This paper focuses on passenger-oriented real-time train rescheduling, considering flexible train composition and rolling stock circulation, by integrating learning-based and optimization-based approaches. A learning-based model predictive control (MPC) approach is developed for real-time train rescheduling with flexible train composition and rolling stock circulation to address time-varying passenger demands. In the proposed approach, first, the values of the integer variables are obtained by pre-trained long short-term memory (LSTM) networks; next, they are fixed and the values of continuous variables are determined via nonlinear constrained optimization. The learning-based MPC approach enables us to jointly consider efficiency and constraint satisfaction by combining learning-based and optimization-based approaches. In order to reduce the number of integer variables, four presolve techniques are developed to prune a subset of integer decision variables. Numerical simulations based on real-life data from the Beijing urban rail transit system are conducted to illustrate the effectiveness of the developed learning-based MPC approach.
A common problem when using model predictive control (MPC) in practice is the satisfaction of safety specifications beyond the prediction horizon. While theoretical works have shown that safety can be guaranteed by enforcing a suitable terminal set constraint or a sufficiently long prediction horizon, these techniques are difficult to apply and thus are rarely used by practitioners, especially in the case of general nonlinear dynamics. To solve this problem, we impose a tradeoff between exact recursive feasibility, computational tractability, and applicability to ''black-box'' dynamics by learning an approximate discrete-time control barrier function and incorporating it into a variational inference MPC (VIMPC), a sampling-based MPC paradigm. To handle the resulting state constraints, we further propose a new sampling strategy that greatly reduces the variance of the estimated optimal control, improving the sample efficiency, and enabling real-time planning on a CPU. The resulting Neural Shield-VIMPC (NS-VIMPC) controller yields substantial safety improvements compared to existing sampling-based MPC controllers, even under badly designed cost functions. We validate our approach in both simulation and real-world hardware experiments.
Data-driven control is a powerful tool that enables the design and implementation of control strategies directly from data without explicitly identifying the underlying system dynamics. While various data-driven control techniques, such as stabilization, linear quadratic regulation, and model predictive control, have been extensively developed, these methods are not inherently suited for multi-linear dynamical systems, where the states are represented as higher-order tensors. In this article, we propose a novel framework for data-driven control of T-product-based dynamical systems (TPDSs), where the system evolution is governed by the T-product between a third-order dynamic tensor and a third-order state tensor. In particular, we offer necessary and sufficient conditions to determine the data informativity for system identification, stabilization by state feedback, and T-product quadratic regulation of TPDSs with detailed complexity analyses. Finally, we validate our framework through numerical examples.
In trajectory optimization, Model Predictive Path Integral (MPPI) control is a sampling-based Model Predictive Control (MPC) framework that generates optimal inputs by efficiently simulating numerous trajectories. In practice, however, MPPI often struggles to guarantee safety assurance and balance efficient sampling in open spaces with the need for more extensive exploration under tight constraints. To address this challenge, we incorporate discrete barrier states (DBaS) into MPPI and propose a novel MPPI-DBaS algorithm that ensures system safety and enables adaptive exploration across diverse scenarios. We evaluate our method in simulation experiments where the vehicle navigates through closely placed obstacles. The results demonstrate that the proposed algorithm significantly outperforms standard MPPI, achieving a higher success rate and lower tracking errors.
Decarbonization plans promote the transition to heat pumps (HPs), creating new opportunities for their energy flexibility in demand response programs, solar photovoltaic integration and optimization of distribution networks. This paper reviews scheduling-based and real-time optimization methods for controlling HPs with a focus on energy flexibility in distribution networks. Scheduling-based methods fall into two categories: rule-based controllers (RBCs), which rely on predefined control rules without explicitly seeking optimal solutions, and optimization models, which are designed to determine the optimal scheduling of operations. Real-time optimization is achieved through model predictive control (MPC), which relies on a predictive model to optimize decisions over a time horizon, and reinforcement learning (RL), which takes a model-free approach by learning optimal strategies through direct interaction with the environment. The paper also examines studies on the impact of HPs on distribution networks, particularly those leveraging energy flexibility strategies. Key takeaways suggest the need to validate control strategies for extreme cold-weather regions that require backup heaters, as well as develop approaches designed for demand charge schemes that integrate HPs with other controllable loads. From a grid impact assessment perspective, studies have focused primarily on RBCs for providing energy flexibility through HP operation, without addressing more advanced methods such as real-time optimization using MPC or RL-based algorithms. Incorporating these advanced control strategies could help identify key limitations, including the impact of varying user participation levels and the cost-benefit trade-offs associated with their implementation.
