Model predictive control can achieve significant energy savings, offer grid flexibility, and mitigate carbon emissions. However, the challenge of identifying individual control-oriented building dynamic models limits large-scale real-world applications. To address this issue, this study proposed a Modularized Neural Network Incorporating Physical Priors (ModNN), capable of establishing a control-oriented and physical-consistent building dynamic model within minutes without substantial modeling effort. This is also the first study to evaluate the physical consistency of a given data-driven model both qualitatively and quantitively. We compared the physical consistency of a classical Long Short-Term Memory (LSTM) model and our ModNN. The ModNN strictly satisfies physical constraints, whereas the LSTM model learned contradictory system dynamics. Additionally, we compared their control performance on an EnergyPlus virtual testbed. While the LSTM model demonstrated slightly better prediction accuracy in dynamic modeling, it failed in control optimization, resulting in an 89{\deg}C-h temperature violation, whereas the ModNN showed only a 0.57{\deg}C-h violation and achieved up to a 78% peak load reduction. Our findings highlight the importance of incorporating physics priors into data-driven models and provide a promising solution for future smart building control optimization. Furthermore, the proposed evaluation framework defines two physical consistency indicators, providing guidelines for selecting and testing control-oriented, data-driven building dynamic models.
Online model predictive control (MPC) for piecewise affine (PWA) systems requires the online solution to an optimization problem that implicitly optimizes over the switching sequence of PWA regions, for which the computational burden can be prohibitive. Alternatively, the computation can be moved offline using explicit MPC; however, the online memory requirements and the offline computation can then become excessive. In this work we propose a solution in between online and explicit MPC, addressing the above issues by partially dividing the computation between online and offline. To solve the underlying MPC problem, a policy, learned offline, specifies the sequence of PWA regions that the dynamics must follow, thus reducing the complexity of the remaining optimization problem that solves over only the continuous states and control inputs. We provide a condition, verifiable during learning, that guarantees feasibility of the learned policy's output, such that an optimal continuous control input can always be found online. Furthermore, a method for iteratively generating training data offline allows the feasible policy to be learned efficiently, reducing the offline computational burden. A numerical experiment demonstrates the effectiveness of the method compared to both online and explicit MPC.
We investigate the problem of teaching a robot manipulator to perform dynamic non-prehensile object transport, also known as the `robot waiter' task, from a limited set of real-world demonstrations. We propose an approach that combines batch reinforcement learning (RL) with model-predictive control (MPC) by pretraining an ensemble of value functions from demonstration data, and utilizing them online within an uncertainty-aware MPC scheme to ensure robustness to limited data coverage. Our approach is straightforward to integrate with off-the-shelf MPC frameworks and enables learning solely from task space demonstrations with sparsely labeled transitions, while leveraging MPC to ensure smooth joint space motions and constraint satisfaction. We validate the proposed approach through extensive simulated and real-world experiments on a Franka Panda robot performing the robot waiter task and demonstrate robust deployment of value functions learned from 50-100 demonstrations. Furthermore, our approach enables generalization to novel objects not seen during training and can improve upon suboptimal demonstrations. We believe that such a framework can reduce the burden of providing extensive demonstrations and facilitate rapid training of robot manipulators to perform non-prehensile manipulation tasks. Project videos and supplementary material can be found at: https://sites.google.com/view/cvmpc.
Closed-loop performance of sequential decision making algorithms, such as model predictive control, depends strongly on the parameters of cost functions, models, and constraints. Bayesian optimization is a common approach to learning these parameters based on closed-loop experiments. However, traditional Bayesian optimization approaches treat the learning problem as a black box, ignoring valuable information and knowledge about the structure of the underlying problem, resulting in slow convergence and high experimental resource use. We propose a time-series-informed optimization framework that incorporates intermediate performance evaluations from early iterations of each experimental episode into the learning procedure. Additionally, probabilistic early stopping criteria are proposed to terminate unpromising experiments, significantly reducing experimental time. Simulation results show that our approach achieves baseline performance with approximately half the resources. Moreover, with the same resource budget, our approach outperforms the baseline in terms of final closed-loop performance, highlighting its efficiency in sequential decision making scenarios.
Incorporating learning-based models, such as artificial neural networks or Gaussian processes, into model predictive control (MPC) strategies can significantly improve control performance and online adaptation capabilities for real-world applications. Still, enabling state-of-the-art implementations of learning-based models for MPC is complicated by the challenge of interfacing machine learning frameworks with real-time optimal control software. This work aims at filling this gap by incorporating external sensitivities in sequential quadratic programming solvers for nonlinear optimal control. To this end, we provide L4acados, a general framework for incorporating Python-based residual models in the real-time optimal control software acados. By computing external sensitivities via a user-defined Python module, L4acados enables the implementation of MPC controllers with learning-based residual models in acados, while supporting parallelization of sensitivity computations when preparing the quadratic subproblems. We demonstrate significant speed-ups and superior scaling properties of L4acados compared to available software using a neural-network-based control example. Last, we provide an efficient and modular real-time implementation of Gaussian process-based MPC using L4acados, which is applied to two hardware examples: autonomous miniature racing, as well as motion control of a full-scale autonomous vehicle for an ISO lane change maneuver.
