Papers

This paper develops an integrated modeling and nonlinear model predictive control (NMPC) framework for coordinating thermal management, flexible workload scheduling, wave-power utilization, and battery operation in a wave-powered subsea data center. Realistic data center workloads are constructed from job-level CPU, memory, and GPU measurements from the MIT Supercloud dataset and divided into interactive and delay-tolerant flexible jobs. Thermal behavior is represented by a three-node lumped model of the IT equipment, recirculating nitrogen, and pressure hull with surrounding seawater as the thermal boundary. The NMPC jointly optimizes the flexible workload power budget and cooling command subject to thermal, battery, and workload constraints. Closed-loop simulations under different workload, thermal, battery, and renewable-generation conditions demonstrate that the proposed framework maintains thermal safety while adapting cooling operation and flexible workload execution to wave-power availability and battery state-of-charge. The parametric studies show that battery capacity and wave-generation capacity strongly affect battery availability and flexible-workload queue accumulation, while excessive renewable generation capacity may lead to increased energy curtailment. Monte Carlo and distance-correlation analyses further show that flexible-job delay is relatively insensitive to the investigated system parameters, whereas terminal battery state-of-charge is primarily influenced by battery energy capacity and wave generation capacity.

Power systems are often represented by high-dimensional dynamic models, making nonlinear control design computationally expensive and limiting its practical application. Oscillation analysis and damping control therefore commonly rely on linearized models, which do not capture the nonlinear oscillatory behavior induced by large disturbances. This paper proposes an isostable-based model reduction method for nonlinear modal analysis of power systems. The method constructs an invariant manifold associated with a selected oscillatory mode and uses isostable coordinates to describe the mode with only two real state variables. The isostable formulation gives linear autonomous modal dynamics, with nonlinear state reconstruction and input response computed on the modal manifold. An optimal damping control problem is then formulated directly in the reduced coordinates. Case studies on the IEEE 39-bus system demonstrate the accuracy of the proposed model in describing nonlinear oscillations and show improved damping compared with control designed using a linear reduced model.

Nonlinear sustained oscillations involving inverter-based resources can happen when device and network interactions produce an attracting limit cycle around an unstable equilibrium. A damping controller must then describe nonlinear dynamics over the region between the two invariant sets, where a local equilibrium linearization can be insufficient. In this paper, a controlled phase–isostable model is first developed on a two-dimensional invariant manifold connecting the equilibrium and the limit cycle. Dynamics on this surface are represented by phase and isostable coordinates, while physical states and control inputs are related to these coordinates through nonlinear reconstruction and response functions. The required functions are computed from connecting trajectories and periodic-orbit data. A control strategy is then designed to provide extra damping while limiting phase distortion. Case studies on a two-area system and an IEEE 39-bus system demonstrate more effective oscillation damping than the compared equilibrium-linearized designs under the same conditions.

We study preventive-maintenance scheduling for a small fleet when several assets compete for a limited number of maintenance slots and their remaining useful lives (RULs) are uncertain. The planning horizon is divided into discrete periods; each asset may be maintained at most once, and at most $K$ assets may be maintained in any one period. Future usage and RUL errors are represented by scenarios. We compare a risk-neutral policy that minimizes expected cost with a risk-aware policy that minimizes expected cost plus conditional value-at-risk (CVaR), where $\operatorname{CVaR}_{0.90}$ is the mean cost among the worst 10% of scenarios. Both policies are solved exactly by enumerating all capacity-feasible schedules. A $3\times5$ experiment combines capacities $K=1,2,3$ with five increasing levels of RUL uncertainty, with ten paired replications for each combination. The risk-aware policy provides its largest benefit when RUL uncertainty is low-to-moderate and more than one maintenance action can be executed per period. In the best observed case, it reduces CVaR by 13.4% with an expected-cost increase of only 0.2 relative cost units. At high uncertainty, the benefit becomes negligible and the two policies can select identical schedules. The results show that risk-aware scheduling creates operational value only when prognostic information is sufficiently informative and the maintenance system has enough flexibility to act on it.

