate safe stabilization in cases where feedback based on the original CLF violates the safety constraint.
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Systems and Control
Mixed-integer optimization for multi-year military aircraft fleet management
Matteo Vescovi, Raffaele Giuseppe Cestari, Roberto Valdambrini et al. (+3 more)
While existing strategies for Flight and Maintenance Planning for the defense sector generally address idealized conditions, real-world planning often involve non-nominal initial fleet states and complex inspection schemes. To address these challenges, we propose a multi-year planning strategy that maximizes long-term fleet availability. The formulation incorporates multiple competing objectives capturing the tight coupling between aircraft usage and maintenance, while enforcing cyclic inspection requirements and limited maintenance-dock capacity. To enhance practical applicability, we introduce three complementary strategies: a receding-horizon approach to reduce computational burden, a
Bayesian Optimization routine to automatically tune cost-function coefficients, and an aircraft-specific weighting scheme that adapts model priorities based on fleet-condition statistics. Results on three realistic
benchmark scenarios demonstrate the effectiveness of the approach.
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All authors Matteo Vescovi, Raffaele Giuseppe Cestari, Roberto Valdambrini, Andrea Mercurio, Valentina Breschi, Mara Tanelli
Systems and Control
Elementwise Positivity of the Solution to Lyapunov Equation for Hurwitz Companion Matrices
Miaomiao Wang, Patrizio Colaneri and Jie Chen
We prove, with the aid of AI, that for every real symmetric forcing
matrix $Q\succeq0$, the unique solution of a continuous-time Lyapunov equation is entrywise nonnegative whenever the state
matrix is a real Hurwitz companion
matrix. This proves an earlier
conjecture. The proof makes no assumption on the spectrum of the state
matrix, and is made possible by means of using Horner
polynomial matrices. We also show that discrete-time counterpart of the
conjecture is false: Counterexamples can be readily constructed to show that Schur companion
matrices, including one generated by a
polynomial with all positive coefficients, yield solutions with negative off-diagonal entries even with identity forcing.
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Systems and Control · Cross-listed from cs.ET
From Grid to Chip: Power Architecture, Stability, and Flexibility of AI Data Centers
Yubo Song, Rui Kong, Takuro Umihara et al. (+3 more)
The rapid growth of artificial intelligence (AI) computing is transforming data centers into large, dynamic electrical loads. Their deployment is primarily constrained by energy availability and grid-connection capacity, which is further aggravated by the ability of power-delivery architectures, control systems, and computing workloads to operate reliably during fast grid disturbances. This article presents a technological perspective on AI data centers as grid-interactive computing systems. First, it reviews grid-integration bottlenecks, evolving connection policies, grid-code requirements, which has fostered new technological trends via spatio-temporal flexibility available through workload orchestration, cooling systems, on-site resources, and energy storage. Second, it maps the
evolution of power-delivery architectures from medium-voltage grid interfaces to chip-level, discussing higher-voltage DC distribution, solid-state
transformers, wide-bandgap devices, advanced chip-level power delivery, and
liquid cooling. Third, it establishes a three-level stability framework spanning rack-level DC-bus dynamics, facility-level converter interactions, and system-level grid-coupled behavior. The framework connects dominant instability mechanisms, including constant power load effects, impedance interactions, forced oscillations, and operating-mode transitions, with suitable modeling, assessment, and mitigation approaches. Synthesizing these topics, this article highlights grid-to-chip co-design as a central requirement for scalable AI infrastructure, linking computing workloads, power-delivery systems, energy buffers, and grid operation.
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All authors Yubo Song, Rui Kong, Takuro Umihara, Pooya Davari, Frede Blaabjerg, Subham Sahoo
Systems and Control · Cross-listed from cs.AI
Distributed Optimization of Modular Production Systems using Model-based Reinforcement Learning with Inverse Models
Andreas Schwung, Steve Yuwono, Sofiene Lassoued et al. (+1 more)
This paper presents a novel approach for data-driven self-learning control of highly flexible, modular manufacturing systems. Specifically, we employ a novel framework for model-based reinforcement learning which introduces approximate inverse process models within the training of reinforcement policies. This approach disentangles the learning of actuation dynamics and the dynamics in state space, resulting in RL-based training solely within the task space. We propose a lightweight feedforward architecture for approximate inverse models and integrate them within the policy network of standard RL
algorithms. We apply the approach to a laboratory modular production testbed with heterogeneous production modules. The results underline the efficiency improvements for modular manufacturing units in terms of both performance and training speed, particularly for off-policy
algorithms.
