Heterogeneity in sensors and actuators across environments poses a significant challenge to building large-scale pre-trained world models on top of this low-dimensional sensor information. In this work, we explore pre-training world models for heterogeneous environments by addressing key transfer barriers in both data diversity and model flexibility. We introduce UniTraj, a unified dataset comprising over one million trajectories from 80 environments, designed to scale data while preserving critical diversity. Additionally, we propose TrajWorld, a novel architecture capable of flexibly handling varying sensor and actuator information and capturing environment dynamics in-context. Pre-training TrajWorld on UniTraj yields substantial gains in transition prediction, achieves a new state-of-the-art for off-policy evaluation, and also delivers superior online performance of model predictive control. To the best of our knowledge, this work, for the first time, demonstrates the transfer benefits of world models across heterogeneous and complex control environments. Code and data are available at https://github.com/thuml/TrajWorld.
This paper proposes a novel adaptive Koopman Model Predictive Control (MPC) framework, termed HPC-AK-MPC, designed to address the dual challenges of time-varying dynamics and safe operation in complex industrial processes. The framework integrates two core strategies: online learning and historically-informed safety constraints. To contend with process time-variance, a Recursive Extended Dynamic Mode Decomposition (rEDMDc) technique is employed to construct an adaptive Koopman model capable of updating its parameters from real-time data, endowing the controller with the ability to continuously learn and track dynamic changes. To tackle the critical issue of safe operation under model uncertainty, we introduce a novel Historical Process Constraint (HPC) mechanism. This mechanism mines successful operational experiences from a historical database and, by coupling them with the confidence level of the online model, generates a dynamic "safety corridor" for the MPC optimization problem. This approach transforms implicit expert knowledge into explicit, adaptive constraints, establishing a dynamic balance between pursuing optimal performance and ensuring robust safety. The proposed HPC-AK-MPC method is applied to a real-world tobacco loosening and conditioning process and systematically validated using an "advisor mode" simulation framework with industrial data. Experimental results demonstrate that, compared to historical operations, the proposed method significantly improves the Process Capability Index (Cpk) for key quality variables across all tested batches, proving its substantial potential in enhancing control performance while guaranteeing operational safety.
Traditional motion planning methods for robots with many degrees-of-freedom, such as mobile manipulators, are often computationally prohibitive for real-world settings. In this paper, we propose a novel multi-model motion planning pipeline, termed Re4MPC, which computes trajectories using Nonlinear Model Predictive Control (NMPC). Re4MPC generates trajectories in a computationally efficient manner by reactively selecting the model, cost, and constraints of the NMPC problem depending on the complexity of the task and robot state. The policy for this reactive decision-making is learned via a Deep Reinforcement Learning (DRL) framework. We introduce a mathematical formulation to integrate NMPC into this DRL framework. To validate our methodology and design choices, we evaluate DRL training and test outcomes in a physics-based simulation involving a mobile manipulator. Experimental results demonstrate that Re4MPC is more computationally efficient and achieves higher success rates in reaching end-effector goals than the NMPC baseline, which computes whole-body trajectories without our learning mechanism.
Robust optimal or min-max model predictive control (MPC) approaches aim to guarantee constraint satisfaction over a known, bounded uncertainty set while minimizing a worst-case performance bound. Traditionally, these methods compute a trajectory that meets the desired properties over a fixed prediction horizon, apply a portion of the resulting input, and then re-solve the MPC problem using newly obtained measurements at the next time step. However, this approach fails to account for the fact that the control trajectory will be updated in the future, potentially leading to conservative designs. In this paper, we present a novel update-aware robust optimal MPC algorithm for decreasing horizon problems on nonlinear systems that explicitly accounts for future control trajectory updates. This additional insight allows our method to provably expand the feasible solution set and guarantee improved worst-case performance bounds compared to existing techniques. Our approach formulates the trajectory generation problem as a sequence of nested existence-constrained semi-infinite programs (SIPs), which can be efficiently solved using local reduction techniques. To demonstrate its effectiveness, we evaluate our approach on a planar quadrotor problem, where it clearly outperforms an equivalent method that does not account for future updates at the cost of increased computation time.
