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.
Data-driven predictive control (DPC), using linear combinations of recorded trajectory data, has recently emerged as a popular alternative to traditional model predictive control (MPC). Without an explicitly enforced prediction model, the effects of commonly used regularization terms (and the resulting predictions) can be opaque. This opacity may lead to practical challenges, such as reliance on empirical tuning of regularization parameters based on closed-loop performance, and potentially misleading heuristic interpretations of norm-based regularizations. However, by examining the structure of the underlying optimal control problem (OCP), more precise and insightful interpretations of regularization effects can be derived. In this paper, we demonstrate how to analyze the predictive behavior of DPC through implicit predictors and the trajectory-specific effects of quadratic regularization. We further extend these results to cover typical DPC modifications, including DPC for affine systems, offset regularizations, slack variables, and terminal constraints. Additionally, we provide a simple but general result on (recursive) feasibility in DPC. This work aims to enhance the explainability and reliability of DPC by providing a deeper understanding of these regularization mechanisms.
This paper considers stochastic linear time-invariant systems subject to constraints on the average number of state-constraint violations over time without knowing the disturbance distribution. We present a novel disturbance-adaptive model predictive control (DAD-MPC) framework, which adjusts the disturbance model based on measured constraint violations. Using a robust invariance method, DAD-MPC ensures recursive feasibility and guarantees asymptotic or robust bounds on average constraint violations. Additionally, the bounds hold even with an inaccurate disturbance model, which allows for data-driven disturbance quantification methods to be used, such as conformal prediction. Simulation results demonstrate that the proposed approach outperforms state-of-the-art methods while satisfying average violation constraints.
Neural networks have proven practical for a synergistic combination of advanced control techniques. This work analyzes the implementation of rectified linear unit neural networks to achieve constrained control in differentially flat systems. Specifically, the class of flat systems enjoys the benefit of feedback linearizability, i.e., the systems can be linearized by means of a proper variable transformation. However, the price for linearizing the dynamics is that the constraint descriptions are distorted geometrically. Our results show that, by using neural networks, these constraints can be represented as a union of polytopes, enabling the use of mixed-integer programming tools to guarantee constraint satisfaction. We further analyze the integration of the characterization into efficient settings such as control Lyapunov function-based and model predictive control (MPC). Interestingly, this description also allows us to explicitly compute the solution of the MPC problem for the nonlinear system. Several examples are provided to illustrate the effectiveness of our framework.
In this paper, we propose an intent-aware Model Predictive Control (MPC) approach for the remain-well-clear (RWC) functionality of a multi-agent aircraft detect-and-avoid (DAA) system and compare its performance with the standardized Airborne Collision Avoidance System Xu (ACAS Xu). The aircraft system is modeled as a linear system for horizontal maneuvering, with advisories on the rate of turn as the control input. Both deterministic and stochastic time delays are considered to account for the lag between control guidance issuance and the response of the aircraft. The capability of the MPC scheme in producing an optimal control profile over the entire horizon is used to mitigate the impact of the delay. We compare the proposed MPC method with ACAS Xu using various evaluation metrics, including loss of DAA well-clear percentage, near mid-air collision percentage, horizontal miss distance, and additional flight distance across different encounter scenarios. It is shown that the MPC scheme achieves better evaluation metrics than ACAS Xu for both deterministic and stochastic scenarios.
This paper presents a novel dynamic model for slug flow crystallizers that addresses the challenges of spatial distribution without backmixing or diffusion, potentially enabling advanced model-based control. The developed model can accurately describe the main characteristics of slug flow crystallizers, including slug-to-slug variability but leads to a high computational complexity due to the consideration of partial differential equations and population balance equations. For that reason, the model cannot be directly used for process optimization and control. To solve this challenge, we propose two different approaches, conformalized quantile regression and Bayesian last layer neural networks, to develop surrogate models with uncertainty quantification capabilities. These surrogates output a prediction of the system states together with an uncertainty of these predictions to account for process variability and model uncertainty. We use the uncertainty of the predictions to formulate a robust model predictive control approach, enabling robust real-time advanced control of a slug flow crystallizer.