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All authors Andreas Schwung, Steve Yuwono, Sofiene Lassoued, Dorothea Schwung
Systems and Control
Critic-Free Policy Iteration for Continuous-Time Zero-Sum Games: A Policy-Space Riccati Approach
Jiacheng Wu, Yang Zhu and Hongye Su
This paper develops a critic-free policy iteration (PI) method for continuous-time linear zero-sum games. The central idea is to characterize the saddle-point policies directly in the joint policy space, rather than treating the quadratic value
matrix as an iterative variable. A policy game Riccati equation (PGRE) is introduced whose unknowns are policy gains only. Its solutions are shown to be in one-to-one correspondence with the symmetric solutions of the game algebraic Riccati equation. Based on a stabilizing anchor, PI is performed directly in the actor space. The actor-space Jacobian is nonsingular at every stabilizing policy, and the resulting policy sequence coincides with that of simultaneous PI. For unknown dynamics, a data-driven
algorithm uses a single batch of data and nullspace projection of endpoint increments to eliminate the value
matrix, yielding an actor-only regression. A necessary and sufficient rank condition for unique policy recovery is established and shown to be iteration-invariant, demonstrating that critic identifiability is unnecessary. A power systems frequency-regulation example verifies convergence and policy recovery, while scalability tests demonstrate substantial reductions in computational and
memory requirements.
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Systems and Control
A Primal-Dual Formulation for Pricing Static Voltage Stability Services within a Unit Commitment Model
Peng Wang and Luis Badesa
In modern power systems with high penetration of Inverter-Based Resources (IBR), most converters operate in Grid-Following (GFL) mode. Some buses exhibit inherently low Short-
Circuit Ratios (SCRs), a property majorly shaped by network
topology. The integration of GFL-IBR onto such weak buses thus demands
attention to static voltage stability. To address this issue,
market mechanisms have been proposed to incentivize generators to provide voltage stability services, such as commitment of synchronous generators for reducing the equivalent impedance at low SCR buses and adaptive reactive power support from GFL-IBR. To compute shadow prices for these services, previously proposed methods such as the `restricted' and `dispatchable' approaches may fail to guarantee operating cost recovery for voltage-stability service providers. As the resulting prices are determined purely from a social surplus maximization objective, the profitability of units is entirely overlooked. This suggests that new pricing methodologies are needed to satisfy cost-recovery requirements. Therefore, this paper proposes a pricing method based on a primal-dual formulation. Case studies demonstrate that the proposed method can consistently produce revenue-adequate shadow prices, enabling all participating units to recover their costs without supplementary uplift payments.
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Systems and Control · Cross-listed from math.OC
Asynchronous Replanning in Two Population Linear Quadratic Mean Field Games: Information Requirements and Stability
Yuxin Jin, Wang Yao and Xiao Zhang
We study asynchronous continuation replanning in a two-population linear–quadratic mean field game with deterministic open-loop controls and heterogeneous, possibly erroneous initial information. At exogenous opportunities, one population recomputes its continuation response from the physical aggregate state reached, with the opponent's active plan frozen. The state–plan target needed to initialize replanning is recoverable from local aggregate observations if and only if a kernel-inclusion condition holds; full recovery of the hidden initial input is unnecessary. For revisions accumulating before the terminal time, spectral stability of the limiting two-response cycle yields bounded physical execution and a finite state left limit. The zero-extended continuation plans then converge strongly to the mean field
equilibrium restarted from that state. A scalar counterexample shows that well-posed continuation problems and a convergent physical state can coexist with divergent remaining plans. We also construct an exact causal implementation from local aggregate observations and establish finite-population robustness on every fixed finite opportunity prefix. Revision records match with probability tending to one, and the mean-square implementation error truncated to the matching event is \(O(N_*^{-1})\), where \(N_*\) is the smaller population size.
