A Study of Conditional Diffusion Models for Open-Loop Control under Dry Friction and Stiction

Diffusion models have recently emerged as expressive generative priors for planning and control. This paper studies Action Diffusion, an action-sequence diffusion formulation used as an open-loop proposal distribution for a point-mass system with dry friction and stiction. In this benchmark, motion starts only when the applied input exceeds a static-friction threshold, so effective controls occupy a small and temporally structured subset of the action-sequence space. A compact conditional 1D U-Net generates bounded control sequences conditioned on initial and target states. We compare it with uniform random shooting, random shooting from the same structured dataset prior, and the Cross-Entropy Method (CEM). Results show that Action Diffusion reduces terminal error and stuck steps, especially in low-sample regimes. These results indicate that conditional diffusion provides an effective mechanism for generating temporally coherent control sequences that overcome stiction by conditioning and recombining structured control primitives from the training prior for state-to-state open-loop control.

XP-JEPA: Cross-Predictive Physics Grounding for Forecastable Latent Dynamics

Latent world models plan by predicting how candidate actions transform learned representations. In self-predictive models, however, the encoder and predictor are optimized jointly and can co-adapt to latent transitions that are easy to predict but only weakly constrained by the physical evolution of the scene. We introduce the cross-predictive JEPA (XP-JEPA), which grounds visual latent dynamics in privileged physical trajectories. XP-JEPA separately encodes visual observations and physical states, advances both through a shared action-conditioned predictor, and matches each prediction to both future representations. This objective encourages unified latent dynamics across the two modalities, grounded in the underlying physical transitions. The physical branch is discarded after training, leaving a visual-only model at deployment. On a multi-task suite spanning six evaluation subfamilies, XP-JEPA reduces rollout drift of a newly fitted predictor from $0.361$ to $0.104$ and increases mean control success from $53.6\%$ to $78.2\%$. Direct physical-state regression raises position decodability but leaves forecastability and control near the visual-only baseline. Cross-predictive physical grounding can therefore produce more forecastable latent dynamics for rollout-based control without privileged inputs at test time.

CausalNav: Reliability-Certified Causal World Models for Control under Physical-Parameter Shift

A world model is only useful for physical AI if it changes what the agent does, and only safe if it declines to do so when it is wrong. We study both halves of that requirement with CausalNav, a controller built around a signed, action-conditioned transition graph over identified state coordinates. At deployment CausalNav simulates a small library of intervention sequences, converts their objective error into policy-logit advice, and admits that advice only when a scale-free predictive-reliability certificate, a policy-margin gate, and an argmax-agreement gate all pass; otherwise it falls back exactly to its own model-based base controller. We evaluate against nine controlled baselines (transformer, recurrent, split-latent, graph, causal-induction, and three recent model-based reasoning modules) on CartPole-v1 and discretized Pendulum-v1 with physical-parameter shifts, under one shared PPO trainer, one interaction budget, and ten held-out seeds (200 runs). CausalNav attains the best average rank (1.25 of ten). The diagnostic result is more informative than the ranking: the learned graph recovers structure well above chance (CartPole F1 = 0.59 +/- 0.09), yet per-seed structural fidelity is uncorrelated with per-seed control benefit (r = -0.15, p = 0.67), and the certificate abstains on 10/10 Pendulum seeds, where forcing the planner on costs return. Model fidelity did not predict downstream control utility in our setting; certified abstention, not better prediction, is what made the world model safe to deploy.