This paper proposes a residual learning-based control framework for heterogeneous vehicle platoons subject to parametric uncertainty and external disturbances. A nominal controller designed via Linear Matrix Inequalities (LMIs), along with disturbance-observer compensation, is enhanced by a Recurrent Equilibrium Network (REN) trained offline using stored trajectories and nominal-model prediction errors. The REN is constrained to satisfy a prescribed $\ell_2$-gain bound, enabling sufficient small-gain conditions for local closed-loop stability and disturbance string stability. Experiments demonstrate reduced spacing and velocity errors relative to the nominal controller.

Hydrogen-diesel dual-fuel (H2DF) combustion engines offer a promising pathway for decarbonising hard-to-electrify transport sectors, yet their highly nonlinear dynamics and coupled process variables demand constraint-aware control strategies. Model Predictive Control (MPC) meets these requirements but requires an online optimisation in every combustion cycle, which limits deployment on low-cost embedded hardware. This paper trains a feedforward deep neural network (DNN) by behaviour cloning (BC) to imitate an MPC expert, using 86,000 engine cycles of demonstration data collected at 1500 min-1 on a modified Cummins QSB 4.5-litre hydrogen dual-fuel engine. Two variants, one with process feedback and one without, are validated experimentally. Both track unseen fast-transient load steps (3-8 bar indicated mean effective pressure, IMEP) with normalised root mean square error (NRMSE) values of 7.80% and 9.03% against the expert's 8.01%, while keeping mean NOx and particulate matter emissions at or below those of the expert. Inference takes 2 ms or less on a Raspberry Pi 400 (ARM Cortex-A72 at 2.2 GHz), including 1 ms communication latency, compared to up to 7 ms for the MPC expert, a 3.5x speedup. Open-loop profiling on a low-cost ESP32 microcontroller at 180 MHz gives 4.3 ms per inference, 4x faster than required for the 18 ms cycle window. Beyond the training range the cloned policy saturates its controls but exceeds the pressure-rise-rate limit. To the authors' knowledge, this is the first experimental BC controller for cycle-to-cycle combustion control of an internal combustion engine (ICE), trained from demonstrations recorded on the engine itself.

Signal-multiplexing network ranging (SM-NR) shares broadcasts across node pairs, but its sequential operation leads to a ranging cycle that grows linearly with network size. This paper proposes a concurrent coded SM-NR (CC-SM-NR) framework for asynchronous half-duplex networks. Firstly, the CC-SM-NR protocol coordinates concurrent transmissions through binary transmit-listen codewords. The transmit-listen schedule defined by these codewords ensures reciprocal observations subject to a finite concurrency limit. Then, we derive the exact minimum number of transmit-listen rounds without a concurrency limit, which reveals that the minimum grows logarithmically with network size. To account for practical scenarios, we establish the necessary and sufficient conditions for the constant-weight feasibility of codewords under a finite concurrency limit. Subsequently, we propose a low-complexity scheduling algorithm that achieves the minimum round count within the constant-weight codeword class. To support higher observation redundancy, this scheduling design is extended through a greedy construction. Finally, simulation results demonstrate the effectiveness of the proposed schemes for network ranging.

This paper proposes an adaptive model reduction approach based on nonlinear participation factors (NPFs) which determines the most effective selection of unimportant generators in a power system to be linearized to accelerate time-domain simulation for the entire system. The method enables a dynamic transition between the full-order model, and a hybrid reduced model. It uses modal energies to rank system modes under contingencies, and computes NPFs for highly energized modes based on Normal Form theory. To accelerate the computation of NPFs and make it achievable online, a tensor contraction technique is introduced. The proposed approach is tested on a 48-machine, 140-bus NPCC system using both partitioned and unpartitioned strategies. It demonstrates significant simulation speedup while preserving better accuracy than a linear participation factor-based method if the nonlinear behaviors of the system cannot be ignored, especially when a near-resonance condition is presented.