This paper presents a hierarchical framework for demand response optimization in air separation units (ASUs) that combines reinforcement learning (RL) with linear model predictive control (LMPC). We investigate two control architectures: a direct RL approach and a control-informed methodology where an RL agent provides setpoints to a lower-level LMPC. The proposed RL-LMPC framework demonstrates improved sample efficiency during training and better constraint satisfaction compared to direct RL control. Using an industrial ASU case study, we show that our approach successfully manages operational constraints while optimizing electricity costs under time-varying pricing. Results indicate that the RL-LMPC architecture achieves comparable economic performance to direct RL while providing better robustness and requiring fewer training samples to converge. The framework offers a practical solution for implementing flexible operation strategies in process industries, bridging the gap between data-driven methods and traditional control approaches.
Model Predictive Control (MPC) is a widely used technique for managing timevarying systems, supported by extensive theoretical analysis. While theoretical studies employing dynamic regret frameworks have established robust performance guarantees, their empirical validation remains sparse. This paper investigates the practical applicability of MPC by empirically evaluating the assumptions and theoretical results proposed by Lin et al. [2022]. Specifically, we analyze the performance of online MPC under varying prediction errors and prediction horizons in Linear Time-Varying (LTV) systems. Our study examines the relationship between dynamic regret, prediction errors, and prediction horizons, providing insights into the trade-offs involved. By bridging theory and practice, this work advances the understanding and application of MPC in real-world scenarios.
A two-layer control architecture is proposed, which promotes scalable implementations for model predictive controllers. The top layer acts as both reference governor for the bottom layer, and as a feedback controller for the regulated network. By employing set-based methods, global theoretical guarantees are obtained by enforcing local constraints upon the variables of the network and of the first layer's implementation. The proposed technique offers recursive feasibility guarantees as one of its central features, and the expressions of the resulting predictive strategies bear a striking resemblance to classical formulations from model predictive control literature, allowing for flexible and easily customizable implementations.
A two-layer control architecture is proposed, which promotes scalable implementations for model predictive controllers. The top layer acts as both reference governor for the bottom layer, and as a feedback controller for the regulated network. By employing set-based methods, global theoretical guarantees are obtained by enforcing local constraints upon the variables of the network and of the first layer's implementation. The proposed technique offers recursive feasibility guarantees as one of its central features, and the expressions of the resulting predictive strategies bear a striking resemblance to classical formulations from model predictive control literature, allowing for flexible and easily customizable implementations.
We propose a novel model for the prediction of robot trajectories on rough offroad terrain from the onboard camera images. This model enforces the laws of classical mechanics through a physics-aware neural symbolic layer while preserving the ability to learn from large-scale data as it is end-to-end differentiable. The proposed hybrid model integrates a black-box component that predicts robot-terrain interaction forces with a neural-symbolic layer. This layer includes a differentiable physics engine that computes the robot's trajectory by querying these forces at the points of contact with the terrain. As the proposed architecture comprises substantial geometrical and physics priors, the resulting model can also be seen as a learnable physics engine conditioned on real images that delivers $10^4$ trajectories per second. We argue and empirically demonstrate that this architecture reduces the sim-to-real gap and mitigates out-of-distribution sensitivity. The differentiability, in conjunction with the rapid simulation speed, makes the model well-suited for various applications including model predictive control, trajectory shooting, supervised and reinforcement learning or SLAM. The codes and data are publicly available.
In this work, we conducted research on deformable object manipulation by robots based on demonstration-enhanced reinforcement learning (RL). To improve the learning efficiency of RL, we enhanced the utilization of demonstration data from multiple aspects and proposed the HGCR-DDPG algorithm. It uses a novel high-dimensional fuzzy approach for grasping-point selection, a refined behavior-cloning method to enhance data-driven learning in Rainbow-DDPG, and a sequential policy-learning strategy. Compared to the baseline algorithm (Rainbow-DDPG), our proposed HGCR-DDPG achieved 2.01 times the global average reward and reduced the global average standard deviation to 45% of that of the baseline algorithm. To reduce the human labor cost of demonstration collection, we proposed a low-cost demonstration collection method based on Nonlinear Model Predictive Control (NMPC). Simulation experiment results show that demonstrations collected through NMPC can be used to train HGCR-DDPG, achieving comparable results to those obtained with human demonstrations. To validate the feasibility of our proposed methods in real-world environments, we conducted physical experiments involving deformable object manipulation. We manipulated fabric to perform three tasks: diagonal folding, central axis folding, and flattening. The experimental results demonstrate that our proposed method achieved success rates of 83.3%, 80%, and 100% for these three tasks, respectively, validating the effectiveness of our approach. Compared to current large-model approaches for robot manipulation, the proposed algorithm is lightweight, requires fewer computational resources, and offers task-specific customization and efficient adaptability for specific tasks.