SoRoMoX: Fast, Differentiable, and Parallelizable Soft Robot Models

Reduced-order models based on Cosserat-rod theory are now well established, and modeling theory is no longer the primary bottleneck in soft-robot control. Their implementations, however, do not support the differentiable, GPU-parallel, and control-oriented workflows that underpin advanced rigid-robotics applications. Here, we fill this gap with SoRoMoX (Soft Robot Models in JAX), a fully numerical, JIT-compilable Python/JAX framework. SoRoMoX implements articulated, Piecewise Constant Strain, and Variable Strain models through a unified, control-ready interface that provides inertia matrices, gravitational and elastic forces, Jacobians, and their derivatives. To our knowledge, it is the first rod/strain-based soft-robot modeling framework that runs directly on GPUs and is end-to-end differentiable with respect to states, inputs, and parameters. Sequential CPU rollouts are up to 18.1x faster than state-of-the-art alternatives, while GPU-parallel rollouts increase throughput by up to 234.6x. This performance enables workflows that were previously impractical or impossible: static-equilibrium system identification with 66% lower marker RMSE; residual-force learning with a further 64% reduction; computed-torque tracking with RMSE reduced by a factor of approximately 500 relative to model-free PD; control-gain optimization with up to 62% lower loss than untuned gains; safety-constrained control using high-order control barrier functions to keep the peak contact force within a prescribed 5 N bound, compared with 33.5 N without the safety constraint; and reinforcement-learning policy training up to 7x faster than a CPU PyElastica discrete-rod baseline through massively parallel rollouts.

Pick-to-Learn Calibration of an MPC Policy for an Origin-to-Destination Flight Problem

This paper illustrates the Pick-to-Learn methodology applied to the calibration of a Model Predictive Control policy. While developed around a specific example, the presentation is meant to highlight a methodology of broad applicability. The example concerns an aircraft traveling from an origin point to a destination point in the presence of uncertain crosswinds and a low-connectivity zone that should be avoided. The MPC policy is parameterized by two hyperparameters, which are selected from data by the P2L procedure. Starting from a dataset of 400 wind realizations, also called scenarios, P2L identifies a final compression set containing only two informative scenarios. The resulting MPC policy avoids the low-connectivity zone on all available scenarios and, according to the P2L theory, satisfies a probabilistic risk bound of $4.8\%$ at confidence level $1-10^{-5}$, where the risk is the probability of entering the low-connectivity zone in a future flight under a new wind realization not included in the sample.

Generalist AI Control: Towards Multi-purpose Adaptive Algorithms

Traditional controllers are designed for specific systems and do not transfer across different system orders and dynamics. We present a Generalist Controller, a learning-based controller capable of controlling systems of varying orders and dynamics. The approach introduces a novel dynamic state-space representation using attention mechanisms with masking, enabling a single neural network, trained in one shot, to handle systems with different dimensions without architectural modifications by assigning a system tag to each system. We generated 314,630 demonstrations from 25 diverse systems, including stable, unstable, minimum-phase, and non-minimum-phase dynamics, spanning linear and nonlinear systems from autonomous underwater and aerospace vehicles to mechanical systems and chemical processes. The model learns cross-system control strategies through multi-scale temporal processing and a mixture-of-experts architecture. Simulation results demonstrate that the proposed generalist controller achieves comparable performance to system-specific LQI controllers across all tested systems, including challenging cases such as non-minimum-phase and unstable dynamics, whilst generalising to unseen operating conditions including actuator saturation, noise, disturbance, and reference trajectories not encountered during training. This work represents a significant step towards generalist control policies within a defined family of dynamical systems, demonstrating effective control across a range of single-input single-output (SISO) systems of varying order and dynamics using a single learned policy without system-specific tuning.

Robustly Invertible Nonlinear Dynamics and the BiLipREN: From Inversion-Based Control to Generative Trajectory Modelling

This paper proposes a new notion of robust invertibility for nonlinear dynamical systems, and introduces constructive parameterizations of recurrent neural network which are robustly invertible by design. We define robust invertibility as the existence of a causal inverse system such that both the forward and inverse systems are contracting and have bounded incremental input-output gains (the system is bi-Lipschitz), implying that both forward prediction and input reconstruction are robust to signal perturbations and initial-state mismatch. We construct robustly invertible recurrent models via series composition of static orthogonal layers and dynamic layers satisfying a strong input-output monotonicity property, and provide a differentiable neural network parameterizations in the form of the bi-Lipschitz recurrent equilibrium network (BiLipREN). Additionally, composition with dynamic orthogonal layers yields a nonlinear minimum-phase/all-pass (a.k.a. inner--outer) factorization. We illustrate the utility of the framework through a series of application examples in data-driven internal model control, dynamic surrogate loss learning, and signal-space normalizing flows, illustrating its utility for robust control, trajectory optimization, and generative modeling of complex trajectory distributions.