In this paper, we propose a hierarchical multi-agent reinforcement learning framework for coordinating robot teams in warehouse environments under communication loss. We partition the robot team into groups, with centralized coordination within each group and distributed coordination across groups. Each group uses a recurrent predictor to estimate unavailable interaction information due to communication loss. A higher-level policy then generates a compact coordination reference that conditions the local control policy within each group. A predictive safety filter evaluates and modifies the proposed controls when they violate safety constraints. Simulation results show improved task completion under communication loss, reduced communication growth as the team size increases, and safe operation in the tested scenarios.

Differentiable optimization brings the structural guarantees of mathematical optimization to network pipelines, allowing them to be trained end-to-end. However, its application remains challenging for nonconvex constrained problems, as existing differentiable solvers often suffer from limited modeling expressiveness due to their reliance on specialized problem structures, while also incurring substantial computation time and memory overhead in both the forward and backward passes. To address these challenges, we propose lapanda, a matrix-free differentiable solver for nonconvex optimization with general constraints. It reformulates the problem to a sequence of augmented Lagrangian subproblems, each handled by a first-order inner solver through a proximal averaged quasi-Newton algorithm with adaptive linesearch, thus enabling efficient forward optimization. We establish local well-posedness of the solution map and convergence of the outer iterations, and further derive a sensitivity alignment between the original problem and the final subproblem in the backward pass, demonstrating that the subproblem sensitivity, which can be computed efficiently in a matrix-free manner, provides a principled approximation to the exact optimizer sensitivity. We evaluate lapanda on nonconvex constrained Rosenbrock benchmarks, imitation learning with several representative constrained optimal control problems, and embedded robotic obstacle-avoidance tasks. Compared with state-of-the-art differentiable solvers, lapanda delivers substantial reductions in computation time and memory footprint while maintaining reliable constraint satisfaction and learning performance.

This paper develops a general minimum-order functional observer framework that contains the classical Darouach functional observer and the reduced-order Luenberger observer as special cases. The required functional dimension is determined from the triple $(A,C,L)$ through a set of functional observability indices. The minimum dimension permitted by the algebraic observer-existence condition is characterized, and the complete family of augmentations attaining this dimension is determined. Necessary-and-sufficient spectral feasibility conditions are then established for this dimension to be the minimum achievable observer order. The resulting existence conditions reduce exactly to the Darouach conditions when no augmentation is required and to the classical observability condition in the reduced-order Luenberger case. More generally, the framework admits minimum-order functional observers of intermediate order, which may exist even when neither classical observer is available.

In systems where controllers operate remotely and communicate with actuators over shared communication channels, it is crucial to efficiently schedule the control data transmission to reduce bandwidth usage and actuator effort. In this article, we investigate a novel scheduling mechanism that jointly coordinates control actions across different controllers and different time steps. We propose an algorithm based on the alternating direction method of multipliers (ADMM) to solve the resulting optimization problem. While ADMM is often treated as a black-box solver, the proposed algorithm offers a clear physical interpretation, ensures convergence to a stationary point, and is computationally efficient. Simulation results validate our theoretical results and demonstrate the effectiveness of our proposed algorithm.

The rapid expansion of large-scale AI data centers (AIDC) is introducing new stability challenges, particularly in weak or low-inertia networks characterized by fast, step-like demand variations and strict requirements on voltage and dynamic performance. This paper investigates the use of grid-forming (GFM) Enhanced STATCOMs (E-STATCOMs) to support reliable integration of such facilities. A power-admittance-based linear modelling framework is developed to capture system interactions and is validated through detailed EMT simulations. The results demonstrate that E-STATCOMs provide fast, well-damped responses to abrupt load changes while effectively mitigating low-frequency oscillations and interactions with network resonances. By enabling tunable dynamic behavior via a load balancer, virtual impedance, and coordinated active-reactive power support, the proposed approach allows precise shaping of system response and improved regulation at the point of connection. These features make E-STATCOMs a flexible and scalable solution for integrating large data centers into weak grids and long transmission systems, supported by a design-oriented framework that facilitates parameter selection and performance assessment without extensive reliance on EMT studies to meet grid codes and AIDC interconnection requirements.