Few-shot adaptation is an important capability for intelligent robots that perform tasks in open-world settings such as everyday environments or flexible production. In this paper, we propose a novel approach for non-prehensile manipulation which incrementally adapts a physics-based dynamics model for model-predictive control (MPC). The model prediction is aligned with a few examples of robot-object interactions collected with the MPC. This is achieved by using a parallelizable rigid-body physics simulation as dynamic world model and sampling-based optimization of the model parameters. In turn, the optimized dynamics model can be used for MPC using efficient sampling-based optimization. We evaluate our few-shot adaptation approach in object pushing experiments in simulation and with a real robot.
This paper develops an Optimal Safe Sequencing (OSS) control framework for Connected and Automated Vehicles (CAVs) navigating a single-lane roundabout in mixed traffic, where both CAVs and Human-Driven Vehicles (HDVs) coexist. The framework jointly optimizes vehicle sequencing and motion control to minimize travel time, energy consumption, and discomfort while ensuring speed-dependent safety guarantees and adhering to velocity and acceleration constraints. This is achieved by integrating (a) a Safe Sequencing (SS) policy that ensures merging safety without requiring any knowledge of HDV behavior, and (b) a Model Predictive Control with Control Lyapunov Barrier Functions (MPC-CLBF) framework, which optimizes CAV motion control while mitigating infeasibility and myopic control issues common in the use of Control Barrier Functions (CBFs) to provide safety guarantees. Simulation results across various traffic demands, CAV penetration rates, and control parameters demonstrate the framework's effectiveness and stability.
Iterative learning control (ILC) improves the performance of a repetitive system by learning from previous trials. ILC can be combined with Model Predictive Control (MPC) to mitigate non-repetitive disturbances, thus improving overall system performance. However, existing approaches either assume perfect model knowledge or fail to actively learn system uncertainties, leading to conservativeness. To address these limitations we propose a binary mixed-integer ILC scheme, combined with a convex MPC scheme, that ensures robust constraint satisfaction, non-increasing nominal cost, and convergence to optimal performance. Our scheme is designed for uncertain nonlinear systems subject to both bounded additive stochastic noise and additive uncertain components. We showcase the benefits of our scheme in simulation.
To address the computational challenges of Model Predictive Control (MPC), recent research has studied on using Deep Neural Networks (DNNs) trained through imitation learning to approximate the MPC. However, this introduces a common issue in learning-based control: the simulation-to-reality (sim-to-real) gap. Therefore, Domain Randomization (DR) has been widely used to mitigate this gap by introducing perturbations in the source domain. However, this led to low data collection efficiency and an overly conservative control strategy. This study proposes a new control framework that deals with this issue from a control perspective inspired by Robust Tube MPC. The framework ensures the DNN operates in the same environment as the source domain, handling the sim-to-real gap with great data collection efficiency. Moreover, a parameter governor is introduced to address the DNN's inability to adapt to model parameter variations, enabling the system to satisfy MPC constraints more robustly under changing conditions. The proposed framework was validated through a cart-pole system case study compared by DR baselines, demonstrating that a single MPC-demonstrated trajectory in the source domain was sufficient for controlling the cart-pole in the target domain. Furthermore, the system effectively handled model parameter variations, allowing for a less conservative control.
Least-square system identification is widely used for data-driven model-predictive control (MPC) of unknown or partially known systems. This letter investigates how the system identification and subsequent MPC is affected when the state and input data is quantized. Specifically, we examine the fundamental connection between model error and quantization resolution and how that affects the stability and boundedness of the MPC tracking error. Furthermore, we demonstrate that, with a sufficiently rich dataset, the model error is bounded by a function of quantization resolution and the MPC tracking error is also ultimately bounded similarly. The theory is validated through numerical experiments conducted on two different linear dynamical systems.
Vehicle rollovers pose a significant safety risk and account for a disproportionately high number of fatalities in road accidents. This paper addresses the challenge of rollover prevention using Data-EnablEd Predictive Control (DeePC), a data-driven control strategy that directly leverages raw input-output data to maintain vehicle stability without requiring explicit system modeling. To enhance computational efficiency, we employ a reduced-dimension DeePC that utilizes singular value decomposition-based dimension reduction to significantly lower computation complexity without compromising control performance. This optimization enables real-time application in scenarios with high-dimensional data, making the approach more practical for deployment in real-world vehicles. The proposed approach is validated through high-fidelity CarSim simulations in both sedan and utility truck scenarios, demonstrating its versatility and ability to maintain vehicle stability under challenging driving conditions. Comparative results with Linear Model Predictive Control (LMPC) highlight the superior performance of DeePC in preventing rollovers while preserving maneuverability. The findings suggest that DeePC offers a robust and adaptable solution for rollover prevention, capable of handling varying road and vehicle conditions.