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Systems and Control
Quantifying the Unintentional Islanding Risk: A Comparative Study on Active Distribution Network
Harshit Nayak, Edoardo Daccò, Jose Luis Rueda Torres et al. (+1 more)
The growing share of Inverter-Based Resources (IBRs) is changing the operation of modern Active Distribution Networks (ADNs), raising concerns for grid stability, protection, and reliability. In this paper, we investigate the dynamic behavior of a Medium-Voltage (MV) portion of an ADN during the transition from grid-connected to islanded operation. The study considers a Grid-Following (GFL) converter and Synchronous Generators (SGs) operated under two distinct regulation modes: a fixed-setpoint, non-regulating condition representative of present-day distribution networks, and an active frequency/voltage-regulating condition representative of SGs equipped with governor and AVR control. Detailed electromagnetic transient (EMT) models of both technologies have been developed in DIgSILENT PowerFactory that quantifies the sensitivity of island persistence to SG regulation mode and inertia. The results show that when DERs operate at a fixed power setpoint, the risk of forming a sustained, undetected electrical island is limited, since the isolated network drifts out of the protection thresholds within tens of seconds. Conversely, enabling frequency and voltage regulation on the SGs is sufficient to sustain an unintentional island indefinitely without triggering conventional protection, regardless of system inertia.
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All authors Harshit Nayak, Edoardo Daccò, Jose Luis Rueda Torres, Davide Falabretti
Systems and Control · Cross-listed from cs.RO
GeoTrussRover: Morphological Computation with Contact-Semantic Control Primitives
Muyuan Ma, Yi Zhang, Yang Yang et al. (+12 more)
Reconfigurable
robots can change their contact geometry when a fixed body cannot negotiate an obstacle. A variable-geometry truss (VGT) distributes this shape change through a load-bearing structure, but coupling it to a mobile base creates a high-dimensional coordination problem. GeoTrussRover combines an electrically actuated VGT, a wheeled base, and contact-semantic morphology planning and control. We solve one source traversal and extract four contact-semantic primitives that describe coordination among 21 members. Physics-constrained projection adapts them to unseen step heights with the same contact
topology. When every phase remains feasible, adaptation does not recompute the complete motion. If one phase violates the new physical constraints, only that phase is recomputed. A full-space QP then tracks the adapted motion and corrects member and wheel errors. For transfer from 0.10m to 0.075m, the method reduces objective-function evaluations by 63.7% relative to full recomputation. Contact-phase feasibility analysis covers step heights from 0.10 to 0.46m, or 1.08 to 4.97 wheel radii, with the upper value near the theoretical feasible boundary. The electric prototype traverses 2.11 wheel radii. The resulting low-dimensional representation stores task coordination in a hyper-redundant, load-bearing morphology and reuses it during locomotion.
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All authors Muyuan Ma, Yi Zhang, Yang Yang, Xuanyan Zheng, Ruiqi Hu, Boxuan Ke, Zhenyu Chen, Yicong Lin, Xin Hao Yang, Daliang Xiao, Zhinan Hou, Wanhao Niu, Yuan Sun, Yan Yang, Yue Xie
Systems and Control · Cross-listed from cs.LG
Estimating Inconsistency Response Surfaces under Uncertainty in Cyber-Physical System Development
Johannes Mäkelburg, Tim Schwabe and Maribel Acosta
Cyber-Physical Systems (CPS) are commonly represented through multiple interconnected models. During development, CPS consistency requires that shared model elements remain compatible across these models. Uncertainty, for example, due to sensor noise or model abstraction, changes the admissible values of model elements and can introduce inconsistencies, i.e., situations in which models can no longer be jointly satisfied. While existing approaches can determine consistency for a given uncertainty configuration, they provide limited support for systematically exploring, analyzing, and explaining inconsistency across large uncertainty spaces. We address this challenge by reformulating inconsistency as an intervention response modeling problem. Using Saltelli sampling and multi-fidelity Monte Carlo estimation, we generate intervention-response
datasets and train a surrogate model that directly predicts inconsistency from the propagated uncertainty geometry. Experiments on 48 scenarios and 10 CPS domains show that the surrogate matches Monte Carlo estimates while reducing evaluation time from milliseconds to microseconds, enabling orders-of-magnitude more response-surface evaluations within fixed computational budgets. Building on the learned response surfaces, we perform sensitivity analysis to identify dominant uncertainty drivers and introduce a gradient-based consistency recourse method to determine minimal uncertainty interventions that restore consistency. The results show that inconsistency under uncertainty can be effectively learned, analyzed, and repaired through response-surface modeling, providing a scalable foundation for uncertainty-aware consistency management in CPS development.
