Navigation of a team of autonomous underwater vehicles (AUVs) coordinated by an unmanned surface vehicle (USV) is efficient and reliable for deep ocean exploration. AUVs depart from and return to the USV after collaborative navigation, data collection, and ocean exploration missions. Efficient path planning and accurate localization are essential, the latter of which is critical due to the lack of global localization signals and poor radio frequency (RF) communication in deep waters. Inertial navigation and acoustic communication are common solutions for localization. However, the former is subject to odometry drifts, and the latter is limited to short distances. This paper proposes a systematic approach for localization-aware energy-efficient collision-free path planning for a USV-AUVs team. Path planning is formulated as finite receding horizon model predictive control (MPC) optimization. A dynamic-aware linear kinodynamic motion equation is developed. The mathematical formulation for the MPC optimization is effectively developed where localization is integrated as consensus graph optimization among AUV nodes. Edges in the optimized AUV-to-USV (A2U) and AUV-to-AUV (A2A) graphs are constrained to the sonar range of acoustic modems. The time complexity of the consensus MPC optimization problem is analyzed, revealing a nonconvex NP-hard problem, which is solved using sequential convex programming. Numerical simulation results are provided to evaluate the proposed method.
This paper studies the leaderless formation flying problem with collision avoidance for a group of unmanned aerial vehicles (UAVs), which requires the UAVs to navigate through cluttered environments without colliding while maintaining the formation. The communication network among the UAVs is structured as a directed graph that includes a directed spanning tree. A novel distributed nonlinear model predictive control (NMPC) method based on the model reference adaptive consensus (MRACon) framework is proposed. Within this framework, each UAV tracks an assigned reference output generated by a linear reference model that utilizes relative measurements as input. Subsequently, the NMPC method penalizes the tracking error between the output of the reference model and that of the actual model while also establishing constraint sets for collision avoidance and physical limitations to achieve distributed and safe formation control. Finally, simulations and hardware experiments are conducted to verify the effectiveness of the proposed method.
This paper demonstrates the applicability of the safe model predictive control (SMPC) framework to autonomous driving scenarios, focusing on the design of adaptive cruise control (ACC) and automated lane-change systems. Building on the SMPC approach with priority-driven constraint softening -- which ensures the satisfaction of \emph{hard} constraints under external disturbances by selectively softening a predefined subset of adjustable constraints -- we show how the algorithm dynamically relaxes lower-priority, comfort-related constraints in response to unexpected disturbances while preserving critical safety requirements such as collision avoidance and lane-keeping. A learning-based algorithm approximating the time consuming SMPC is introduced to enable real-time execution. Simulations in real-world driving scenarios subject to unpredicted disturbances confirm that this prioritized softening mechanism consistently upholds stringent safety constraints, underscoring the effectiveness of the proposed method.
This paper presents a modified model predictive control (MPC) framework for real-time power system operation. The framework incorporates a diffusion model tailored for time series generation to enhance the accuracy of the load forecasting module used in the system operation. In the absence of explicit state transition law, a model-identification procedure is leveraged to derive the system dynamics, thereby eliminating a barrier when applying MPC to a renewables-dominated power system. Case study results on an industry park system and the IEEE 30-bus system demonstrate that using the diffusion model to augment the training dataset significantly improves load-forecasting accuracy, and the inferred system dynamics are applicable to the real-time grid operation with solar and wind.
Gaussian Process (GP) regression is shown to be effective for learning unknown dynamics, enabling efficient and safety-aware control strategies across diverse applications. However, existing GP-based model predictive control (GP-MPC) methods either rely on approximations, thus lacking guarantees, or are overly conservative, which limits their practical utility. To close this gap, we present a sampling-based framework that efficiently propagates the model's epistemic uncertainty while avoiding conservatism. We establish a novel sample complexity result that enables the construction of a reachable set using a finite number of dynamics functions sampled from the GP posterior. Building on this, we design a sampling-based GP-MPC scheme that is recursively feasible and guarantees closed-loop safety and stability with high probability. Finally, we showcase the effectiveness of our method on two numerical examples, highlighting accurate reachable set over-approximation and safe closed-loop performance.