Qantara: Bridge-Flow Training for Multi-Paradigm JEPA Control

Joint-Embedding Predictive Architectures (JEPAs) underpin a growing family of latent world models for control from raw pixels, but every existing JEPA world model commits at training time to a single inference paradigm: either trajectory optimisation in a learned dynamics model, or direct behaviour cloning. A single checkpoint that serves both would defer this choice to inference, when deployment constraints (rollout cost, observation accessibility) determine which path wins. We present Qantara, an end-to-end JEPA whose joint training objective pairs a Brownian-bridge interpolant between consecutive clean latents on the state axis with noise-to-data flow matching on the action axis. The same checkpoint serves three inference paradigms without retraining: latent planning, behaviour-cloning action sampling, and inverse dynamics, which we query through a video-inverse composition that first predicts the next latent without action conditioning, then extracts the action. Training concentrates mass on the edges of the (action-time, state-time) noise square, where inference queries the predictor: replacing it with uniform interior sampling drops Push-T planning from 90.1 to 53.3 SR at matched compute. On the LeWM control suite, Qantara reaches a 91.2 SR three-train-seed average and sets new SOTA on OGBench-Cube (+7.7 SR over DINO-WM, +19.7 over LeWM). From the same weights, the behaviour-cloning and video-inverse paths reach 82-83 SR on Push-T and 71-73 SR on Cube. These results move JEPA world models from single-paradigm planners to multi-paradigm controllers.

Integrating Physics-Informed Neural Networks for Safe Reinforcement Learning in a 1-DoF Helicopter System

Deep reinforcement learning (DRL) offers powerful control for industrial cyber-physical systems (ICPSs), but its "black-box" exploration risks violating strict hardware safety limits. Typically, these constraints are managed through complex reward shaping. In this work-in-progress paper, we embed a differentiable physics model directly into the proximal policy optimization (PPO) actor loss function. By simulating short-horizon future trajectories during training, the policy is penalized for anticipated safety violations independent of the task-reward signal. Evaluated on a simulated 1-degree-of-freedom helicopter testbed with strict pitch constraints, our physics-informed soft regularizations substantially reduce constraint violations while maintaining reliable target tracking.

Rank-Then-Act: Reward-Free Control from Frame-Order Progress

We introduce Rank-Then-Act (RTA), a framework for learning control policies from expert video demonstrations without environment rewards. RTA trains a Vision-Language Model (VLM) offline as a progress-based ordinal scorer, using a Group Relative Policy Optimization (GRPO) objective over shuffled frame sequences, which forces the model to recover temporal ordering from visual semantics rather than trivial time cues. Importantly, instead of using the scorer directly as a scalar reward model, we propose a correlation-based reward function for reinforcement learning: at each interaction window, we compute the Spearman rank correlation between predicted progress rankings and true temporal indices, yielding a bounded, scale-invariant learning signal. This design decouples reward learning from absolute calibration and enables stable transfer across tasks and environments. We evaluate RTA on discrete control benchmarks (PyBoy: Catrap, Kirby) and continuous control tasks (PointMaze, MetaWorld). RTA consistently matches or outperforms prior video-based reward learning methods and rank-based baselines, while demonstrating strong cross-task reuse of a single pretrained progress scorer. Our results suggest that correlation-structured supervision over video-derived ordinal signals is sufficient for policy learning, offering a scalable alternative to explicit reward design.