Direct torque sensing is a growing need in the robotics community to enable precise control and interactions where torque estimation from motor current is not sufficient. This paper presents a novel disk-shaped magnetoelastic torque sensor with a compact axial envelope of about 1 cm, suitable for integration in robotic joints. A four-magnetometer architecture is used to measure the field modulated by the stress affecting a narrow magnetized region while rejecting the effects of parasitic cross forces. A custom-designed magnetic shield enhances the torque sensitivity while reducing the external stray fields by a factor 7x. The device measures the torque with an accuracy of 1.34 %FS relative to the 50 Nm full scale (FS). The paper details the development of the sensor through the mechanical design, the magnetization procedure, and the experimental validation. The results demonstrate the potential of the proposed sensor for robotic applications.

We present DAOCP, a dual active set solver for linear quadratic optimal control problems with stage-wise equality and inequality constraints. Active set methods are leading Model Predictive Control benchmarks for full-body robotics, but existing solvers operate on dense QPs, while typical problem dimensions favor methods that exploit the optimal control structure. DAOCP combines the warm-starting capabilities of active set algorithms with the better computational scaling of structure exploiting solvers, by relying on a generalization of the relationship between the Riccati recursion and the Cholesky factorization of the condensed Hessian. This result enables dual active set iterations to operate directly on the original optimal control problem through recursive computations, without explicitly forming the condensed quadratic program. On robotics benchmarks, DAOCP is the fastest of four solvers in four of five scenarios, cutting average solve time on a 58-state Atlas model by 9$\times$ relative to state of the art solvers DAQP and HPIPM.

Signal Temporal Logic (STL) enables rigorous verification and control of cyber-physical systems, but writing correct specifications requires expertise that most requirement holders lack. Large language models can translate natural-language (NL) requirements into STL, yet stronger translators alone approach an accuracy ceiling. We argue that this ceiling stems from how the task is posed: one-shot, open-loop translation is somewhat ill-defined. Natural language is ambiguous, and, more fundamentally, what a person writes may not always be what they intend, so the target specification is not fully contained in the input text. We therefore reformulate NL-to-STL translation as a closed-loop feedback process. Each generated formula is translated back into natural language for the user to check, and natural-language corrections drive revision until the user accepts the specification. Users never read or write formal syntax. This framework rests on an asymmetry familiar from feedback control theory. The forward path, from ambiguous language to formal logic, is hard and error-prone. The feedback path, from structured STL back to language, can be made highly precise, and a precise feedback path lets an imprecise forward path achieve precise closed-loop behavior. Experiments on 500 expert-authored requirements and seven LLMs support this view. Back-translated explanations agree with expert judgments in 99.5% of cases. Closed-loop refinement raises strong models from about 89% open-loop accuracy to 98.0–99.2%, and yields gains of over 30 percentage points for weaker models (e.g., 17.6%$\rightarrow$48.0%). Ablations show these gains come from the semantic content of the feedback rather than from repeated attempts. An expert audit and a 280-session user study further confirm the reliability of the loop. We also identify a capability threshold above which feedback no longer helps.

We design adaptive overlapping temporal decomposition (AOTD), a parallel sequential quadratic programming (SQP) method for long-horizon nonlinear optimal control problems (OCPs). As designed, AOTD is the first overlapping temporal decomposition (OTD) algorithm that adapts the overlap size online, eliminating the need to fix a suitable overlap a priori. Specifically, at each iteration, it partitions the long horizon into overlapping nonlinear subproblems, performs one SQP step on each in parallel, and adaptively selects both the overlap size and the accuracy to which the resulting local KKT systems are solved. Two conditions govern the accepted step: an adaptive residual condition bounding the distance from the concatenated inexact direction to the exact Newton direction of the full problem, and a descent condition on the adaptive penalty parameters that certifies descent for a carefully chosen exact augmented Lagrangian. The residual condition is solver independent and accommodates both deterministic iterative solvers and randomized sketching solvers. Under standard regularity assumptions, we prove that the KKT residual converges to zero from any initialization and establish a local linear rate for sequences converging to a strict local minimizer. We validate AOTD on a power-system frequency regulation OCP and a Burgers PDE OCP, attaining a reduction in estimated FLOPs of approximately $2.5\times$ to the best fixed-overlap variant while converging across multiple horizon lengths with a single parameter setting.

