This paper addresses the problem of controlling constrained systems subject to disturbances in the case where controller and system are connected over a lossy network. To do so, we propose a novel framework that splits the concept of tube-based model predictive control into two parts. One runs locally on the system and is responsible for disturbance rejection, while the other runs remotely and provides optimal input trajectories that satisfy the system's state and input constraints. Key to our approach is the presence of a nominal model and an ancillary controller on the local system. Theoretical guarantees regarding the recursive feasibility and the tracking capabilities in the presence of disturbances and packet losses in both directions are provided. To test the efficacy of the proposed approach, we compare it to a state-of-the-art solution in the case of controlling a cartpole system. Extensive simulations are carried out with both linearized and nonlinear system dynamics, as well as different packet loss probabilities and disturbances. The code for this work is available at https://github.com/EricssonResearch/Robust-Tracking-MPC-over-Lossy-Networks
Recent advancements in machine learning based energy management approaches, specifically reinforcement learning with a safety layer (OptLayerPolicy) and a metaheuristic algorithm generating a decision tree control policy (TreeC), have shown promise. However, their effectiveness has only been demonstrated in computer simulations. This paper presents the real-world validation of these methods, comparing against model predictive control and simple rule-based control benchmark. The experiments were conducted on the electrical installation of 4 reproductions of residential houses, which all have their own battery, photovoltaic and dynamic load system emulating a non-controllable electrical load and a controllable electric vehicle charger. The results show that the simple rules, TreeC, and model predictive control-based methods achieved similar costs, with a difference of only 0.6%. The reinforcement learning based method, still in its training phase, obtained a cost 25.5\% higher to the other methods. Additional simulations show that the costs can be further reduced by using a more representative training dataset for TreeC and addressing errors in the model predictive control implementation caused by its reliance on accurate data from various sources. The OptLayerPolicy safety layer allows safe online training of a reinforcement learning agent in the real-world, given an accurate constraint function formulation. The proposed safety layer method remains error-prone, nonetheless, it is found beneficial for all investigated methods. The TreeC method, which does require building a realistic simulation for training, exhibits the safest operational performance, exceeding the grid limit by only 27.1 Wh compared to 593.9 Wh for reinforcement learning.
This paper addresses navigation in crowded environments by integrating goal-conditioned generative models with Sampling-based Model Predictive Control (SMPC). We introduce goal-conditioned autoregressive models to generate crowd behaviors, capturing intricate interactions among individuals. The model processes potential robot trajectory samples and predicts the reactions of surrounding individuals, enabling proactive robotic navigation in complex scenarios. Extensive experiments show that this algorithm enables real-time navigation, significantly reducing collision rates and path lengths, and outperforming selected baseline methods. The practical effectiveness of this algorithm is validated on an actual robotic platform, demonstrating its capability in dynamic settings.
Despite the availability of international prize-money competitions, scaled vehicles, and simulation environments, research on autonomous racing and the control of sports cars operating close to the limit of handling has been limited by the high costs of vehicle acquisition and management, as well as the limited physics accuracy of open-source simulators. In this paper, we propose a racing simulation platform based on the simulator Assetto Corsa to test, validate, and benchmark autonomous driving algorithms, including reinforcement learning (RL) and classical Model Predictive Control (MPC), in realistic and challenging scenarios. Our contributions include the development of this simulation platform, several state-of-the-art algorithms tailored to the racing environment, and a comprehensive dataset collected from human drivers. Additionally, we evaluate algorithms in the offline RL setting. All the necessary code (including environment and benchmarks), working examples, datasets, and videos are publicly released and can be found at: https://assetto-corsa-gym.github.io
Nonlinear model predictive control (NMPC) has proven to be an effective control method, but it is expensive to compute. This work demonstrates the use of hardware FPGA neural network controllers trained to imitate NMPC with supervised learning. We use these Neural Controllers (NCs) implemented on inexpensive embedded FPGA hardware for high frequency control on physical cartpole and F1TENTH race car. Our results show that the NCs match the control performance of the NMPCs in simulation and outperform it in reality, due to the faster control rate that is afforded by the quick FPGA NC inference. We demonstrate kHz control rates for a physical cartpole and offloading control to the FPGA hardware on the F1TENTH car. Code and hardware implementation for this paper are available at https:// github.com/SensorsINI/Neural-Control-Tools.