Koopman operator theory: fundamentals, control, and applications

The Koopman operator has gained considerable attention due to its ability to provide a global linear representation of highly complex dynamical systems. The operator describes nonlinear dynamics in a linear way through the lens of real- or complex-valued observable functions. Recently proposed data-driven techniques, like extended dynamic mode decomposition (EDMD), its kernelized variant, and machine-learning methods, can be used to generate finite-dimensional approximations accompanied by finite-data error bounds. In this tutorial paper, we provide a concise introduction into Koopman operator theory and its use in systems and control. A particular focus is put on data-driven surrogate models, their extension to systems with inputs, and controller design using Koopman operator theory. Moreover, we demonstrate the key techniques, i.e., EDMD and Koopman MPC. To this end, we provide simulation studies including source code on GitHub to enable the interested reader to experience the Koopman operator in systems and control step by step.

Model Predictive Current Control with Harmonic Correction for Single-Phase AC-DC EV Charging

The increasing integration of Electric Vehicles (EVs) has imposed a growing harmonic challenge on the power grid. For AC/DC Power Factor Correction (PFC) in single-phase On-Board Chargers (OBCs), Model Predictive Current Control (MPCC) improves the current quality by predicting and tracking the inductor current. However, finite control set MPCC selects switching states, resulting in discrete control actions and a limited optimisation space. Moreover, the MPCC cost function based on instantaneous current tracking error has limited capability to compensate for low-order harmonic disturbances induced by dead time, control delay, and model parameter mismatch. This paper proposes a duty cycle predictive MPCC incorporating a real-time harmonic estimation reference. The proposed method dynamically estimates the low-order harmonic components of the input current and corrects the MPCC reference current, enabling continuous duty cycle control and targeted suppression of dominant low-order harmonics. Simulation results on a single-phase OBC demonstrate that the proposed duty cycle predictive MPCC reduces the steady-state current THD_i from 11.47% to 6.10% compared with the switching state predictive MPCC. With the harmonic reference, the THD_i is further reduced to 2.85%.

Closed-Loop Control with Rule-Aligned Small Language Models and Multi-Agent Self-Correction

A key step toward autonomous industrial operation is the ability to create and reconfigure control policies from natural-language requirement specifications, with minimal or no manual redesign. In this setting, policy generation by AI agents can be a credible path when paired with a plant-aware validator (e.g., a digital twin) that can check generated candidate actions before execution. However, practical deployment is constrained by inference latency and compute footprint: large cloud-based models are often too slow, opaque, or data-sensitive for edge closed-loop use. This work investigates whether a compact Small Language Model (SLM) can be retrained for control reasoning and embedded in a validator-guided correction loop. We use a Qwen2.5-1.5B model aligned via Group Relative Policy Optimization (GRPO), combined with (i) an action agent, (ii) a symbolic/digital-twin-style validation layer, and (iii) a reprompting agent that iteratively steers outputs toward valid actions. In randomized thermal-control simulations (30 experiments with 500 steps each), the framework achieves 91.5% average action-alignment accuracy (86.3%--100% across cases) at 3.84\,s mean inference latency. Under symbolic re-mapping, it maintains a 95% in-range rate, indicating robust physical regulation despite reduced token-level agreement. These results support SLM+validator architectures as a practical path toward reconfigurable autonomous control at the edge.

Power-Budgeted Underwater Vehicle Control via Constrained Reinforcement Learning

Underwater vehicles operate from a fixed onboard energy budget that propulsion rapidly depletes, so a controller that completes its task while drawing less thruster power directly extends mission range and endurance. Reinforcement learning yields capable model-free controllers for station-keeping and trajectory tracking, but optimizing task accuracy alone drives the policy toward oscillatory, energy-wasting actuation. The established remedy subtracts an energy penalty from the reward, yet this sets the task-power trade-off through a single weight with no physical units: a target power level cannot be specified, the weight must be re-tuned for every vehicle and task, and a mismatched weight can even raise power. This paper instead formulates energy-efficient underwater control as a constrained Markov decision process in which average thruster power is subject to an explicit budget, solved with a PPO-Lagrangian algorithm. The power level is set by declaring a budget in physical units, and a single dual variable is updated online to meet it for each vehicle and task, without manual weight search. Across three vehicles and four tasks in the MarineGym simulator, the energy-constrained policy draws the least power in all twelve settings, reducing it by 14--65\% (up to 64.9\%) over a task-only baseline and below an energy-reward baseline everywhere, while remaining the smoothest in ten settings and preserving task accuracy except in one deliberately power-limited regime. Imposing energy as an explicit constraint thus offers a tuning-free route to energy-efficient underwater control that needs no per-vehicle, per-task weight search.