In these notes, we view control as a dynamically constrained sampling problem on the state-space of a control system. With this viewpoint, we extend methods from generative modeling, such as flow matching, normalizing flows and denoising diffusions to control problems. Concepts such as controllability, optimal control and trajectory planning play an important role in guiding the extension and understanding well-posedeness of the corresponding algorithms, with application to steering systems to target states or distributions and sampling from reachable sets. The notes are intended as an accessible introduction for readers with a background in control theory and robotics.

Policy gradient methods for the linear quadratic regulator optimize feedback gains using a cost over an infinite horizon. When this cost is evaluated at one fixed initial state, it need not diverge near every part of the stability boundary. We study whether the Euclidean gradient flow can reach this boundary in finite optimization time. For controllable planar systems with one input and positive definite quadratic weights, an exact representation of the cost yields a necessary and sufficient condition for the existence of such a collision. The condition reduces to a scalar root calculation and includes the critical case, where a double direction root attracts an open set of stabilizing gains. For a triangular family, the criterion gives an explicit algebraic parameter region, and every trajectory either converges to the Riccati gain or collides with the stability boundary. A sharp threshold for compact cost sublevels provides a convergence certificate. Along every colliding trajectory, the stability margin and the smallest eigenvalue of the accumulated state Gramian vanish linearly, although the Gramian remains positive definite before collision. Numerical experiments examine the dependence on initialization, slow passage near a critical direction, and the effect of adding excitation in a second state direction.

This paper studies the nonconvex optimization landscape of Linear Quadratic Gaussian (LQG) control under direct state-space parameterization. Although the LQG cost may possess suboptimal stationary points, whether it admits suboptimal local minima has remained open. We answer this question negatively: Every local minimum of the full-order LQG cost is globally optimal. More generally, at any controller order, every local minimum corresponding to an uncontrollable or unobservable realization attains the globally optimal LQG cost over all stabilizing policies of arbitrary orders. We further show that any suboptimal policy can be augmented with decoupled stable controller states, so that the augmented policy admits a direction of negative curvature with probability one. Consequently, any suboptimal stationary point in full-order LQG cost can be converted into a strict saddle with probability one. One key proof idea connects the state-space Hessian to a frequency-domain global-optimality condition derived from the Youla parameterization. These results reveal a benign local-minimum landscape despite the presence of suboptimal stationary points.

This paper presents a path-following controller for a quadrotor system to guarantee safe maneuvers, in terms of forward path invariance, in the presence of cyber-physical attacks. We assume that an adversarial agent can control any one of the rotors through a false data injection (FDI) type of attack. A feedback controller is designed using transverse feedback linearization which guarantees that the system follows a class of smooth curves under FDI attacks. Our proposed controller is computationally efficient, with a closed-form analytical expression, that not only mitigates the effect of bounded malicious signal but also ensures mission success. We provide theoretical guarantees of forward path invariance under FDI attacks with realistic assumptions and demonstrate the effectiveness of our approach through simulation.