This work formally introduces Y-wise Affine Neural Networks (YANNs), a fully-explainable network architecture that continuously and efficiently represent piecewise affine functions with polytopic subdomains. Following from the proofs, it is shown that the development of YANNs requires no training to achieve the functionally equivalent representation. YANNs thus maintain all mathematical properties of the original formulations. Multi-parametric model predictive control is utilized as an application showcase of YANNs, which theoretically computes optimal control laws as a piecewise affine function of states, outputs, setpoints, and disturbances. With the exact representation of multi-parametric control laws, YANNs retain essential control-theoretic guarantees such as recursive feasibility and stability. This sets YANNs apart from the existing works which apply neural networks for approximating optimal control laws instead of exactly representing them. By optimizing the inference speed of the networks, YANNs can evaluate substantially faster in real-time compared to traditional piecewise affine function calculations. Numerical case studies are presented to demonstrate the algorithmic scalability with respect to the input/output dimensions and the number of subdomains. YANNs represent a significant advancement in control as the first neural network-based controller that inherently ensures both feasibility and stability. Future applications can leverage them as an efficient and interpretable starting point for data-driven modeling/control.
The majority of electric vehicles (EVs) are charged domestically overnight, where the precise timing of power allocation is not important to the user, thus representing a source of flexibility that can be leveraged by charging control algorithms. In this paper, we relax the common assumption, that EVs require full charge every morning, enabling additional flexibility to defer charging of surplus energy to subsequent nights, which can enhance the performance of controlled charging. In particular, we consider a simple domestic smart plug, scheduling power delivery with the objective to minimize CO$_2$ emissions over prediction horizons of multiple sessions -- up to seven days ahead -- utilising model predictive control (MPC). Based on carbon intensity data from the UK National Grid, we demonstrate significant potential for emission reductions with multi-session planning of 40 to 46\% compared to uncontrolled charging and 19 to 26\% compared to single-session planning. Furthermore, we assess, how the driving and charging behaviour of EV users affects the available flexibility and consequentially the potential for emission reductions. Finally, using grid carbon intensity data from 14 different UK regions, we report significant variations in absolute emission reductions based on the local energy mix.
This paper presents a novel learning economic model predictive control scheme for uncertain nonlinear systems subject to input and state constraints and unknown dynamics. We design a fast and accurate Lipschitz regression method using input and output data that combines clustering and kernel regression to learn the unknown dynamics. In each cluster, the parallel convex optimization problems are solved to estimate the kernel weights and reduce the Lipschitz constant of the predictor, hence limiting the error propagation in the prediction horizon. We derive the two different bounds of learning errors in deterministic and probabilistic forms and customize a new robust constraint-tightening strategy for the discontinuous predictor. Then, the learning economic model predictive control algorithm is formulated by introducing a stabilized optimization problem to construct a Lyapunov function. Sufficient conditions are derived to ensure the recursive feasibility and input-to-state stability of the closed-loop system. The effectiveness of the proposed algorithm is verified by simulations of a numerical example and a continuously stirred tank reactor.
Can we build accurate world models out of large language models (LLMs)? How can world models benefit LLM agents? The gap between the prior knowledge of LLMs and the specified environment's dynamics usually bottlenecks LLMs' performance as world models. To bridge the gap, we propose a training-free "world alignment" that learns an environment's symbolic knowledge complementary to LLMs. The symbolic knowledge covers action rules, knowledge graphs, and scene graphs, which are extracted by LLMs from exploration trajectories and encoded into executable codes to regulate LLM agents' policies. We further propose an RL-free, model-based agent "WALL-E 2.0" through the model-predictive control (MPC) framework. Unlike classical MPC requiring costly optimization on the fly, we adopt an LLM agent as an efficient look-ahead optimizer of future steps' actions by interacting with the neurosymbolic world model. While the LLM agent's strong heuristics make it an efficient planner in MPC, the quality of its planned actions is also secured by the accurate predictions of the aligned world model. They together considerably improve learning efficiency in a new environment. On open-world challenges in Mars (Minecraft like) and ALFWorld (embodied indoor environments), WALL-E 2.0 significantly outperforms existing methods, e.g., surpassing baselines in Mars by 16.1%-51.6% of success rate and by at least 61.7% in score. In ALFWorld, it achieves a new record 98% success rate after only 4 iterations.
This paper presents a novel distributed model predictive control (MPC) formulation without terminal cost and a corresponding distributed synthesis approach for distributed linear discrete-time systems with coupled constraints. The proposed control scheme introduces an explicit stability condition as an additional constraint based on relaxed dynamic programming. As a result, contrary to other related approaches, system stability with the developed controller does not rely on designing a terminal cost. A distributed synthesis approach is then introduced to handle the stability constraint locally within each local agent. To solve the underlying optimization problem for distributed MPC, a violation-free distributed optimization approach is developed, using constraint tightening to ensure feasibility throughout iterations. A numerical example demonstrates that the proposed distributed MPC approach ensures closed-loop stability for each feasible control sequence, with each agent computing its control input in parallel.