Offline Reinforcement Learning for Warehouse SLAM Throughput Control

We present an offline reinforcement learning (RL) framework for optimizing SLAM throughput control in a warehouse fulfillment environment. SLAM (Scan/Label/Apply/Manifest) throughput directly influences system congestion and operational efficiency. Our RL-based control approach dynamically recommends SLAM throughput settings that adaptively balance throughput maximization with downstream stability through intelligent adjustment of throttling behavior. We include a history-informed state representation, action space abstraction for delayed-impact control, and a reward function that captures both upstream and downstream operational metrics. Our approach is algorithm-agnostic, enabling integration of multiple offline RL methods under a unified architecture. We instantiate our framework with three state-of-the-art offline RL algorithms, and trained the models offline using de-identified historical operational logs from a large-scale warehouse. Policy performance is evaluated using a comprehensive multi-method strategy. These include model-free approaches including immediate reward estimation via regression models and long-horizon Fitted Q Evaluation (FQE), as well as model-based Deep Koopman dynamics evaluation. Empirical results reveal that the CQL policy consistently outperforms alternatives, improving system health by 22.97% and reducing average throttling duration by 3.18%. These findings demonstrate the potential of offline RL for safe and scalable warehouse throughput control optimization.

Sensorimotor World Models: Perception for Action via Inverse Dynamics

Perception for action suggests that representations of the world should be shaped not by visual fidelity alone, but by their relevance for actions. At the same time, latent JEPA-style world models advocate learning compact predictive states from high-dimensional observations to facilitate the prediction of future states, but end-to-end training of these models is nontrivial because representations may collapse if our only goal is to construct a latent state that is easy to predict. We introduce a sensorimotor world model (SMWM): a latent world model trained end-to-end with inverse dynamics regularization. This single regularizer addresses both issues: it prevents representation collapse and induces action-aligned representations. By forcing latent states to preserve information about the action underlying a transition, it biases the model toward the controllable degrees of freedom of the environment while discarding uncontrollable distractors. This yields stable latent world models trained from offline, reward-free trajectories, without frozen encoders, exponential moving averages, or complex latent regularizers. Empirically, SMWM learns compact, interpretable latent spaces and enables competitive planning performance across simple 2D and 3D control tasks.

Evaluating LLMs as Interpretable Controllers for Dynamical Systems

Large Language Models (LLMs) are increasingly used for decision-making and reasoning tasks, yet their potential as controllers for physical systems remains largely unexplored. This work investigates whether LLMs can function as interpretable controllers for a dynamic thermal environment, examining their ability to follow setpoints, interpret natural-language commands, reason about actuator effects, and incorporate prior model-based knowledge. Five LLMs of varying scales are evaluated under multiple scenarios, including settings with penalties on heater or fan usage and cases where the models have access to a physics-based prediction tool. The results show that control performance depends on model complexity: while low- and mid-scale models frequently misinterpret actuator dynamics or generate inconsistent reasoning, high-complexity models such as Qwen-3~14B and GPT-4o achieve accurate temperature tracking, stable actuator usage, and coherent explanations aligned with physical principles. Incorporating a physics-based model significantly improves control smoothness and energy efficiency by enabling anticipatory decision-making. A detailed reasoning taxonomy further reveals a clear progression from causal misinterpretation in smaller models to cohesive and temporally aware reasoning in larger ones. The findings demonstrate that LLMs can act as interpretable controllers when sufficiently capable and appropriately grounded in domain knowledge, highlighting promising opportunities for hybrid model-based and language-driven control strategies that can provide plausible explanations.