Nonlinear dynamics arise whenever multifarious entities of a system cooperate, compete, or interfere. For example, cardiovascular system involves a great level of complexity. Multi-lead ECG signals are generated through orchestrated depolarization and repolarization of cells and manifest significant nonlinear dynamics. Nonlinear dynamical systems defy understanding based on the traditional reductionist's approach, in which one attempts to understand a system's behavior by combining all constituent parts that have been analyzed separately. In order to cope with system complexity, modern healthcare systems are investing in advanced physiological sensing and patient monitoring, thereby giving rise to big data. Realizing the full potential of big data for healthcare intelligence requires fundamentally new methodologies to harness and exploit complexity. However, available nonlinear dynamics techniques are either not concerned with healthcare analytical objectives or fail to effectively analyze big data to extract useful information for improving healthcare services. There is an urgent need to develop analytical methodologies that fully exploit the underlying nonlinear dynamics in physiological systems for advancing healthcare services with exceptional features such as personalization, responsiveness, and superior quality. This chapter presents some theoretical developments and tools to advance the applications of nonlinear dynamics principles in health care. Specifically, we focus on sensor-based characterization and modeling of nonlinear dynamics (i.e., multifractal analysis and multiscale recurrence quantification). Then, current developments and applications of these methodologies are examined for characterizing and exploiting heart rate variability and space-time ECG signals.

We present Schur-Neural KF (SN-KF), a learning-based correction to the extended Kalman filter (EKF) that preserves the probabilistic conditioning interpretation of the EKF. The method perturbs the predictive state-measurement cross-covariance and the Cholesky factor of the measurement noise covariance so that the resulting joint predictive covariance is always positive semidefinite. The positive semidefiniteness is ensured by a Schur complement-based parametrization. We instantiate the parametrization with a recurrent neural architecture whose matrix outputs are modulated by amplitude gates. We prove that incorporating a measurement does not increase the filter's state uncertainty, and show that no measurement can induce an arbitrarily large state correction relative to its statistical surprise. We also present a perturbative analysis suggesting SN-KF's structural strength in the data-scarce regime. We provide two numerical experiments to illustrate the practical benefits of SN-KF. In a two-radar experiment, enforcing Schur-consistency provides a much broader failure-free hyperparameter region and reduces RMSE for small training subsets, consistent with our theoretical analysis in the data-scarce regime. In the unicycle experiment, SN-KF achieves the best precision, recall, false alarm rate, and gated RMSE under innovation-based sensor-fault rejection.

Models of vehicle dynamics learned from logged states and commands complement physics-based models, and latent world models, which predict in a learned representation, are used to plan and train controllers in other domains. Vehicle controllers are usually specified in physical terms: costs, limits, and references depend on position, yaw angle, speed, and yaw rate, and the optimizer compares or differentiates predicted outcomes across nearby commands. A latent model placed in such a controller must therefore let these quantities be recovered and must change its predictions with commands as the vehicle does, and prediction error on its own latent targets measures neither. We contribute a measurement protocol for action-conditioned latent predictors with a physical readout that separately tests retention, physical-neighborhood organization, forecasting, and local response to command perturbations, using an untrained-encoder reference and three matched response paths that locate errors in the representation or the predictor. In a case study of a temporal joint-embedding predictive model trained on signals logged in IPG CarMaker, the representations retain the measured planar outputs, though an untrained encoder of the same architecture retains them slightly better; future-command input improves one-second forecasts with retention nearly unchanged; and responses to small command pulses diverge from the simulator already in latent coordinates, raising regret when choosing among nearby commands in all comparisons. Updating the predictor on responses corrects them locally at a cost in forecast accuracy. Measuring retention, forecasting, and local response separately is thus what qualifies a predictive latent as a candidate model for control, and the protocol provides the basis for its closed-loop evaluation.

As AI models grow in size and usage, their energy demands increase dramatically, raising sustainability and economic concerns. Neuromorphic hardware, inspired by the energy efficiency of the brain, seeks to address this challenge by offering low-power, fast-processing alternatives to conventional computing. Such hardware is particularly well-suited to control systems deployed in resource-constrained environments, which are best trained via reinforcement learning (RL). This contribution presents the design and implementation of a fully on-chip, closed-loop Loihi 2 RL agent. Our neuromorphic circuit consists of a fully embedded Q-learning algorithm and an on-chip simulation of the CartPole-v0 environment on Loihi 2. Our Q-learning algorithm trained the same number of successful agents as the CPU implementation in only half the execution time and with two orders of magnitude less dynamic power. These findings demonstrate the viability of RL on neuromorphic hardware and highlight its promise for building energy-efficient, real-time, embedded AI systems.