This letter proposes an Adversarial Inverse Reinforcement Learning (AIRL)-based energy management method for a smart home, which incorporates an implicit thermal dynamics model. In the proposed method, historical optimal decisions are first generated using a neural network-assisted Hierarchical Model Predictive Control (HMPC) framework. These decisions are then used as expert demonstrations in the AIRL module, which aims to train a discriminator to distinguish expert demonstrations from transitions generated by a reinforcement learning agent policy, while simultaneously updating the agent policy that can produce transitions to confuse the discriminator. The proposed HMPC-AIRL method eliminates the need for explicit thermal dynamics models, prior or predictive knowledge of uncertain parameters, or manually designed reward functions. Simulation results based on real-world traces demonstrate the effectiveness and data efficiency of the proposed method.
The controller is one of the most important modules in the autonomous driving pipeline, ensuring the vehicle reaches its desired position. In this work, a reinforcement learning based lateral control approach, despite the imperfections in the vehicle models due to measurement errors and simplifications, is presented. Our approach ensures comfortable, efficient, and robust control performance considering the interface between controlling and other modules. The controller consists of the conventional Model Predictive Control (MPC)-PID part as the basis and the demonstrator, and the Deep Reinforcement Learning (DRL) part which leverages the online information from the MPC-PID part. The controller's performance is evaluated in CARLA using the ground truth of the waypoints as inputs. Experimental results demonstrate the effectiveness of the controller when vehicle information is incomplete, and the training of DRL can be stabilized with the demonstration part. These findings highlight the potential to reduce development and integration efforts for autonomous driving pipelines in the future.
Nonlinear Model Predictive Control (NMPC) offers a powerful approach for controlling complex nonlinear systems, yet faces two key challenges. First, accurately modeling nonlinear dynamics remains difficult. Second, variables directly related to control objectives often cannot be directly measured during operation. Although high-cost sensors can acquire these variables during model development, their use in practical deployment is typically infeasible. To overcome these limitations, we propose a Predictive Virtual Sensor Identification (PVSID) framework that leverages temporary high-cost sensors during the modeling phase to create virtual sensors for NMPC implementation. We validate PVSID on a Two-Degree-of-Freedom (2-DoF) direct-drive robotic arm with complex joint interactions, capturing tip position via motion capture during modeling and utilize an Inertial Measurement Unit (IMU) in NMPC. Experimental results show our NMPC with identified virtual sensors achieves precise tip trajectory tracking without requiring the motion capture system during operation. PVSID offers a practical solution for implementing optimal control in nonlinear systems where the measurement of key variables is constrained by cost or operational limitations.
Thermally induced laser noise poses a critical limitation to the sensitivity of quantum sensor arrays employing ultra-stable amplified lasers, primarily stemming from nonlinear gain-temperature coupling effects in tapered amplifiers (TAs). To address this challenge, we present a robust intelligent control strategy that synergistically integrates an encoder-decoder physics-informed gated recurrent unit (PI-GRU) network with a model predictive control (MPC) framework. Our methodology incorporates physical soft constraints into the neural network architecture, yielding a predictive model with enhanced physical consistency that demonstrates robust extrapolation capabilities beyond the training data distribution. Leveraging the PI-GRU model's accurate multi-step predictive performance, we implement a hierarchical parallel MPC architecture capable of real-time thermal instability compensation. This hybrid approach achieves cross-domain consistent thermal stabilization in TAs under diverse laser power operations. Remarkably, while trained exclusively on low-power operational data, our system demonstrates exceptional generalization, improving prediction accuracy by 58.2% and temperature stability by 69.1% in previously unseen high-power operating regimes, as experimentally validated. The novel synchronization of physics-informed neural networks with advanced MPC frameworks presented in this work establishes a groundbreaking paradigm for addressing robustness challenges in cross-domain predictive control applications, overcoming conventional modeling limitations.