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Systems and Control · Cross-listed from math.OC
Optimal chemo-immunotherapy scheduling: A hybrid QPSO-SQP approach with Michaelis-Menten pharmacodynamics
Bereket Sitotaw Kidane, Md Samiul Haque Motayed and Shuo Wang
Optimal scheduling of combined chemo-immunotherapy is often formulated as a control-affine optimal control problem, which generically yields boundary-selected (bang-bang-type) protocols unless singular arcs occur. This structure, while convenient, neglects saturating pharmacodynamics at high dose rates. We incorporate Michaelis-Menten saturation directly into the therapy channels, making the dynamics non-control-affine and the
Hamiltonian nonlinear in each control. With strictly positive exposure penalties, the
Hamiltonian admits an explicit three-regime pointwise minimization law: each input is chosen at the lower bound, the upper bound, or as a unique interior minimizer. On interior intervals the strict Legendre condition holds, so continuously modulated dosing arises as a regular interior extremal rather than a singular-arc or smoothing artifact. The resulting transcription is nonconvex; we therefore use a hybrid
Quantum Particle Swarm Optimization (QPSO)-Sequential Quadratic Programming (SQP) pipeline, where QPSO provides a constraint-aware warm start and SQP enforces feasibility and Karush-Kuhn-Tucker (KKT) optimality on a collocation grid. Costate reconstruction corroborates the Pontryagin Minimum Principle (PMP) structure and the predicted boundary/interior regime transitions.
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Systems and Control · Cross-listed from math.OC
Optimal Control for Cancer Chemotherapy Using Hybrid Quantum Particle Swarm Optimization
Bereket Sitotaw Kidane, Md Samiul Haque Motayed and Shuo Wang
Optimal control in cancer chemotherapy is challenged by tumor heterogeneity and mutations, which complicate treatment effectiveness. Traditional methods, such as Pontryagin's maximum principle (PMP), are often hindered by their reliance on an initial guess for the costate equation, affecting accuracy and convergence. To address these limitations, this work introduces a hybrid
quantum particle swarm optimization (QPSO) method based on regularization. QPSO is employed for global exploration to approximate the optimal control trajectory, followed by a regularization-based refinement to ensure smoothness and consistency with optimality conditions. The
Hamiltonian function is used for first- and second-order optimality checks, verifying solution quality. Numerical case studies explore various drug effectiveness functions, demonstrating the role of periodic and localized drug delivery in achieving robust tumor suppression and providing insights into the impact of different drug combinations on optimal chemotherapy strategies.
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Systems and Control
A Counterexample to Two Representative Unit Aggregation Formulations for Unit Commitment
Zixuan Duan and Zhengshuo Li
Unit aggregation removes
symmetry among identical generators in unit commitment, but an aggregate formulation is feasible-region exact only if every aggregate trajectory it admits has a feasible unit-level realization. This letter shows that two commonly used aggregation formulations for slow-ramping units, i.e., p-clustered unit commitment (PCUC) and tight unit aggregation (TUA), cannot satisfy this requirement. We construct a counterexample that satisfies all aggregate constraints of both formulations yet admits no feasible disaggregation. This counterexample reveals a limitation common to both formulations: they do not guarantee intertemporal consistency of unit-level output allocations. Experiments on the replication cases reported in published literature further verify that such infeasibility of disaggregation can even occur in optimal solutions of aggregate models. This letter demonstrates that PCUC and TUA can still overestimate ramping flexibility. Developing exact aggregation models that can be solved efficiently for identical slow-ramping units remains a challenge.
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Systems and Control
Exact PID and PI Gain Regions for Uncertain Non-Affine MIMO Systems
Cheng Zhao
Characterizing all PID gains that guarantee uniform exponential regulation of uncertain nonlinear systems remains a fundamental problem. Most existing results provide only sufficient conditions derived from a particular Lyapunov construction. This paper gives exact gain regions, defined directly by uniform regulation over the entire uncertainty class, for two classes of nonaffine
MIMO systems with $m\ge2$ controlled coordinates and input channels. For systems of second order under PID control, we independently characterize a common quadratic inner region and an outer region based on a linear subclass. The two regions coincide and therefore characterize the PID gain region exactly at the system level. For systems of first order under PI control, a lossless reduction to a linear family on the uncertainty boundary, combined with a common quadratic certificate, yields the exact PI region. Both regions strictly enlarge existing sufficient regions, and the PID result also provides a sequential tuning rule. A compact linear family with one uncertain parameter shows that common quadratic certification is not generally lossless. These results establish endpoint coincidence and boundary family equivalence as two routes to exact gain regions and motivate the broader question of which nonlinear uncertainty classes admit such characterizations.