The urgent energy transition requirements towards a sustainable future stretch across various industries and are a significant challenge facing humanity. Hydrogen promises a clean, carbon-free future, with the opportunity to integrate with existing solutions in the transportation sector. However, adding hydrogen to existing technologies such as diesel engines requires additional modeling effort. Reinforcement Learning (RL) enables interactive data-driven learning that eliminates the need for mathematical modeling. The algorithms, however, may not be real-time capable and need large amounts of data to work in practice. This paper presents a novel approach which uses offline model learning with RL to demonstrate safe control of a 4.5 L Hydrogen Diesel Dual-Fuel (H2DF) engine. The controllers are demonstrated to be constraint compliant and can leverage a novel state-augmentation approach for sample-efficient learning. The offline policy is subsequently experimentally validated on the real engine where the control algorithm is executed on a Raspberry Pi controller and requires 6 times less computation time compared to online Model Predictive Control (MPC) optimization.
Realistic driving simulation requires that NPCs not only mimic natural driving behaviors but also react to the behavior of other simulated agents. Recent developments in diffusion-based scenario generation focus on creating diverse and realistic traffic scenarios by jointly modelling the motion of all the agents in the scene. However, these traffic scenarios do not react when the motion of agents deviates from their modelled trajectories. For example, the ego-agent can be controlled by a stand along motion planner. To produce reactive scenarios with joint scenario models, the model must regenerate the scenario at each timestep based on new observations in a Model Predictive Control (MPC) fashion. Although reactive, this method is time-consuming, as one complete possible future for all NPCs is generated per simulation step. Alternatively, one can utilize an autoregressive model (AR) to predict only the immediate next-step future for all NPCs. Although faster, this method lacks the capability for advanced planning. We present a rolling diffusion based traffic scene generation model which mixes the benefits of both methods by predicting the next step future and simultaneously predicting partially noised further future steps at the same time. We show that such model is efficient compared to diffusion model based AR, achieving a beneficial compromise between reactivity and computational efficiency.
This paper proposes a stochastic model predictive control method for linear systems affected by additive Gaussian disturbances. Closed-loop satisfaction of probabilistic constraints and recursive feasibility of the underlying convex optimization problem is guaranteed. Optimization over feedback policies online increases performance and reduces conservatism compared to fixed-feedback approaches. The central mechanism is a finitely determined maximal admissible set for probabilistic constraints, together with the reconditioning of the predicted probabilistic constraints on the current knowledge at every time step. The proposed method's reduced conservatism and improved performance in terms of the achieved closed-loop cost is demonstrated in a numerical example.
Implementing carbon capture technology on-board ships holds promise as a solution to facilitate the reduction of carbon intensity in international shipping, as mandated by the International Maritime Organization. In this work, we address the energy-efficient operation of shipboard carbon capture processes by proposing a hybrid modeling-based economic predictive control scheme. Specifically, we consider a comprehensive shipboard carbon capture process that encompasses the ship engine system and the shipboard post-combustion carbon capture plant. To accurately and robustly characterize the dynamic behaviors of this shipboard plant, we develop a hybrid dynamic process model that integrates available imperfect physical knowledge with neural networks trained using process operation data. An economic model predictive control approach is proposed based on the hybrid model to ensure carbon capture efficiency while minimizing energy consumption required for the carbon capture process operation. The cross-entropy method is employed to efficiently solve the complex non-convex optimization problem associated with the proposed hybrid model-based economic model predictive control method. Extensive simulations, analyses, and comparisons are conducted to verify the effectiveness and illustrate the superiority of the proposed framework.
Despite the success of Gaussian process based Model Predictive Control (MPC) in robotic control, its applicability scope is greatly hindered by multimodal disturbances that are prevalent in real-world settings. Here we propose a novel Mixture of Gaussian Processes based Distributionally Robust MPC (MoGP-DR-MPC) framework for linear time invariant systems subject to potentially multimodal state-dependent disturbances. This framework utilizes MoGP to automatically determine the number of modes from disturbance data. Using the mean and variance information provided by each mode-specific predictive distribution, it constructs a data-driven state-dependent ambiguity set, which allows for flexible and fine-grained disturbance modeling. Based on this ambiguity set, we impose Distributionally Robust Conditional Value-at Risk (DR-CVaR) constraints to effectively achieve distributional robustness against errors in the predictive distributions. To address the computational challenge posed by these constraints in the resulting MPC problem, we equivalently reformulate the DR-CVaR constraints into tractable second-order cone constraints. Furthermore, we provide theoretical guarantees on the recursive feasibility and stability of the proposed framework. The enhanced control performance of MoGP-DR-MPC is validated through both numerical experiments and simulations on a quadrotor system, demonstrating notable reductions in closed-loop cost by 17% and 4% respectively compared against Gaussian process based MPC.
