Optimal control methods provide solutions to safety-critical problems but easily become intractable. Control Barrier Functions (CBFs) have emerged as a popular technique that facilitates their solution by provably guaranteeing safety, through their forward invariance property, at the expense of some performance loss. This approach involves defining a performance objective alongside CBF-based safety constraints that must always be enforced. Unfortunately, both performance and solution feasibility can be significantly impacted by two key factors: (i) the selection of the cost function and associated parameters, and (ii) the calibration of parameters within the CBF-based constraints, which capture the trade-off between performance and conservativeness. %as well as infeasibility. To address these challenges, we propose a Reinforcement Learning (RL)-based Receding Horizon Control (RHC) approach leveraging Model Predictive Control (MPC) with CBFs (MPC-CBF). In particular, we parameterize our controller and use bilevel optimization, where RL is used to learn the optimal parameters while MPC computes the optimal control input. We validate our method by applying it to the challenging automated merging control problem for Connected and Automated Vehicles (CAVs) at conflicting roadways. Results demonstrate improved performance and a significant reduction in the number of infeasible cases compared to traditional heuristic approaches used for tuning CBF-based controllers, showcasing the effectiveness of the proposed method.
The integration of various power sources, including renewables and electric vehicles, into smart grids is expanding, introducing uncertainties that can result in issues like voltage imbalances, load fluctuations, and power losses. These challenges negatively impact the reliability and stability of online scheduling in smart grids. Existing research often addresses uncertainties affecting current states but overlooks those that impact future states, such as the unpredictable charging patterns of electric vehicles. To distinguish between these, we term them static uncertainties and dynamic uncertainties, respectively. This paper introduces WDR-MPC, a novel approach that stands for two-stage Wasserstein-based Distributionally Robust (WDR) optimization within a Model Predictive Control (MPC) framework, aimed at effectively managing both types of uncertainties in smart grids. The dynamic uncertainties are first reformulated into ambiguity tubes and then the distributionally robust bounds of both dynamic and static uncertainties can be established using WDR optimization. By employing ambiguity tubes and WDR optimization, the stochastic MPC system is converted into a nominal one. Moreover, we develop a convex reformulation method to speed up WDR computation during the two-stage optimization. The distinctive contribution of this paper lies in its holistic approach to both static and dynamic uncertainties in smart grids. Comprehensive experiment results on IEEE 38-bus and 94-bus systems reveal the method's superior performance and the potential to enhance grid stability and reliability.
This paper addresses the particularities in optimal control of the uranium extraction-scrubbing operation in the PUREX process. The control problem requires optimally stabilizing the system at a desired solvent saturation level, guaranteeing constraints, disturbance rejection, and adapting to set point variations. A qualified simulator named PAREX was developed by the French Alternative Energies and Atomic Energy Commission (CEA) to simulate liquid-liquid extraction operations in the PUREX process. However, since the mathematical model is complex and is described by a system of nonlinear, stiff, high-dimensional differential-algebraic equations (DAE), applying optimal control methods will lead to a large-scale nonlinear programming problem with a huge computational burden. The solution we propose in this work is to train a neural network to predict the process outputs using the measurement history. This neural network architecture, which employs the long short-term memory (LSTM), linear regression and logistic regression networks, allows reducing the number of state variables, thus reducing the complexity of the optimization problems in the control scheme. Furthermore, nonlinear model predictive control (NMPC) and moving horizon estimation (MHE) problems are developed and solved using the PSO (Particle Swarm Optimization) algorithm. Simulation results show that the proposed adaptive optimal control scheme satisfies the requirements of the control problem and provides promise for experimental testing.
The modeling of nonlinear dynamics based on Koopman operator theory, which is originally applicable only to autonomous systems with no control, is extended to non-autonomous control system without approximation to input matrix B. Prevailing methods using a least square estimate of the B matrix may result in an erroneous input matrix, misinforming the controller about the structure of the input matrix in a lifted space. Here, a new method for constructing a Koopman model that comprises the exact input matrix B is presented. A set of state variables are introduced so that the control inputs are linearly involved in the dynamics of actuators. With these variables, a lifted linear model with the exact control matrix, called a Control-Coherent Koopman Model, is constructed by superposing control input terms, which are linear in local actuator dynamics, to the Koopman operator of the associated autonomous nonlinear system. The proposed method is applied to multi degree-of-freedom robotic arms and multi-cable manipulation systems. Model Predictive Control is applied to the former. It is demonstrated that the prevailing Dynamic Mode Decomposition with Control (DMDc) using an approximate control matrix B does not provide a satisfactory result, while the Control-Coherent Koopman Model performs well with the correct B matrix.
