We propose a distributed model predictive control (MPC) framework for coordinating heterogeneous, nonlinear multi-agent systems under individual and coupling constraints. The cooperative task is encoded as a shared objective function minimized collectively by the agents. Each agent optimizes an artificial reference as an intermediate step towards the cooperative objective, along with a control input to track it. We establish recursive feasibility, asymptotic stability, and transient performance bounds under suitable assumptions. The solution to the cooperative task is not predetermined but emerges from the optimized interactions of the agents. We demonstrate the framework on numerical examples inspired by satellite constellation control, collision-free narrow-passage traversal, and coordinated quadrotor flight.
In this work, we propose an output-feedback tube-based model predictive control (MPC) scheme for linear systems under dynamic uncertainties that are described via integral quadratic constraints (IQC). By leveraging IQCs, a large class of nonlinear and dynamic uncertainties can be addressed. We leverage recent IQC synthesis tools to design a dynamic controller and an observer that are robust to these uncertainties and minimize the size of the resulting constraint tightening in the MPC. Thereby, we show that the robust estimation problem using IQCs with peak-to-peak performance can be convexified. We guarantee recursive feasibility, robust constraint satisfaction, and input-to-state stability of the resulting MPC scheme.
Real-time optimal control remains a fundamental challenge in robotics, especially for nonlinear systems with stringent performance requirements. As one of the representative trajectory optimization algorithms, the iterative Linear Quadratic Regulator (iLQR) faces limitations due to their inherently sequential computational nature, which restricts the efficiency and applicability of real-time control for robotic systems. While existing parallel implementations aim to overcome the above limitations, they typically demand additional computational iterations and high-performance hardware, leading to only modest practical improvements. In this paper, we introduce Quattro, a transformer-accelerated iLQR framework employing an algorithm-hardware co-design strategy to predict intermediate feedback and feedforward matrices. It facilitates effective parallel computations on resource-constrained devices without sacrificing accuracy. Experiments on cart-pole and quadrotor systems show an algorithm-level acceleration of up to 5.3$\times$ and 27$\times$ per iteration, respectively. When integrated into a Model Predictive Control (MPC) framework, Quattro achieves overall speedups of 2.8$\times$ for the cart-pole and 17.8$\times$ for the quadrotor compared to the one that applies traditional iLQR. Transformer inference is deployed on FPGA to maximize performance, achieving further up to 20.8$\times$ speedup over prevalent embedded CPUs with over 11$\times$ power reduction than GPU and low hardware resource overhead.
There is an increasing need for effective control of systems with complex dynamics, particularly through data-driven approaches. System Level Synthesis (SLS) has emerged as a powerful framework that facilitates the control of large-scale systems while accounting for model uncertainties. SLS approaches are currently limited to linear systems and time-varying linear control policies, thus limiting the class of achievable control strategies. We introduce a novel closed-loop parameterization for time-varying affine control policies, extending the SLS framework to a broader class of systems and policies. We show that the closed-loop behavior under affine policies can be equivalently characterized using past system trajectories, enabling a fully data-driven formulation. This parameterization seamlessly integrates affine policies into optimal control problems, allowing for a closed-loop formulation of general Model Predictive Control (MPC) problems. To the best of our knowledge, this is the first work to extend SLS to affine policies in both model-based and data-driven settings, enabling an equivalent formulation of MPC problems using closed-loop maps. We validate our approach through numerical experiments, demonstrating that our model-based and data-driven affine SLS formulations achieve performance on par with traditional model-based MPC.
Approximating nonlinear systems as linear ones is a common workaround to apply control tools tailored for linear systems. This motivates our present work where we developed a data-driven model predictive controller (MPC) based on the Koopman operator framework, allowing the embedding of nonlinear dynamics in a higher dimensional, but linear function space. The controller, termed adaptive Koopman model predictive control (KMPC), uses online closed-loop feedback to learn and incrementally update a linear representation of nonlinear system dynamics, without the prior knowledge of a model. Adaptive KMPC differs from most other Koopman-based control frameworks that aim to identify high-validity-range models in advance and then enter closed-loop control without further model adaptations. To validate the controller, trajectory tracking experiments are conducted with 1R and 2R robots under force disturbances and changing model parameters. We compare the controller to classical linearization MPC and Koopman-based MPC without model updates, denoted static KMPC. The results show that adaptive KMPC can, opposed to static KMPC, generalize over unforeseen force disturbances and can, opposed to linearization MPC, handle varying dynamic parameters, while using a small set of basis functions to approximate the Koopman operator.