Solving real-time quadratic programming (QP) is a ubiquitous task in control engineering, such as in model predictive control and control barrier function-based QP. In such real-time scenarios, certifying that the employed QP algorithm can either return a solution within a predefined level of optimality or detect QP infeasibility before the predefined sampling time is a pressing requirement. This article considers convex QP (including linear programming) and adopts its homogeneous formulation to achieve infeasibility detection. Exploiting this homogeneous formulation, this article proposes a novel infeasible interior-point method (IPM) algorithm with the best theoretical $O(\sqrt{n})$ iteration complexity that feasible IPM algorithms enjoy. The iteration complexity is proved to be \textit{exact} (rather than an upper bound), \textit{simple to calculate}, and \textit{data independent}, with the value $\left\lceil\frac{\log(\frac{n+1}{\epsilon})}{-\log(1-\frac{0.414213}{\sqrt{n+1}})}\right\rceil$ (where $n$ and $\epsilon$ denote the number of constraints and the predefined optimality level, respectively), making it appealing to certify the execution time of online time-varying convex QPs. The proposed algorithm is simple to implement without requiring a line search procedure (uses the full Newton step), and its C-code implementation (offering MATLAB, Julia, and Python interfaces) and numerical examples are publicly available at https://github.com/liangwu2019/EIQP.
Reinforcement learning (RL) and model predictive control (MPC) offer a wealth of distinct approaches for automatic decision-making. Given the impact both fields have had independently across numerous domains, there is growing interest in combining the general-purpose learning capability of RL with the safety and robustness features of MPC. To this end, this paper presents a tutorial-style treatment of RL and MPC, treating them as alternative approaches to solving Markov decision processes. In our formulation, RL aims to learn a global value function through offline exploration in an uncertain environment, whereas MPC constructs a local value function through online optimization. This local-global perspective suggests new ways to design policies that combine robustness and goal-conditioned learning. Robustness is incorporated into the RL and MPC pipelines through a scenario-based approach. Goal-conditioned learning aims to alleviate the burden of engineering a reward function for RL. Combining the two leads to a single policy that unites a robust, high-level RL terminal value function with short-term, scenario-based MPC planning for reliable constraint satisfaction. This approach leverages the benefits of both RL and MPC, the effectiveness of which is demonstrated on classical control benchmarks.
We develop a model predictive control (MPC) policy for station-keeping (SK) on a Near-Rectilinear Halo Orbit (NRHO). The proposed policy achieves full-state tracking of a reference NRHO via a two-maneuver control horizon placed one revolution apart. Our method abides by the typical mission requirement that at most one maneuver is used for SK during each NRHO revolution. Simultaneously, the policy has sufficient controllability for full-state tracking, making it immune to phase deviation issues in the along-track direction of the reference NRHO, a common drawback of existing SK methods with a single maneuver per revolution. We report numerical simulations with a navigation filter to demonstrate the MPC's performance with output feedback. Our approach successfully maintains the spacecraft's motion in the vicinity of the reference in both space and phase, with tighter tracking than state-of-the-art SK methods and comparable delta-V performance.
In this paper, we discuss incentive design for hierarchical model predictive control (MPC) systems viewed as Stackelberg games. We consider a hierarchical MPC formulation where, given a lower-level convex MPC (LoMPC), the upper-level system solves a bilevel MPC (BiMPC) subject to the constraint that the lower-level system inputs are optimal for the LoMPC. Such hierarchical problems are challenging due to optimality constraints in the BiMPC formulation. We analyze an incentive Stackelberg game variation of the problem, where the BiMPC provides additional incentives for the LoMPC cost function, which grants the BiMPC influence over the LoMPC inputs. We show that for such problems, the BiMPC can be reformulated as a simpler optimization problem, and the optimal incentives can be iteratively computed without knowing the LoMPC cost function. We extend our formulation for the case of multiple LoMPCs and propose an algorithm that finds bounded suboptimal solutions for the BiMPC. We demonstrate our algorithm for a dynamic price control example, where an independent system operator (ISO) sets the electricity prices for electric vehicle (EV) charging with the goal of minimizing a social cost and satisfying electricity generation constraints. Notably, our method scales well to large EV population sizes.