Efficient energy management in prosumer households is key to alleviating grid stress in an energy transition marked by electric vehicles (EV), renewable energies and battery storage. However, it is unclear how households optimize prosumer EV charging. Here we study real-world data from 90 households on fixed-rate electricity tariffs in German-speaking countries to investigate the potential of Deep Reinforcement Learning (DRL) and other control approaches (Rule-Based, Model Predictive Control) to manage the dynamic and uncertain environment of Home Energy Management (HEM) and optimize household charging patterns. The DRL agent efficiently aligns charging of EV and battery storage with photovoltaic (PV) surplus. We find that frequent EV charging transactions, early EV connections and PV surplus increase optimization potential. A detailed analysis of nine households (1 hour resolution, 1 year) demonstrates that high battery capacity facilitates self optimization; in this case further algorithmic control shows little value. In cases with relatively low battery capacity, algorithmic control with DRL improves energy management and cost savings by a relevant margin. This result is further corroborated by our simulation of a synthetic household. We conclude that prosumer households with optimization potential would profit from DRL, thus benefiting also the full electricity system and its decarbonization.
This paper analyzes the stability of interconnected continuous-time (CT) and discrete-time (DT) systems coupled through sampling and zero-order hold mechanisms. The DT system updates its output at regular intervals $T>0$ by applying an $n$-fold composition of a given map. This setup is motivated by online and sampled-data implementations of optimization-based controllers - particularly model predictive control (MPC) - where the DT system models $n$ iterations of an algorithm approximating the solution of an optimization problem. We introduce the concept of a reduced model, defined as the limiting behavior of the sampled-data system as $T \to 0^+$ and $n \to +\infty$. Our main theoretical contribution establishes that when the reduced model is contractive, there exists a threshold duration $T(n)$ for each iteration count $n$ such that the CT-DT interconnection achieves exponential stability for all sampling periods $T < T(n)$. Finally, under the stronger condition that both the CT and DT systems are contractive, we show exponential stability of their interconnection using a small-gain argument. Our theoretical results provide new insights into suboptimal MPC stability, showing that convergence guarantees hold even when using a single iteration of the optimization algorithm - a practically significant finding for real-time control applications.
We propose KnotGym, an interactive environment for complex, spatial reasoning and manipulation. KnotGym includes goal-oriented rope manipulation tasks with varying levels of complexity, all requiring acting from pure image observations. Tasks are defined along a clear and quantifiable axis of complexity based on the number of knot crossings, creating a natural generalization test. KnotGym has a simple observation space, allowing for scalable development, yet it highlights core challenges in integrating acute perception, spatial reasoning, and grounded manipulation. We evaluate methods of different classes, including model-based RL, model-predictive control, and chain-of-thought reasoning, and illustrate the challenges KnotGym presents. KnotGym is available at https://github.com/lil-lab/knotgym.
In this paper, we consider the design of model predictive control (MPC) algorithms based on deep operator neural networks (DeepONets). These neural networks are capable of accurately approximating real and complex valued solutions of continuous time nonlinear systems without relying on recurrent architectures. The DeepONet architecture is made up of two feedforward neural networks: the branch network, which encodes the input function space, and the trunk network, which represents dependencies on temporal variables or initial conditions. Utilizing the original DeepONet architecture as a predictor within MPC for Multi Input Multi Output (MIMO) systems requires multiple branch networks, to generate multi output predictions, one for each input. Moreover, to predict multiple time steps into the future, the network has to be evaluated multiple times. Motivated by this, we introduce a multi step DeepONet (MS-DeepONet) architecture that computes in one shot multi step predictions of system outputs from multi step input sequences, which is better suited for MPC. We prove that the MS DeepONet is a universal approximator in terms of multi step sequence prediction. Additionally, we develop automated hyper parameter selection strategies and implement MPC frameworks using both the standard DeepONet and the proposed MS DeepONet architectures in PyTorch. The implementation is publicly available on GitHub. Simulation results demonstrate that MS-DeepONet consistently outperforms the standard DeepONet in learning and predictive control tasks across several nonlinear benchmark systems: the van der Pol oscillator, the quadruple tank process, and a cart pendulum unstable system, where it successfully learns and executes multiple swing up and stabilization policies.