Model Predictive Control (MPC) has been demonstrated to be effective in continuous control tasks. When a world model and a value function are available, planning a sequence of actions ahead of time leads to a better policy. Existing methods typically obtain the value function and the corresponding policy in a model-free manner. However, we find that such an approach struggles with complex tasks, resulting in poor policy learning and inaccurate value estimation. To address this problem, we leverage the strengths of MPC itself. In this work, we introduce Bootstrapped Model Predictive Control (BMPC), a novel algorithm that performs policy learning in a bootstrapped manner. BMPC learns a network policy by imitating an MPC expert, and in turn, uses this policy to guide the MPC process. Combined with model-based TD-learning, our policy learning yields better value estimation and further boosts the efficiency of MPC. We also introduce a lazy reanalyze mechanism, which enables computationally efficient imitation learning. Our method achieves superior performance over prior works on diverse continuous control tasks. In particular, on challenging high-dimensional locomotion tasks, BMPC significantly improves data efficiency while also enhancing asymptotic performance and training stability, with comparable training time and smaller network sizes. Code is available at https://github.com/wertyuilife2/bmpc.
Co-optimization of both vehicle speed and gear position via model predictive control (MPC) has been shown to offer benefits for fuel-efficient autonomous driving. However, optimizing both the vehicle's continuous dynamics and discrete gear positions may be too computationally intensive for a real-time implementation. This work proposes a learning-based MPC scheme to address this issue. A policy is trained to select and fix the gear positions across the prediction horizon of the MPC controller, leaving a significantly simpler continuous optimization problem to be solved online. In simulation, the proposed approach is shown to have a significantly lower computation burden and a comparable performance, with respect to pure MPC-based co-optimization.
A large body of simulation research suggests that model predictive control (MPC) and reinforcement learning (RL) for heating, ventilation, and air-conditioning (HVAC) in residential and commercial buildings could reduce energy costs, pollutant emissions, and strain on power grids. Despite this potential, neither MPC nor RL has seen widespread industry adoption. Field demonstrations could accelerate MPC and RL adoption by providing real-world data that support the business case for deployment. Here we review 24 papers that document field demonstrations of MPC and RL in residential buildings and 80 in commercial buildings. After presenting demographic information -- such as experiment scopes, locations, and durations -- this paper analyzes experiment protocols and their influence on performance estimates. We find that 71% of the reviewed field demonstrations use experiment protocols that may lead to unreliable performance estimates. Over the remaining 29% that we view as reliable, the weighted-average cost savings, weighted by experiment duration, are 16% in residential buildings and 13% in commercial buildings. While these savings are potentially attractive, making the business case for MPC and RL also requires characterizing the costs of deployment, operation, and maintenance. Only 13 of the 104 reviewed papers report these costs or discuss related challenges. Based on these observations, we recommend directions for future field research, including: Improving experiment protocols; reporting deployment, operation, and maintenance costs; designing algorithms and instrumentation to reduce these costs; controlling HVAC equipment alongside other distributed energy resources; and pursuing emerging objectives such as peak shaving, arbitraging wholesale energy prices, and providing power grid reliability services.
Quadrupedal robots exhibit remarkable adaptability in unstructured environments, making them well-suited for formation control in real-world applications. However, keeping stable formations while ensuring collision-free navigation presents significant challenges due to dynamic obstacles, communication constraints, and the complexity of legged locomotion. This paper proposes a distributed model predictive control framework for multi-quadruped formation control, integrating Control Lyapunov Functions to ensure formation stability and Control Barrier Functions for decentralized safety enforcement. To address the challenge of dynamically changing team structures, we introduce Scale-Adaptive Permutation-Invariant Encoding (SAPIE), which enables robust feature encoding of neighboring robots while preserving permutation invariance. Additionally, we develop a low-latency Data Distribution Service-based communication protocol and an event-triggered deadlock resolution mechanism to enhance real-time coordination and prevent motion stagnation in constrained spaces. Our framework is validated through high-fidelity simulations in NVIDIA Omniverse Isaac Sim and real-world experiments using our custom quadrupedal robotic system, XG. Results demonstrate stable formation control, real-time feasibility, and effective collision avoidance, validating its potential for large-scale deployment.
A key challenge in tuning Model Predictive Control (MPC) cost function parameters is to ensure that the system performance stays consistently above a certain threshold. To address this challenge, we propose a novel method, COAT-MPC, Constrained Optimal Auto-Tuner for MPC. With every tuning iteration, COAT-MPC gathers performance data and learns by updating its posterior belief. It explores the tuning parameters' domain towards optimistic parameters in a goal-directed fashion, which is key to its sample efficiency. We theoretically analyze COAT-MPC, showing that it satisfies performance constraints with arbitrarily high probability at all times and provably converges to the optimum performance within finite time. Through comprehensive simulations and comparative analyses with a hardware platform, we demonstrate the effectiveness of COAT-MPC in comparison to classical Bayesian Optimization (BO) and other state-of-the-art methods. When applied to autonomous racing, our approach outperforms baselines in terms of constraint violations and cumulative regret over time.