In this article, a model predictive control (MPC) method is proposed for constrained linear systems to track bounded references with arbitrary dynamics. Besides control inputs to be determined, artificial reference is introduced as additional decision variable, which serves as an intermediate target to cope with sudden changes of reference and enlarges domain of attraction. Cost function penalizes both artificial state error and reference error, while terminal constraint is imposed on artificial state error and artificial reference. We specify the requirements for terminal constraint and cost function to guarantee recursive feasibility of the proposed method and asymptotic stability of tracking error. Then, periodic and non-periodic references are considered and the method to determine required cost function and terminal constraint is proposed. Finally, the efficiency of the proposed MPC controller is demonstrated with simulation examples.
In this study, we formulate the drone delivery problem as a control problem and solve it using Model Predictive Control. Two experiments are performed: The first is on a less challenging grid world environment with lower dimensionality, and the second is with a higher dimensionality and added complexity. The MPC method was benchmarked against three popular Multi-Agent Reinforcement Learning (MARL): Independent $Q$-Learning (IQL), Joint Action Learners (JAL), and Value-Decomposition Networks (VDN). It was shown that the MPC method solved the problem quicker and required fewer optimal numbers of drones to achieve a minimized cost and navigate the optimal path.
In this work, we propose a Model Predictive Control (MPC) formulation incorporating two distinct horizons: a prediction horizon and a constraint horizon. This approach enables a deeper understanding of how constraints influence key system properties such as suboptimality, without compromising recursive feasibility and constraint satisfaction. In this direction, our contributions are twofold. First, we provide a framework to estimate closed-loop optimality as a function of the number of enforced constraints. This is a generalization of existing results by considering partial constraint enforcement over the prediction horizon. Second, when adopting this general framework under the lens of safety-critical applications, our method improves conventional Control Barrier Function (CBF) based approaches. It mitigates myopic behaviour in Quadratic Programming (QP)-CBF schemes, and resolves compatibility issues between Control Lyapunov Function (CLF) and CBF constraints via the prediction horizon used in the optimization. We show the efficacy of the method via numerical simulations for a safety critical application.
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.
Current closed-loop insulin delivery algorithms need to be informed of carbohydrate intake disturbances. This can be a burden on people using these systems. Pramlintide is a hormone that delays gastric emptying, which enables insulin kinetics to align with the kinetics of carbohydrate absorption. Integrating pramlintide into an automated insulin delivery system can be helpful in reducing the postprandial glucose excursion and may be helpful in enabling fully-closed loop whereby meals do not need to be announced. We present an AI-enabled dual-hormone model predictive control (MPC) algorithm that delivers insulin and pramlintide without requiring meal announcements that uses a neural network to automatically detect and deliver meal insulin. The MPC algorithm includes a new pramlintide pharmacokinetics and pharmacodynamics model that was identified using data collected from people with type 1 diabetes undergoing a meal challenge. Using a simulator, we evaluated the performance of various pramlintide delivery methods and controller models, as well as the baseline insulin-only scenario. Meals were automatically dosed using a neural network meal detection and dosing (MDD) algorithm. The primary outcome was the percent time glucose is in the target range (TIR: 70-180 mg/dL). Results show that delivering pramlintide at a fixed ratio of 6 mcg pramlintide:1 u insulin using an MPC that is aware of the pramlintide achieved the most significant improved TIR compared with an insulin-only MPC (91.6% vs. 64.1%). Delivering pramlintide as a fixed ratio was better than delivering basal pramlintide at a constant rate, indicating the benefit of the MDD algorithm. There was no advantage of independent control of insulin and pramlintide compared with insulin and pramlintide delivered as a fixed ratio. Preliminary real-world results from a human subject further indicate the benefit of pramlintide delivery.