This paper proposes a proof of stability for Model Predictive Control formulations involving a prediction horizon that might be too short to meet the reachability condition generally invoked as a sufficient condition for closed-loop stability. This condition is replaced by a contraction condition on the stage cost. But unlike the contraction based existing formulations where the prediction horizon becomes a decision variable, the formulation proposed in this paper remains standard in that it uses constant and short prediction horizon. An illustrative example is provided to assess the relevance of the proposed formulation.
This article presents a unified approach to quadratic optimal control for both linear and nonlinear discrete-time systems, with a focus on trajectory tracking. The control strategy is based on minimizing a quadratic cost function that penalizes deviations of system states and control inputs from their desired trajectories. For linear systems, the classical Linear Quadratic Regulator (LQR) solution is derived using dynamic programming, resulting in recursive equations for feedback and feedforward terms. For nonlinear dynamics, the Iterative Linear Quadratic Regulator (iLQR) method is employed, which iteratively linearizes the system and solves a sequence of LQR problems to converge to an optimal policy. To implement this approach, a software service was developed and tested on several canonical models, including: Rayleigh oscillator, inverted pendulum on a moving cart, two-link manipulator, and quadcopter. The results confirm that iLQR enables efficient and accurate trajectory tracking in the presence of nonlinearities. To further enhance performance, it can be seamlessly integrated with Model Predictive Control (MPC), enabling online adaptation and improved robustness to constraints and system uncertainties.
Nowadays, unmanned aerial vehicles (UAVs) are increasingly utilized in search and rescue missions, a trend driven by technological advancements, including enhancements in automation, avionics, and the reduced cost of electronics. In this work, we introduce a collaborative model predictive control (MPC) framework aimed at addressing the joint problem of guidance and state estimation for tracking multiple castaway targets with a fleet of autonomous UAV agents. We assume that each UAV agent is equipped with a camera sensor, which has a limited sensing range and is utilized for receiving noisy observations from multiple moving castaways adrift in maritime conditions. We derive a nonlinear mixed integer programming (NMIP) -based controller that facilitates the guidance of the UAVs by generating non-myopic trajectories within a receding planning horizon. These trajectories are designed to minimize the tracking error across multiple targets by directing the UAV fleet to locations expected to yield targets measurements, thereby minimizing the uncertainty of the estimated target states. Extensive simulation experiments validate the effectiveness of our proposed method in tracking multiple castaways in maritime environments.
This paper proposes a state reduction method for learning-based model predictive control (MPC) for train rescheduling in urban rail transit systems. The state reduction integrates into a control framework where the discrete decision variables are determined by a learning-based classifier and the continuous decision variables are computed by MPC. Herein, the state representation is designed separately for each component of the control framework. While a reduced state is employed for learning, a full state is used in MPC. Simulations on a large-scale train network highlight the effectiveness of the state reduction mechanism in improving the performance and reducing the memory usage.
Model predictive control (MPC) is capable of controlling nonlinear systems with guaranteed constraint satisfaction and stability. However, MPC requires solving optimization problems online periodically, which often exceeds the local system's computational capabilities. A potential solution is to leverage external processing, such as a central industrial server. Yet, this central computer typically serves multiple systems simultaneously, leading to significant hardware demands due to the need to solve numerous optimization problems concurrently. In this work, we tackle this challenge by developing an event-triggered model predictive control (ET-MPC) that provably stabilizes multiple nonlinear systems under disturbances while solving only optimization problems for a fixed-size subset at any given time. Unlike existing ET-MPC methods, which primarily reduce average computational load yet still require hardware capable of handling all systems simultaneously, our approach reduces the worst-case computational load. This significantly lowers central server hardware requirements by diminishing peak computational demands. We achieve our improvements by leveraging recent advancements in distributed event-triggered linear control and integrating them with a robust MPC that employs constraint tightening.