For quadrotors, achieving safe and autonomous flight in complex environments with wind disturbances and dynamic obstacles still faces significant challenges. Most existing methods address wind disturbances in either trajectory planning or control, which may lead to hazardous situations during flight. The emergence of dynamic obstacles would further worsen the situation. Therefore, we propose an efficient and reliable framework for quadrotors that incorporates wind disturbance estimations during both the planning and control phases via a generalized proportional integral observer. First, we develop a real-time adaptive spatial-temporal trajectory planner that utilizes Hamilton-Jacobi (HJ) reachability analysis for error dynamics resulting from wind disturbances. By considering the forward reachability sets propagation on an Euclidean Signed Distance Field (ESDF) map, safety is guaranteed. Additionally, a Nonlinear Model Predictive Control (NMPC) controller considering wind disturbance compensation is implemented for robust trajectory tracking. Simulation and real-world experiments verify the effectiveness of our framework. The video and supplementary material will be available at https://github.com/Ma29-HIT/SEAL/.
In reinforcement learning (RL), world models serve as internal simulators, enabling agents to predict environment dynamics and future outcomes in order to make informed decisions. While previous approaches leveraging discrete latent spaces, such as DreamerV3, have demonstrated strong performance in discrete action settings and visual control tasks, their comparative performance in state-based continuous control remains underexplored. In contrast, methods with continuous latent spaces, such as TD-MPC2, have shown notable success in state-based continuous control benchmarks. In this paper, we demonstrate that modeling discrete latent states has benefits over continuous latent states and that discrete codebook encodings are more effective representations for continuous control, compared to alternative encodings, such as one-hot and label-based encodings. Based on these insights, we introduce DCWM: Discrete Codebook World Model, a self-supervised world model with a discrete and stochastic latent space, where latent states are codes from a codebook. We combine DCWM with decision-time planning to get our model-based RL algorithm, named DC-MPC: Discrete Codebook Model Predictive Control, which performs competitively against recent state-of-the-art algorithms, including TD-MPC2 and DreamerV3, on continuous control benchmarks. See our project website www.aidanscannell.com/dcmpc.
Inspired by the recent successes of Inverse Optimization (IO) across various application domains, we propose a novel offline Reinforcement Learning (ORL) algorithm for continuous state and action spaces, leveraging the convex loss function called ``sub-optimality loss" from the IO literature. To mitigate the distribution shift commonly observed in ORL problems, we further employ a robust and non-causal Model Predictive Control (MPC) expert steering a nominal model of the dynamics using in-hindsight information stemming from the model mismatch. Unlike the existing literature, our robust MPC expert enjoys an exact and tractable convex reformulation. In the second part of this study, we show that the IO hypothesis class, trained by the proposed convex loss function, enjoys ample expressiveness and achieves competitive performance comparing with the state-of-the-art (SOTA) methods in the low-data regime of the MuJoCo benchmark while utilizing three orders of magnitude fewer parameters, thereby requiring significantly fewer computational resources. To facilitate the reproducibility of our results, we provide an open-source package implementing the proposed algorithms and the 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.
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.
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.
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.
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.
The use of connected automated vehicle (CAV) is advocated to mitigate traffic oscillations in mixed traffic flow consisting of CAVs and human driven vehicles (HDVs). This study proposes an adaptive deep Koopman predictive control framework (AdapKoopPC) for regulating mixed traffic flow. Firstly, a Koopman theory-based adaptive trajectory prediction deep network (AdapKoopnet) is designed for modeling HDVs car-following behavior. AdapKoopnet enables the representation of HDVs behavior by a linear model in a high-dimensional space. Secondly, the model predictive control is employed to smooth the mixed traffic flow, where the combination of the linear dynamic model of CAVs and linear prediction blocks from AdapKoopnet is embedded as the predictive model into the AdapKoopPC. Finally, the predictive performance of the prosed AdapKoopnet is verified using the HighD naturalistic driving dataset. Furthermore, the control performance of AdapKoopPC is validated by the numerical simulations. Results demonstrate that the AdapKoopnet provides more accuracy HDVs predicted trajectories than the baseline nonlinear models. Moreover, the proposed AdapKoopPC exhibits more effective control performance with less computation cost compared with baselines in mitigating traffic oscillations, especially at the low CAVs penetration rates. The code of proposed AdapKoopPC is open source.