Neural ODEs learn dynamics from trajectory losses, but their adjoint gradients lack the regressor-times-parameter-error structure on which Lyapunov analyses of online adaptation rest, so training on streaming data comes without stability guarantees. We show that this structure is in fact present: the adjoint gradient decomposes exactly into a positive semi-definite trajectory operator acting on the parameter error plus a nonlinear perturbation with explicit, horizon-dependent bounds. A quadratic Lyapunov function then certifies online Neural ODE training over sliding windows under computable gain and horizon conditions, and the same certificate extends to stored data: its drift branch recovers concurrent learning, and its trajectory branch yields NODE-CL, a stored-segment Gauss-Newton method built on batched forward sensitivities that needs no state-derivative estimates. On four DeepMind Control Suite domains, NODE-CL attains the lowest median prediction error on three under velocity measurement noise, where observer-based concurrent learning degrades by up to 8x; with clean measurements it is best on the pendulum and within a factor of 1.6 of the best stored-data baseline on the cartpole and reacher.

Feedback linearization is a powerful tool in nonlinear control, but finding the linearizing coordinate transform remains challenging. Feedback linearizing transforms are governed by well-established partial differential equations (PDEs) whose well-posedness is based on the Lie-algebraic Frobenius theorem, but solving the PDEs becomes computationally intractable for large system dimensions. To address this challenge, we propose a cascaded physics-informed neural network (PINN) framework to approximately solve these PDEs. By separately parameterizing terms of different Lie derivative orders, we mitigate the compounding errors inherent in fitting high-order Lie derivatives of neural networks. Furthermore, we use the learned transform to design a tracking controller and establish theoretical bounds on its error with respect to inaccuracies in the learned feedback-linearizing representation. We validate our method on a broad class of feedback linearizable systems, including a multi-input, multi-output planar quadrotor and synthetic examples for which analytical approaches are impractical, and demonstrate that our approach can computationally discover effective feedback-linearizing representations of nonlinear systems for control tasks.

This letter proposes a novel form of energy function (EF), called neural-analytic EF, for the stability analysis of power systems. The neural-analytic EF is designed as the sum of neural networks (NNs)-based components and an analytic EF, with the structure informed by the existing EFs derived analytically. It thus integrates NN's expressivity with the generalizability and scalability of analytic EFs. The satisfactory neural-analytic EF is further derived by iterative NN training with a tailored loss function. Numerical results finally demonstrate its superiority.

This letter proposes a novel method to establish decentralized stability conditions (DSCs) of power systems. This method formulates DSCs with meticulously crafted neural networks, based on the insight into the structure and properties of the existing analytically derived DSCs. A tailored loss function is further devised to iteratively train the neural networks, ensuring validity and reducing conservatism of the DSCs. Numerical results demonstrate that the resultant neural DSCs are less conservative than the conventional analytical DSCs, and become generalizable if a relatively large-scale system is used for training.

Foundation-model agents are often modeled as policies over an observed state. In deployed systems, however, a runtime may intervene only after the model has emitted a semantic proposal, making the proposal both an action candidate and a decision-time observation generated by a history-conditioned process. We show that collapsing this structure into a state-only proposal envelope can preserve proposal coverage while destroying certifiability. In a finite robust interface, the viability kernel of the collapsed model is contained in the physical projection of the history-augmented kernel, and the collapse is lossless exactly when every proposal-conditioned collapsed fiber retains a common robust-safe intervention. This gap can be maximal even with constant-size proposal and history alphabets. The same common-action condition yields a dual result: observing the current proposal can restore robust feasibility when it separates latent modes requiring incompatible interventions. We extend these one-step results over time using exact finite beliefs and standard safety and reachability fixed points, separating indefinite operational viability from finite worst-case verified progress. Controlled model-in-the-loop tests reproduce the predicted obstructions when telemetry or effect verification is removed or intervention authority is restricted. Thus, our contribution is not a new fixed-point calculus, but a characterization of when proposal–history correlation at the model–tool boundary is necessary for certification.