This study introduces a novel approach utilizing Gaussian process model predictive control (MPC) to stabilize the output voltage of a polymer electrolyte fuel cell (PEFC) system by simultaneously regulating hydrogen and airflow rates. Two Gaussian process models are developed to capture PEFC dynamics, taking into account constraints including hydrogen pressure and input change rates, thereby aiding in mitigating errors inherent to PEFC predictive control. The dynamic performance of the physical model and Gaussian process MPC in constraint handling and system inputs is compared and analyzed. Simulation outcomes demonstrate that the proposed Gaussian process MPC effectively maintains the voltage at the target 48 V while adhering to safety constraints, even amidst workload disturbances ranging from 110-120 A. In comparison to traditional MPC using detailed system models, Gaussian process MPC exhibits a 43\% higher overshoot and 25\% slower response time. Nonetheless, it offers the advantage of not requiring the underlying true system model and needing less system information.
We consider a problem of optimal swarm tracking which can be formulated as a tracking problem for distributions in the Wasserstein space. Optimal solutions to this problem are non-causal and require knowing the time-trajectory of the reference distribution in advance. We propose a scheme where these non-causal solutions can be used together with a predictive model for the reference to achieve causal tracking of a priori-unknown references. We develop a model-predictive control scheme built around the simple case where the reference is constant-in-time. A computational algorithm based on particle methods and discrete optimal mass transport is presented, and numerical simulations are provided for various classes of reference signals. The results demonstrate that the proposed control algorithm achieves reasonable performance even when using simple predictive models.
Advancements in underwater vehicle technology have significantly expanded the potential scope for deploying autonomous or remotely operated underwater vehicles in novel practical applications. However, the efficiency and maneuverability of these vehicles remain critical challenges, particularly in the dynamic aquatic environment. In this work, we propose a novel control scheme for creating multi-agent distributed formation control with limited communication between individual agents. In addition, the formation of the multi-agent can be reconfigured in real-time and the network connectivity can be maintained. The proposed use case for this scheme includes creating underwater mobile communication networks that can adapt to environmental or network conditions to maintain the quality of communication links for long-range exploration, seabed monitoring, or underwater infrastructure inspection. This work introduces a novel Distributed Nonlinear Model Predictive Control (DNMPC) strategy, integrating Control Lyapunov Functions (CLF) and Control Barrier Functions (CBF) with a relaxed decay rate, specifically tailored for 6-DOF underwater robotics. The effectiveness of our proposed DNMPC scheme was demonstrated through rigorous MATLAB simulations for trajectory tracking and formation reconfiguration in a dynamic environment. Our findings, supported by tests conducted using Software In The Loop (SITL) simulation, confirm the approach's applicability in real-time scenarios.
Autonomous driving depends on perception systems to understand the environment and to inform downstream decision-making. While advanced perception systems utilizing black-box Deep Neural Networks (DNNs) demonstrate human-like comprehension, their unpredictable behavior and lack of interpretability may hinder their deployment in safety critical scenarios. In this paper, we develop an Ensemble of DNN regressors (Deep Ensemble) that generates predictions with quantification of prediction uncertainties. In the scenario of Adaptive Cruise Control (ACC), we employ the Deep Ensemble to estimate distance headway to the lead vehicle from RGB images and enable the downstream controller to account for the estimation uncertainty. We develop an adaptive cruise controller that utilizes Stochastic Model Predictive Control (MPC) with chance constraints to provide a probabilistic safety guarantee. We evaluate our ACC algorithm using a high-fidelity traffic simulator and a real-world traffic dataset and demonstrate the ability of the proposed approach to effect speed tracking and car following while maintaining a safe distance headway. The out-of-distribution scenarios are also examined.
The European Economic Area Electricity Network Benchmark (EEA-ENB) is a multi-area power system representing the European network of transmission systems for electricity to facilitate the application of distributed control techniques. In the EEA-ENB we consider the Load Frequency Control (LFC) problem in the presence of renewable energy sources (RESs), and energy storage systems (ESSs). RESs are known to cause instability in power networks due to their inertia-less and intermittent characteristics, while ESSs are introduced as a resource to mitigate the problem. In the EEA-ENB, particular attention is dedicated to Distributed Model Predictive Control (DMPC), whose application is often limited to small and homogeneous test cases due to the lack of standardized large-scale scenarios for testing, and due to the large computation time required to obtain a centralized MPC action for performance comparison with DMPC strategies under consideration. The second problem is exacerbated when the scale of the system grows. To address these challenges and to provide a real-world-based and control-independent benchmark, the EEA-ENB has been developed. The benchmark includes a centralized MPC strategy providing performance and computation time metrics to compare distributed control within a repeatable and realistic simulation environment.