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Systems and Control
Quantifying the Reality Gap for RL-Based UAV Placement at mmWave and Sub-THz
Abdullateef Almohamad, Mostafa Ibrahim, Sabit Ekin et al. (+1 more)
Reinforcement learning (RL) policies for unmanned aerial vehicle (
UAV) placement in mmWave and sub-terahertz networks are typically trained on simplified analytical channels. We quantify the resulting sim-to-real gap on a real urban map of Doha, Qatar, at carriers {28, 140, 183, 300} GHz and altitudes {50, 75, 100, 125} m, evaluating three channel pipelines: an analytical model (FSPL + atmospheric absorption + cuboid LoS), full Monte-Carlo ray tracing in Sionna RT with ITU-R P.676-13 absorption, and a deterministic-LoS hybrid that reuses Sionna's mesh under a closed-form path-gain expression. We formalize the gap on the spatial SNR distribution via four metrics, namely bias, RMSE, Jensen-Shannon divergence, and optimum-deployment displacement. Three findings emerge: at 28/140 GHz, $\sim$70% of the apparent -5.6/-4.8 dB Sionna bias is Monte-Carlo undersampling and shrinks to -1.7/-1.5 dB after mitigation; at 183 GHz a -9.2 dB residual isolates the atmospheric absorption / ITU-R P.676 line-shape disagreement; at 300 GHz the
stochastic ray tracer agrees with the analytical model only coincidentally, with a +3.8 dB structural offset exposed by the deterministic-LoS pipeline. Across all carriers the linear-domain regret of the analytical-trained policy stays $\geq$ 0.93, indicating practical near-optimality but with a carrier-resolved SNR bias that warrants explicit reporting.
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All authors Abdullateef Almohamad, Mostafa Ibrahim, Sabit Ekin, Khalid Qaraqe
Systems and Control · Cross-listed from cs.RO
Freehand Sketching for End-User Programming of Robot Swarms
Riwa Karam, Ian Kuo and Magnus Egerstedt
Robot swarms are increasingly used in applications where accessible interaction with non-expert users is desirable. This paper investigates freehand sketching as an end-user programming interface for specifying
robot swarm geometries. Users communicate spatial intent through a drawing, while the swarm autonomously extracts target formation points, constructs a rigid formation graph, assigns
robots to formation nodes, and executes distributed formation control with a guarantee against unintended reflected formations. The resulting sketch-to-swarm framework is evaluated through a human study examining the usability of freehand formation specification. Twenty participants generated $42$
geometric shapes, and the interface achieved a mean System Usability Scale score of $84.25$, which conventionally indicates high perceived usability. The results support freehand sketching as an intuitive interaction abstraction for human-swarm collaboration without requiring robotics or programming expertise.
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Systems and Control
Fusion Estimation in Multi-sensor Systems for Data Packets with Disrupted Identities
Haoyuan Xu and Yuzhe Li
In this paper, we explore the problem of fusion estimation for a multi-sensor system where the identity of the data packet received by each sensor may be disrupted or incorrect due to confusion in device identity allocation, communication protocol defects, or the lack of a clear sensor identifier. This can result in a random shuffle of the data components during the fusion estimation process, compromising the performance of the fusion estimation. To address this issue, we introduce the concepts of permutations and
symmetry groups to describe this phenomenon as data packet permutation. We construct statistics to simplify the information set, developing two
algorithms: a
Bayesian approach, which performs fusion using posterior arrangement probabilities, and a greedy approach, which effectively improves estimation performance by guessing the likely data arrangement. We compare these two
algorithms and demonstrate that both are expectation error-bounded. We improve
algorithms for information-scarce scenarios. By employing the expectation-maximization
algorithm, we fill in the prior information of data arrangement where the correct convergence is proven. Finally, we present numerical simulations to validate our results.
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Systems and Control · Cross-listed from cs.CR
BenchShield: Formal Model-Backed Instrumentation for Reward Integrity in LLM-Agent Evaluation Infrastructure
Shenghan Zheng, Zonglin Di, Yimin Liu et al. (+19 more)
LM-
agent benchmarks increasingly function as interactive evaluation infrastructure.