The rapid decline in groundwater around the world poses a significant challenge to sustainable agriculture. To address this issue, agricultural managed aquifer recharge (Ag-MAR) is proposed to recharge the aquifer by artificially flooding agricultural lands using surface water. Ag-MAR requires a carefully selected flooding schedule to avoid affecting the oxygen absorption of crop roots. However, current Ag-MAR scheduling does not take into account complex environmental factors such as weather and soil oxygen, resulting in crop damage and insufficient recharging amounts. This paper proposes MARLP, the first end-to-end data-driven control system for Ag-MAR. We first formulate Ag-MAR as an optimization problem. To that end, we analyze four-year in-field datasets, which reveal the multi-periodicity feature of the soil oxygen level trends and the opportunity to use external weather forecasts and flooding proposals as exogenous clues for soil oxygen prediction. Then, we design a two-stage forecasting framework. In the first stage, it extracts both the cross-variate dependency and the periodic patterns from historical data to conduct preliminary forecasting. In the second stage, it uses weather-soil and flooding-soil causality to facilitate an accurate prediction of soil oxygen levels. Finally, we conduct model predictive control (MPC) for Ag-MAR flooding. To address the challenge of large action spaces, we devise a heuristic planning module to reduce the number of flooding proposals to enable the search for optimal solutions. Real-world experiments show that MARLP reduces the oxygen deficit ratio by 86.8% while improving the recharging amount in unit time by 35.8%, compared with the previous four years.
Trajectory planning for autonomous driving is challenging because the unknown future motion of traffic participants must be accounted for, yielding large uncertainty. Stochastic Model Predictive Control (SMPC)-based planners provide non-conservative planning, but do not rule out a (small) probability of collision. We propose a control scheme that yields an efficient trajectory based on SMPC when the traffic scenario allows, still avoiding that the vehicle causes collisions with traffic participants if the latter move according to the prediction assumptions. If some traffic participant does not behave as anticipated, no safety guarantee can be given. Then, our approach yields a trajectory which minimizes the probability of collision, using Constraint Violation Probability Minimization techniques. Our algorithm can also be adapted to minimize the anticipated harm caused by a collision. We provide a thorough discussion of the benefits of our novel control scheme and compare it to a previous approach through numerical simulations from the CommonRoad database.
Transportation is a major contributor to CO2 emissions, making it essential to optimize traffic networks to reduce energy-related emissions. This paper presents a novel approach to traffic network control using Differentiable Predictive Control (DPC), a physics-informed machine learning methodology. We base our model on the Macroscopic Fundamental Diagram (MFD) and the Networked Macroscopic Fundamental Diagram (NMFD), offering a simplified representation of citywide traffic networks. Our approach ensures compliance with system constraints by construction. In empirical comparisons with existing state-of-the-art Model Predictive Control (MPC) methods, our approach demonstrates a 4 order of magnitude reduction in computation time and an up to 37% improvement in traffic performance. Furthermore, we assess the robustness of our controller to scenario shifts and find that it adapts well to changes in traffic patterns. This work proposes more efficient traffic control methods, particularly in large-scale urban networks, and aims to mitigate emissions and alleviate congestion in the future.
Controlled charging of electric vehicles, EVs, is a major potential source of flexibility to facilitate the integration of variable renewable energy and reduce the need for stationary energy storage. To offer system services from EVs, fleet aggregators must address the uncertainty of individual driving and charging behaviour. This paper introduces a means of forecasting the service volume available from EVs by considering several EV batteries as one conceptual battery with aggregate power and energy boundaries. Aggregation avoids the difficult prediction of individual driving behaviour. The predictability of the boundaries is demonstrated using a multiple linear regression model which achieves a normalised root mean square error of 20% - 40% for a fleet of 1,000 EVs. A two-stage stochastic model predictive control algorithm is used to schedule reserve services on a day-ahead basis addressing risk trade-offs by including Conditional Value-at-Risk in the objective function. A case study with 1.2 million domestic EV charge records from Great Britain illustrates that increasing fleet size improves prediction accuracy, thereby increasing reserve revenues and decreasing an aggregator's operational costs. For fleet sizes of 400 or above, cost reductions plateau at 60% compared to uncontrolled charging, with an average of 1.8kW of reserve provided per vehicle.