Many countries are facing energy shortage today and most of the global energy is consumed by HVAC systems in buildings. For the scenarios where the energy system is not sufficiently supplied to HVAC systems, a priority-based allocation scheme based on distributed model predictive control is proposed in this paper, which distributes the energy rationally based on priority order. According to the scenarios, two distributed allocation strategies, i.e., one-to-one priority strategy and multi-to-one priority strategy, are developed in this paper and validated by simulation in a building containing three zones and a building containing 36 rooms, respectively. Both priority-based strategies fully exploit the potential of predictive control solutions. The experiment shows that our scheme has good scalability and achieve the performance of centralized strategy while making the calculation tractable.
Satellite attitude cotrol is a crucial part of aerospace technology, and model predictive control(MPC) is one of the most promising controllers in this area, which will be less effective if real-time online optimization can not be achieved. Explicit MPC converts the online calculation into a table lookup process, however the solution is difficult to obtain if the system dimension is high or the constraints are complex. The lattice piecewise affine(PWA) function was used to represent the control law of explicit MPC, although the online calculation complexity is reduced, the offline calculation is still prohibitive for complex problems. In this paper, we use the sample points in the feasible region with their corresponding affine functions to construct the lattice PWA approximation of the optimal MPC controller designed for satellite attitude control. The asymptotic stability of satellite attitude control system under lattice PWA approximation has been proven, and simulations are executed to verify that the proposed method can achieve almost the same performance as linear online MPC with much lower online computational complexity and use less fuel than LQR method.
Mechanistic dynamic process models may be too computationally expensive to be usable as part of a real-time capable predictive controller. We present a method for end-to-end learning of Koopman surrogate models for optimal performance in a specific control task. In contrast to previous contributions that employ standard reinforcement learning (RL) algorithms, we use a training algorithm that exploits the differentiability of environments based on mechanistic simulation models to aid the policy optimization. We evaluate the performance of our method by comparing it to that of other training algorithms on an existing economic nonlinear model predictive control (eNMPC) case study of a continuous stirred-tank reactor (CSTR) model. Compared to the benchmark methods, our method produces similar economic performance while eliminating constraint violations. Thus, for this case study, our method outperforms the others and offers a promising path toward more performant controllers that employ dynamic surrogate models.
Autonomous control systems face significant challenges in performing complex tasks in the presence of latent risks. To address this, we propose an integrated framework that combines Large Language Models (LLMs), numerical optimization, and optimization-based control to facilitate efficient subtask learning while ensuring safety against latent risks. The framework decomposes complex tasks into a sequence of context-aware subtasks that account for latent risks. These subtasks and their parameters are then refined through a multi-time-scale process: high-layer multi-turn in-context learning, mid-layer LLM Chain-of-Thought reasoning and numerical optimization, and low-layer model predictive control. The framework iteratively improves decisions by leveraging qualitative feedback and optimized trajectory data from lower-layer optimization processes and a physics simulator. We validate the proposed framework through simulated case studies involving robot arm and autonomous vehicle scenarios. The experiments demonstrate that the proposed framework can mediate actions based on the context and latent risks and learn complex behaviors efficiently.
This study presents a method for deep neural network nonlinear model predictive control (DNN-MPC) to reduce computational complexity, and we show its practical utility through its application in optimizing the energy management of hybrid electric vehicles (HEVs). For optimal power management of HEVs, we first design the online NMPC to collect the data set, and the deep neural network is trained to approximate the NMPC solutions. We assess the effectiveness of our approach by conducting comparative simulations with rule and online NMPC-based power management strategies for HEV, evaluating both fuel consumption and computational complexity. Lastly, we verify the real-time feasibility of our approach through process-in-the-loop (PIL) testing. The test results demonstrate that the proposed method closely approximates the NMPC performance while substantially reducing the computational burden.