We study a problem of simultaneous system identification and model predictive control of nonlinear systems. Particularly, we provide an algorithm for systems with unknown residual dynamics that can be expressed by Koopman operators. Such residual dynamics can model external disturbances and modeling errors, such as wind and wave disturbances to aerial and marine vehicles, or inaccurate model parameters. The algorithm has finite-time near-optimality guarantees and asymptotically converges to the optimal non-causal controller. Specifically, the algorithm enjoys sublinear \textit{dynamic regret}, defined herein as the suboptimality against an optimal clairvoyant controller that knows how the unknown dynamics will adapt to its states and actions. To this end, we assume the algorithm is given Koopman observable functions such that the unknown dynamics can be approximated by a linear dynamical system. Then, it employs model predictive control based on the current learned model of the unknown residual dynamics. This model is updated online using least squares in a self-supervised manner based on the data collected while controlling the system. We validate our algorithm in physics-based simulations of a cart-pole system aiming to maintain the pole upright despite inaccurate model parameters.
In this paper, we study homothetic tube model predictive control (MPC) of discrete-time linear systems subject to bounded additive disturbance and mixed constraints on the state and input. Different from most existing work on robust MPC, we assume that the true disturbance set is unknown but a conservative surrogate is available a priori. Leveraging the real-time data, we develop an online learning algorithm to approximate the true disturbance set. This approximation and the corresponding constraints in the MPC optimisation are updated online using computationally convenient linear programs. We provide statistical gaps between the true and learned disturbance sets, based on which, probabilistic recursive feasibility of homothetic tube MPC problems is discussed. Numerical simulations are provided to demonstrate the efficacy of our proposed algorithm and compare with state-of-the-art MPC algorithms.
In the past couple of decades, the use of ``non-quadratic" convex cost functions has revolutionized signal processing, machine learning, and statistics, allowing one to customize solutions to have desired structures and properties. However, the situation is not the same in control where the use of quadratic costs still dominates, ostensibly because determining the ``value function", i.e., the optimal expected cost-to-go, which is critical to the construction of the optimal controller, becomes computationally intractable as soon as one considers general convex costs. As a result, practitioners often resort to heuristics and approximations, such as model predictive control that only looks a few steps into the future. In the quadratic case, the value function is easily determined by solving Riccati equations. In this work, we consider a special class of convex cost functions constructed from Bregman divergence and show how, with appropriate choices, they can be used to fully extend the framework developed for the quadratic case. The resulting optimal controllers are infinite horizon, come with stability guarantees, and have state-feedback, or estimated state-feedback, laws. They exhibit a much wider range of behavior than their quadratic counterparts since the feedback laws are nonlinear. The approach can be applied to several cases of interest, including safety control, sparse control, and bang-bang control.
This paper introduces a novel trajectory planner for autonomous robots, specifically designed to enhance navigation by incorporating dynamic obstacle avoidance within the Robot Operating System 2 (ROS2) and Navigation 2 (Nav2) framework. The proposed method utilizes Model Predictive Control (MPC) with a focus on handling the uncertainties associated with the movement prediction of dynamic obstacles. Unlike existing Nav2 trajectory planners which primarily deal with static obstacles or react to the current position of dynamic obstacles, this planner predicts future obstacle positions using a stochastic Vector Auto-Regressive Model (VAR). The obstacles' future positions are represented by probability distributions, and collision avoidance is achieved through constraints based on the Mahalanobis distance, ensuring the robot avoids regions where obstacles are likely to be. This approach considers the robot's kinodynamic constraints, enabling it to track a reference path while adapting to real-time changes in the environment. The paper details the implementation, including obstacle prediction, tracking, and the construction of feasible sets for MPC. Simulation results in a Gazebo environment demonstrate the effectiveness of this method in scenarios where robots must navigate around each other, showing improved collision avoidance capabilities.
Navigating autonomous vehicles in open scenarios is a challenge due to the difficulties in handling unseen objects. Existing solutions either rely on small models that struggle with generalization or large models that are resource-intensive. While collaboration between the two offers a promising solution, the key challenge is deciding when and how to engage the large model. To address this issue, this paper proposes opportunistic collaborative planning (OCP), which seamlessly integrates efficient local models with powerful cloud models through two key innovations. First, we propose large vision model guided model predictive control (LVM-MPC), which leverages the cloud for LVM perception and decision making. The cloud output serves as a global guidance for a local MPC, thereby forming a closed-loop perception-to-control system. Second, to determine the best timing for large model query and service, we propose collaboration timing optimization (CTO), including object detection confidence thresholding (ODCT) and cloud forward simulation (CFS), to decide when to seek cloud assistance and when to offer cloud service. Extensive experiments show that the proposed OCP outperforms existing methods in terms of both navigation time and success rate.