This paper addresses the identification of models for offset-free model predictive control (MPC), where LTI models are augmented with (fictitious) uncontrollable integrating modes, called integrating disturbances. The states and disturbances are typically estimated with a Kalman filter. The disturbance estimates effectively provide integral control, so the quality of the disturbance model (and resulting filter) directly influences the control performance. We implement eigenvalue constraints to protect against undesirable filter behavior (unstable or marginally stable modes, high-frequency oscillations). Specifically, we consider the class of linear matrix inequality (LMI) regions for eigenvalue constraints. These LMI regions are open sets by default, so we introduce a barrier function method to create tightened, but closed, eigenvalue constraints. To solve the resulting nonlinear semidefinite program, we approximate it as a nonlinear program using a Cholesky factorization method that exploits known sparsity structures of semidefinite optimization variables and matrix inequalities. The algorithm is applied to real-world data taken from two physical systems: first, a low-cost benchmark temperature microcontroller suitable for classroom laboratories, and second, an industrial-scale chemical reactor at Eastman Chemical's plant in Kingsport, TN.
The growing complexity of power system management has led to an increased interest in reinforcement learning (RL). To validate their effectiveness, RL algorithms have to be evaluated across multiple case studies. Case study design is an arduous task requiring the consideration of many aspects, among them the influence of available forecasts and the level of decentralization in the control structure. Furthermore, vanilla RL controllers cannot themselves ensure the satisfaction of system constraints, which makes devising a safeguarding mechanism a necessary task for every case study before deploying the system. To address these shortcomings, we introduce the Python tool CommonPower, the first general framework for the modeling and simulation of power system management tailored towards machine learning. Its modular architecture enables users to focus on specific elements without having to implement a simulation environment. Another unique contribution of CommonPower is the automatic synthesis of model predictive controllers and safeguards. Beyond offering a unified interface for single-agent RL, multi-agent RL, and optimal control, CommonPower includes a training pipeline for machine-learning-based forecasters as well as a flexible mechanism for incorporating feedback of safeguards into the learning updates of RL controllers.
With neural networks being used to control safety-critical systems, they increasingly have to be both accurate (in the sense of matching inputs to outputs) and robust. However, these two properties are often at odds with each other and a trade-off has to be navigated. To address this issue, this paper proposes a method to generate an approximation of a neural network which is certifiably more robust. Crucially, the method is fully convex and posed as a semi-definite programme. An application to robustifying model predictive control is used to demonstrate the results. The aim of this work is to introduce a method to navigate the neural network robustness/accuracy trade-off.
Model predictive control can optimally deal with nonlinear systems under consideration of constraints. The control performance depends on the model accuracy and the prediction horizon. Recent advances propose to use reinforcement learning applied to a parameterized model predictive controller to recover the optimal control performance even if an imperfect model or short prediction horizons are used. However, common reinforcement learning algorithms rely on first order updates, which only have a linear convergence rate and hence need an excessive amount of dynamic data. Higher order updates are typically intractable if the policy is approximated with neural networks due to the large number of parameters. In this work, we use a parameterized model predictive controller as policy, and leverage the small amount of necessary parameters to propose a trust-region constrained Quasi-Newton training algorithm for policy optimization with a superlinear convergence rate. We show that the required second order derivative information can be calculated by the solution of a linear system of equations. A simulation study illustrates that the proposed training algorithm outperforms other algorithms in terms of data efficiency and accuracy.
Model-based Reinforcement Learning (MBRL) has shown many desirable properties for intelligent control tasks. However, satisfying safety and stability constraints during training and rollout remains an open question. We propose a new Model-based RL framework to enable efficient policy learning with unknown dynamics based on learning model predictive control (LMPC) framework with mathematically provable guarantees of stability. We introduce and explore a novel method for adding safety constraints for model-based RL during training and policy learning. The new stability-augmented framework consists of a neural-network-based learner that learns to construct a Lyapunov function, and a model-based RL agent to consistently complete the tasks while satisfying user-specified constraints given only sub-optimal demonstrations and sparse-cost feedback. We demonstrate the capability of the proposed framework through simulated experiments.