Model-based reinforcement learning (MBRL) offers an intuitive way to increase the sample efficiency of model-free RL methods by simultaneously training a world model that learns to predict the future. MBRL methods have progressed by largely prioritising the actor; optimising the world model learning has been neglected meanwhile. Improving the fidelity of the world model and reducing its time to convergence can yield significant downstream benefits, one of which is improving the ensuing performance of any actor it may train. We propose a novel approach that anticipates and actively seeks out high-entropy states using short-horizon latent predictions generated by the world model, offering a principled alternative to traditional curiosity-driven methods that chase once-novel states well after they were stumbled into. While many model predictive control (MPC) based methods offer similar alternatives, they typically lack commitment, synthesising multi step plans after every step. To mitigate this, we present a hierarchical planner that dynamically decides when to replan, planning horizon length, and the weighting between reward and entropy. While our method can theoretically be applied to any model that trains its own actors with solely model generated data, we have applied it to just Dreamer as a proof of concept. Our method finishes the Miniworld procedurally generated mazes 50% faster than base Dreamer at convergence and the policy trained in imagination converges in only 60% of the environment steps that base Dreamer needs.
Configuration-Constrained Tube Model Predictive Control (CCTMPC) offers flexibility by using a polytopic parameterization of invariant sets and the optimization of an associated vertex control law. This flexibility, however, often demands computational trade-offs between set parameterization accuracy and optimization complexity. This paper proposes two innovations that help the user tackle this trade-off. First, a structured framework is proposed, which strategically limits optimization degrees of freedom, significantly reducing online computation time while retaining stability guarantees. This framework aligns with Homothetic Tube MPC (HTMPC) under maximal constraints. Second, a template refinement algorithm that iteratively solves quadratic programs is introduced to balance polytope complexity and conservatism. Simulation studies on an illustrative benchmark problem as well as a high-dimensional ten-state system demonstrate the approach's efficiency, achieving robust performance with minimal computational overhead. The results validate a practical pathway to leveraging CCTMPC's adaptability without sacrificing real-time viability.
In model predictive control (MPC), the choice of cost-weighting matrices and designing the Hessian matrix directly affects the trade-off between rapid state regulation and minimizing the control effort. However, traditional MPC in quadratic programming relies on fixed design matrices across the entire horizon, which can lead to suboptimal performance. This letter presents a Riccati equation-based method for adjusting the design matrix within the MPC framework, which enhances real-time performance. We employ a penalized least-squares (PLS) approach to derive a quadratic cost function for a discrete-time linear system over a finite prediction horizon. Using the method of weighting and enforcing the constraint equation by introducing a large penalty parameter, we solve the constrained optimization problem and generate control inputs for forward-shifted horizons. This process yields a recursive PLS-based Riccati equation that updates the design matrix as a regularization term in each shift, forming the foundation of the regularized MPC (Re-MPC) algorithm. To accomplish this, we provide a convergence and stability analysis of the developed algorithm. Numerical analysis demonstrates its superiority over traditional methods by allowing Riccati equation-based adjustments.
Neural networks are powerful tools for data-driven modeling of complex dynamical systems, enhancing predictive capability for control applications. However, their inherent nonlinearity and black-box nature challenge control designs that prioritize rigorous safety and recursive feasibility guarantees. This paper presents algorithmic methods for synthesizing control invariant sets specifically tailored to neural network based dynamical models. These algorithms employ set recursion, ensuring termination after a finite number of iterations and generating subsets in which closed-loop dynamics are forward invariant, thus guaranteeing perpetual operational safety. Additionally, we propose model predictive control designs that integrate these control invariant sets into mixed-integer optimization, with guaranteed adherence to safety constraints and recursive feasibility at the computational level. We also present a comprehensive theoretical analysis examining the properties and guarantees of the proposed methods. Numerical simulations in an autonomous driving scenario demonstrate the methods' effectiveness in synthesizing control-invariant sets offline and implementing model predictive control online, ensuring safety and recursive feasibility.