Agents observe state, call tools, modify workspaces, submit artifacts, and receive rewards from outcome procedures. This interactivity makes evaluations vulnerable to reward hacking: an
agent improves its measured score by exploiting the reward-relevant trajectory instead of solving the intended task. Existing defenses rely largely on task-specific patches,
prompt instructions, or post-hoc detectors. They do not provide reusable evidence that a concrete run remained within its intended evaluation boundary. This paper presents BenchShield, a model-backed instrumentation layer for reward integrity in LLM-
agent evaluation. BenchShield grounds detection in a finite lifecycle model of an evaluation's reward-relevant events. Within the
benchmark infrastructure, two complementary analyses operate over this model. A static, phase-aware taint analysis exposes reward-hacking paths before a run. Its runtime counterpart uses infrastructure-side evidence to attribute concrete
agent use and emit evidence-backed claims. We construct BenchShield Trajectories, a human-labeled corpus of 456 adjudicated trajectories from more than 31,000 public
agent runs across three
benchmarks. Compared with an agentic hackability scanner baseline on the same tasks and model, BenchShield improves full-chain recall from 23-94% to 77-100%, same-vector coverage from 16-56% to 43-78%, and reduces per-task cost by up to 65%. Its runtime analysis achieves 96% accuracy in detecting reward hacking from infrastructure-side evidence.
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All authors Shenghan Zheng, Zonglin Di, Yimin Liu, Kyoung Whan Choe, Jiankai Sun, Heguang Lin, Penghao Jiang, Yifeng He, Xiao Cheng, Jicheng Wang, Wenbo Chen, Alex Yates, Yinzhe Zhao, Bingran You, Yuan Gao, Ayush Munot, Shubham Gaur, Zhe Ye, Hao Wang, Xiangyi Li, Dawn Song, Christophe Hauser
Systems and Control
Structured Stochastic Representations of Integrated Dynamic Strategies
Fredy Vides
Dynamic allocation decisions couple present resource use to evolving internal conditions, delayed returns, and future costs. We represent this interaction by four probability localizations linked through regime-indexed, graph-constrained column-
stochastic operators. Pre-action state or context selects a locally affine model, while action-dependent changes update subsequent regimes, yielding a causal switched representation of nonlinear
evolution. We characterize operator identifiability relative to the graph, the
stochastic constraints, and the sampled
embedding, separating coefficient recovery from predictive equivalence on the decision domain. Decision making is then formulated through implementable return–cost acceptability regions. Finite-horizon error propagation supplies conservative classification margins, and simultaneous intervals distinguish model-relative near-optimality from certified $\epsilon$-optimality over a declared finite policy class. Regime-indexed
stochastic feedback is admitted when it satisfies the same certification test. Reproducible synthetic laboratories for personal preparation, supplier participation, and customer retention illustrate exact, operator-supplied, and noisy feedback cases. Multinomial experiments show improving recovery of the feedback function and fewer unresolved decisions with increasing sample size, while unrestricted off-policy recovery remains limited. The contribution is a structure-preserving representation–identification–decision workflow, not a domain-specific physiological or commercial calibration.
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Systems and Control · Cross-listed from cs.IT
A Mathematical Theory of Pragmatic Information
Kai Niu and Ping Zhang
We propose a mathematical theory of pragmatic information that connects communication, control, and decision-making. Its central notion is the isoteleia mapping, which formalizes equifinality: distinct semantic paths that lead to the same optimal action are treated as pragmatically equivalent. This mapping yields a three-tier hierarchy of syntactic, semantic, and pragmatic information, in which each successive abstraction removes distinctions that are irrelevant to the task. We then define pragmatic
entropy, up/down pragmatic mutual information, channel capacity, and rate-distortion, and prove lossless source coding, channel coding, and rate-distortion
theorems that extend Shannon's results. These measures quantify decision uncertainty, reliable transmission, and task-oriented compression at the level of terminal actions. We further introduce pragmatic value of information (VoI) and pragmatic cost of information (CoI) as decision-theoretic duals to rate-distortion and capacity, and develop a Lagrangian dual framework for cross-layer optimization. The resulting pragmatic efficiency bound $\mathcal{E}_p(\lambda)=\sup_R[\Phi_p(R)-\lambda\mathrm{CoI}_p(R)]$ characterizes the maximum net utility attainable by a resource-constrained intelligent system under a given resource price, yielding a behavioral capacity that extends Shannon's symbol-level capacity to goal-directed action. Extensions to continuous messages provide closed-form expressions for Gaussian channels and sources, while dynamic settings are addressed through a Bellman equation for sequential decision-making. The framework supports task-oriented communication, networked control, autonomous systems, and embodied AI by shifting emphasis from symbol fidelity to the effectiveness of information in guiding actions. In this way, it offers a common
language for systems that extract value from information under resource constraints.
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