Safe, socially compliant, and efficient navigation of low-speed autonomous vehicles (AVs) in pedestrian-rich environments necessitates considering pedestrians' future positions and interactions with the vehicle and others. Despite the inevitable uncertainties associated with pedestrians' predicted trajectories due to their unobserved states (e.g., intent), existing deep reinforcement learning (DRL) algorithms for crowd navigation often neglect these uncertainties when using predicted trajectories to guide policy learning. This omission limits the usability of predictions when diverging from ground truth. This work introduces an integrated prediction and planning approach that incorporates the uncertainties of predicted pedestrian states in the training of a model-free DRL algorithm. A novel reward function encourages the AV to respect pedestrians' personal space, decrease speed during close approaches, and minimize the collision probability with their predicted paths. Unlike previous DRL methods, our model, designed for AV operation in crowded spaces, is trained in a novel simulation environment that reflects realistic pedestrian behaviour in a shared space with vehicles. Results show a 40% decrease in collision rate and a 15% increase in minimum distance to pedestrians compared to the state of the art model that does not account for prediction uncertainty. Additionally, the approach outperforms model predictive control methods that incorporate the same prediction uncertainties in terms of both performance and computational time, while producing trajectories closer to human drivers in similar scenarios.
This paper presents an adaptive tracking model predictive control (MPC) scheme to control unknown nonlinear systems based on an adaptively estimated linear model. The model is determined based on linear system identification using a moving window of past measurements, and it serves as a local approximation of the underlying nonlinear dynamics. We prove that the presented scheme ensures practical exponential stability of the (unknown) optimal reachable equilibrium for a given output setpoint. Finally, we apply the proposed scheme in simulation and compare it to an alternative direct data-driven MPC scheme based on the Fundamental Lemma.
Integrating electric vehicles (EVs) into the power grid can revolutionize energy management strategies, offering both challenges and opportunities for creating a more sustainable and resilient grid. In this context, model predictive control (MPC) emerges as a powerful tool for addressing the complexities of Grid-to-vehicle (G2V) and vehicle-to-grid (V2G) enabled demand response management. By leveraging advanced optimization techniques, MPC algorithms can anticipate future grid conditions and dynamically adjust EV charging and discharging schedules to balance supply and demand while minimizing operational costs and maximizing flexibility. However, no standard tools exist to evaluate novel energy management strategies based on MPC approaches. Our research focuses on harnessing the potential of MPC in G2V and V2G applications, by providing a simulation tool that allows to maximize EV flexibility and support demand response initiatives while mitigating the impact on EV battery health. In this paper, we propose an open-source MPC controller for G2V and V2G-enabled demand response management. The proposed approach is capable of tackling the uncertainties inherent in demand response operations. Through extensive simulation and analysis, we demonstrate the efficacy of our approach in maximizing the benefits of G2V and V2G while assessing the impact on the longevity and reliability of EV batteries. Specifically, our controller enables Charge Point Operators (CPOs) to optimize EV charging and discharging schedules in real-time, taking into account fluctuating energy prices, grid constraints, and EV user preferences.
Multi-Objective Learning Model Predictive Control is a novel data-driven control scheme which improves a linear system's closed-loop performance with respect to several convex control objectives over iterations of a repeated task. At each task iteration, collected system data is used to construct terminal components of a Model Predictive Controller. The formulation presented in this paper ensures that closed-loop control performance improves between successive iterations with respect to each objective. We provide proofs of recursive feasibility and performance improvement, and show that the converged policy is Pareto optimal. Simulation results demonstrate the applicability of the proposed approach.
This paper proposes a novel tube-based Model Predictive Control (MPC) framework for tracking varying setpoint references with linear systems subject to additive and multiplicative uncertainties. The MPC controllers designed using this framework exhibit recursively feasible for changing references, and robust asymptotic stability for piecewise constant references. The framework leverages configuration-constrained polytopes to parameterize the tubes, offering flexibility to optimize their shape. The efficacy of the approach is demonstrated through two numerical examples. The first example illustrates the theoretical results, and the second uses the framework to design a lane-change controller for an autonomous vehicle.
This paper proposes a novel real-time affordable solution to the trajectory tracking control problem for self-driving cars subject to longitudinal and steering angular velocity constraints. To this end, we develop a dual-mode Model Predictive Control (MPC) solution starting from an input-output feedback linearized description of the vehicle kinematics. First, we derive the state-dependent input constraints acting on the linearized model and characterize their worst-case time-invariant inner approximation. Then, a dual-mode MPC is derived to be real-time affordable and ensuring, by design, constraints fulfillment, recursive feasibility, and uniformly ultimate boundedness of the tracking error in an ad-hoc built robust control invariant region. The approach's effectiveness and performance are experimentally validated via laboratory experiments on a Quanser Qcar. The obtained results show that the proposed solution is computationally affordable and with tracking capabilities that outperform two alternative control schemes.