PolyFlow: Safe and Efficient Polytope-Constrained Flow Matching with Constraint Embedding and Projection-free Update

While flow-based generative models have demonstrated strong performance across a wide range of domains, deploying them in safety-critical physical systems remains challenging due to strict constraint requirements. Existing approaches typically enforce safety through post-hoc corrections, which incur substantial computational overhead and may distort the learned distribution. We propose PolyFlow, a polytope-constrained flow matching framework that embeds constraints directly into the model and flow dynamics. PolyFlow introduces a discrete-time flow formulation and a projection-free architecture, which eliminate the discretization error and guarantee strict satisfaction of arbitrary polyhedral constraints, without the need for expensive iterative solvers. Experimental results show that PolyFlow achieves zero constraint violation while maintaining high distributional fidelity across a range of planning and control tasks. Compared to state-of-the-art constrained generation baselines, PolyFlow significantly reduces inference latency and demonstrates a favorable trade-off between safety, efficiency, and generative quality. Code is available on https://github.com/MJianM/PolyFlow.

Uncovering Extreme Event Mechanisms for Prediction and Control with Sensitivity-Balanced Projections

Extreme events -- such as earthquakes and coronal mass ejections -- are common in many chaotic dynamical systems, yet are difficult to characterize and predict due to the subtle instability mechanisms that drive them. In this work, we develop an interpretable technique that reveals the underlying mechanisms behind extreme events and uses them to build data-driven forecasts and intuitive event suppression controllers. In particular, we utilize the covariance balancing reduction using adjoint snapshots (CoBRAS) method to identify linear oblique projections that best capture the sensitivity of a quantity of interest and reconstruct the original state. Importantly, we bypass the need for cumbersome adjoint calculations, instead using backpropagation via modern automatically differentiable numerical frameworks. To accommodate spatially localized events, we also introduce a new variant of CoBRAS to obtain local sensitivity-balanced projections. We demonstrate the utility of this approach to characterize extreme events across a diverse set of challenging systems, including turbulent bursts of energy dissipation in the 2D Kolmogorov Flow, spontaneous synchronization in networks of coupled FitzHugh-Nagumo oscillators, and the localized formation of ocean rogue waves from a modified nonlinear Schrödinger equation. For each example, we show that our simple forecast models accurately predict extreme events and that the underlying mechanisms may be used to design control laws to prevent these events. Finally, we demonstrate that by learning a neural network surrogate model of the dynamics directly from data, we may extend this approach to experimental systems and systems that are not natively written in an automatically differentiable programming language.

Meta-Learning for Rapid Adaptation in Reference Tracking of Uncertain Nonlinear Systems

In this paper, we address the problem of reference tracking for uncertain nonlinear systems. Since collecting data from the target system (i.e., the system of interest) is often challenging, our objective is to design optimal controllers using limited target system data. Meta-learning provides a promising paradigm by leveraging offline data from source systems (systems sharing structural similarities with the target system) to accelerate training and enhance control performance. Motivated by this idea, we propose a meta-learning-based control framework that tailors the implicit model-agnostic meta-learning (iMAML) algorithm to the control setting. The framework operates in two phases: an (offline) meta-training phase, where an aggregated representation is learned from source data to capture the shared system dynamics among similar systems, and an (online) meta-adaptation phase, where this representation is fine-tuned on the target system using only a few data samples and limited adaptation steps. We formulate this framework as a bi-level optimization problem and provide an efficient solution with reduced storage complexity and few approximations. The proposed framework is general, allowing various learning algorithms to be integrated. To demonstrate this flexibility, we propose two specific learning algorithms that can be incorporated into our framework based on a neural state-space model and a deep Q-network, respectively. The primary distinction between these approaches is whether explicit system identification is required. Numerical simulations and hardware experiments demonstrate that the proposed methods enhance control performance and consistently outperform baseline approaches.