This paper presents a comprehensive overview of data-driven model predictive control, highlighting state-of-the-art methodologies and their numerical implementation. The discussion begins with a brief review of conventional model predictive control (MPC), which discusses both linear MPC (LMPC) and nonlinear MPC (NMPC). This is followed by a section on data-driven LMPC, outlining fundamental concepts and the implementation of various approaches, including subspace predictive control and prediction error methods. Subsequently, the focus shifts to data-driven NMPC, emphasizing approaches based on recurrent neural network-based models. The paper concludes with a review of recent advancements in data-driven MPC and explores potential directions for future research.
As climate change increases the threat of weather-related disasters, research on weather control is gaining importance. The objective of weather control is to mitigate disaster risks by administering interventions with optimal timing, location, and intensity. However, the optimization process is highly challenging due to the vast scale and complexity of weather phenomena, which introduces two major challenges. First, obtaining accurate gradient information for optimization is difficult. In addition, numerical weather prediction (NWP) models demand enormous computational resources, necessitating parameter optimization with minimal function evaluations. To address these challenges, this study proposes a method for designing weather interventions based on black-box optimization, which enables efficient exploration without requiring gradient information. The proposed method is evaluated in two distinct control scenarios: one-shot initial value intervention and sequential intervention based on model predictive control. Furthermore, a comparative analysis is conducted among four representative black-box optimization methods in terms of total rainfall reduction. Experimental results show that Bayesian optimization achieves higher control effectiveness than the others, particularly in high-dimensional search spaces. These findings suggest that Bayesian optimization is a highly effective approach for weather intervention computation.
This paper delves into the challenges posed by the increasing complexity of modern control systems, specifically focusing on bilinear systems, a prevalent subclass of non-linear systems characterized by state dynamics influenced by the interaction of state and control variables. Traditional control strategies, such as PID controllers, often fall short in adequately addressing the intricacies of such systems due to their predictive limitations. To bridge this gap, we introduce Model Predictive Control (MPC), a sophisticated technique that utilizes system models to forecast future behaviors, allowing for the computation of an optimal control sequence by minimizing deviations and control efforts. The Koopman operator emerges as a pivotal tool in this framework by providing a means to linearize the nonlinear dynamics of bilinear systems. By integrating the principles of Lyapunov theory with the linearizing capabilities of the Koopman operator into the MPC framework, we give rise to Koopman Lyapunov-based Model Predictive Control (Koopman LMPC). This approach not only retains MPC's predictive capabilities but also harnesses the Koopman operator's ability to transform complex nonlinear behaviors into a linear framework, thereby enhancing the robustness and applicability of LMPC. With the stability assurances from Lyapunov theory, Koopman LMPC presents a robust solution to effectively control and stabilize bilinear systems. The paper underscores the efficacy of Koopman LMPC, emphasizing its significance in achieving optimal performance and system stability, marking it as a promising approach for the future of advanced control systems.
This study presents an innovative approach to Model Predictive Control (MPC) by leveraging the powerful combination of Koopman theory and Deep Reinforcement Learning (DRL). By transforming nonlinear dynamical systems into a higher-dimensional linear regime, the Koopman operator facilitates the linear treatment of nonlinear behaviors, paving the way for more efficient control strategies. Our methodology harnesses the predictive prowess of Koopman-based models alongside the optimization capabilities of DRL, particularly using the Proximal Policy Optimization (PPO) algorithm, to enhance the controller's performance. The resulting end-to-end learning framework refines the predictive control policies to cater to specific operational tasks, optimizing both performance and economic efficiency. We validate our approach through rigorous NMPC and eNMPC case studies, demonstrating that the Koopman-RL controller outperforms traditional controllers by achieving higher stability, superior constraint satisfaction, and significant cost savings. The findings indicate that our model can be a robust tool for complex control tasks, offering valuable insights into future applications of RL in MPC.