This paper develops a controller for Connected and Automated Vehicles (CAVs) traversing a single-lane roundabout. The controller simultaneously determines the optimal sequence and associated optimal motion control jointly minimizing travel time and energy consumption while providing speed-dependent safety guarantees, as well as satisfying velocity and acceleration constraints. This is achieved by integrating (a) Model Predictive Control (MPC) to enable receding horizon optimization with (b) Control Lyapunov-Barrier Functions (CLBFs) to guarantee convergence to a safe set in finite time, thus providing an extended stability region compared to the use of classic Control Barrier Functions (CBFs). The proposed MPC-CLBF framework addresses both infeasibility and myopic control issues commonly encountered when controlling CAVs over multiple interconnected control zones in a traffic network, which has been a limitation of prior work on CAVs going through roundabouts, while still providing safety guarantees. Simulations under varying traffic demands demonstrate the controller's effectiveness and stability.
In addressing wireless networked control systems (WNCS) subject to unexpected packet loss and uncertainties, this paper presents a practical Model Predictive Control (MPC) based control scheme with considerations of of packet dropouts, latency, process noise and measurement noise. A discussion of the quasi-static Rayleigh fading channel is presented herein to enhance the realism of the underlying assumption in a real-world context. To achieve a desirable performance, the proposed control scheme leverages the predictive capabilities of a direct multiple shooting MPC, employs a compensation strategy to mitigate the impact of wireless channel imperfections. Instead of feeding noisy measurements into the MPC, we employ an Extended Kalman Filter (EKF) to mitigate the influence of measurement noise and process disturbances. Finally, we implement the proposed MPC algorithm on a simulated Unmanned Ground Vehicle (UGV) and conduct a series of experiments to evaluate the performance of our control scheme across various scenarios. Through our simulation results and comparative analyses, we have substantiated the effectiveness and improvements brought about by our approach through the utilization of multiple metrics.
The configuration of most robotic systems lies in continuous transformation groups. However, in mobile robot trajectory tracking, many recent works still naively utilize optimization methods for elements in vector space without considering the manifold constraint of the robot configuration. In this letter, we propose a geometric model predictive control (MPC) framework for wheeled mobile robot trajectory tracking. We first derive the error dynamics of the wheeled mobile robot trajectory tracking by considering its manifold constraint and kinematic constraint simultaneously. After that, we utilize the relationship between the Lie group and Lie algebra to convexify the tracking control problem, which enables us to solve the problem efficiently. Thanks to the Lie group formulation, our method tracks the trajectory more smoothly than existing nonlinear MPC. Simulations and physical experiments verify the effectiveness of our proposed methods. Our pure Python-based simulation platform is publicly available to benefit further research in the community.
This paper presents model predictive control strategies for battery electric endurance race cars accounting for interactions with the competitors. In particular, we devise an optimization framework capturing the impact of the actions of the ego vehicle when interacting with competitors in a probabilistic fashion, jointly accounting for the optimal pit stop decision making, the charge times and the driving style in the course of the race. We showcase our method for a simulated 1h endurance race at the Zandvoort circuit, using real-life data of internal combustion engine race cars from a previous event. Our results show that optimizing both the race strategy as well as the decision making during the race is very important, resulting in a significant 21s advantage over an always overtake approach, whilst revealing the competitiveness of e-race cars w.r.t. conventional ones.
Safe Multi-agent reinforcement learning (safe MARL) has increasingly gained attention in recent years, emphasizing the need for agents to not only optimize the global return but also adhere to safety requirements through behavioral constraints. Some recent work has integrated control theory with multi-agent reinforcement learning to address the challenge of ensuring safety. However, there have been only very limited applications of Model Predictive Control (MPC) methods in this domain, primarily due to the complex and implicit dynamics characteristic of multi-agent environments. To bridge this gap, we propose a novel method called Deep Learning-Based Model Predictive Control for Safe Multi-Agent Reinforcement Learning (DeepSafeMPC). The key insight of DeepSafeMPC is leveraging a entralized deep learning model to well predict environmental dynamics. Our method applies MARL principles to search for optimal solutions. Through the employment of MPC, the actions of agents can be restricted within safe states concurrently. We demonstrate the effectiveness of our approach using the Safe Multi-agent MuJoCo environment, showcasing significant advancements in addressing safety concerns in MARL.
In this work, we propose a framework for adapting the controller's parameters based on learning optimal solutions from contextual black-box optimization problems. We consider a class of control design problems for dynamical systems operating in different environments or conditions represented by contextual parameters. The overarching goal is to identify the controller parameters that maximize the controlled system's performance, given different realizations of the contextual parameters.We formulate a contextual Bayesian optimization problem in which the solution is actively learned using Gaussian processes to approximate the controller adaptation strategy. We demonstrate the efficacy of the proposed framework with a sim-to-real example. We learn the optimal weighting strategy of a model predictive control for connected and automated vehicles interacting with human-driven vehicles from simulations and then deploy it in a real-time experiment.