We derive stability results for finite control set and mixed-integer model predictive control with a downstream oversampling phase. The presentation rests upon the inherent robustness of model predictive control with stabilizing terminal conditions and techniques for solving mixed-integer optimal control problems by continuous optimization. Partial outer convexification and binary relaxation transform mixed-integer problems into common optimal control problems. We deduce nominal asymptotic stability for the resulting relaxed system formulation and implement sum-up rounding to restore efficiently integer feasibility on an oversampling time grid. If fast control switching is technically possible and inexpensive, we can approximate the relaxed system behavior in the state space arbitrarily close. We integrate input perturbed model predictive control with practical asymptotic stability. Numerical experiments illustrate practical relevance of fast control switching.
Model predictive control has gained popularity for its ability to satisfy constraints and guarantee robustness for certain classes of systems. However, for systems whose dynamics are characterized by a high state dimension, substantial nonlinearities, and stiffness, suitable methods for online nonlinear MPC are lacking. One example of such a system is a vehicle thermal management system (TMS) with integrated thermal energy storage (TES), also referred to as a hybrid TMS. Here, hybrid refers to the ability to achieve cooling through a conventional heat exchanger or via melting of a phase change material, or both. Given increased electrification in vehicle platforms, more stringent performance specifications are being placed on TMS, in turn requiring more advanced control methods. In this paper, we present the design and real-time implementation of a nonlinear model predictive controller with 77 states on an experimental hybrid TMS testbed. We show how, in spite of high-dimension and stiff dynamics, an explicit integration method can be obtained by linearizing the dynamics at each time step within the MPC horizon. This integration method further allows the first-order gradients to be calculated with minimal additional computational cost. Through simulated and experimental results, we demonstrate the utility of the proposed solution method and the benefits of TES for mitigating highly transient heat loads achieved by actively controlling its charging and discharging behavior.
This paper presents a longitudinal slip control system for a rear-wheel-driven electric endurance race car. The control system integrates Model Predictive Control (MPC) with Extremum Seeking Control (ESC) to optimize the traction and regenerative braking performance of the powertrain. The MPC contains an analytical solution which results in a negligible computation time, whilst providing an optimal solution to a multi-objective optimization problem. The ESC algorithm allows continuous estimation of the optimal slip reference without assuming any prior knowledge of the tire dynamics. Finally, the control parameters are determined using a human-driven preference-based optimization algorithm in order to obtain the desired response. Simulation results and comparisons with other methods demonstrate the system's capability to automatically determine and track the optimal slip values, showing stability and performance under varying conditions.
In this paper, a multi-agent motion planning problem is studied aiming to minimize energy consumption of connected automated vehicles (CAVs) in lane change scenarios. We model this interactive motion planning as a generalized Nash equilibrium problem and formalize how vehicle-to-vehicle intention sharing enables solution of the game between multiple CAVs as an optimal control problem for each agent, to arrive at a generalized Nash equilibrium. The method is implemented via model predictive control (MPC) and compared with an advanced baseline MPC which utilizes unilateral predictions of other agents' future states. A ROS-based in-the-loop testbed is developed: the method is first evaluated in software-in-the-loop and then vehicle-in-the-loop experiments are conducted. Experimental results demonstrate energy and travel time benefits of the presented method in interactive lane change maneuvers.
Cooperative Distributed Model Predictive Control (DiMPC) architecture employs local MPC controllers to control different subsystems, exchanging information with each other through an iterative procedure to enhance overall control performance compared to the decentralized architecture. However, this method can result in high communication between the controllers and computational costs. In this work, the amount of information exchanged and the computational costs of DiMPC are reduced significantly by developing novel iteration-free solution algorithms based on multiparametric (mp) programming. These algorithms replace the iterative procedure with simultaneous solutions of explicit mpDiMPC control law functions. The reduced communication among local controllers decreases system latency, which is crucial for real-time control applications. The effectiveness of the proposed iteration-free mpDiMPC algorithms is demonstrated through comprehensive numerical simulations involving groups of coupled linear subsystems, which are interconnected through their inputs and a cooperative plant-wide cost function.
We propose a novel Stochastic Model Predictive Control (MPC) for uncertain linear systems subject to probabilistic constraints. The proposed approach leverages offline learning to extract key features of affine disturbance feedback policies, significantly reducing the computational burden of online optimization. Specifically, we employ offline data-driven sampling to learn feature components of feedback gains and approximate the chance-constrained feasible set with a specified confidence level. By utilizing this learned information, the online MPC problem is simplified to optimization over nominal inputs and a reduced set of learned feedback gains, ensuring computational efficiency. In a numerical example, the proposed MPC approach achieves comparable control performance in terms of Region of Attraction (ROA) and average closed-loop costs to classical MPC optimizing over disturbance feedback policies, while delivering a 10-fold improvement in computational speed.
Shared autonomous electric vehicles can provide on-demand transportation for passengers while also interacting extensively with the electric distribution system. This interaction is especially beneficial after a disaster when the large battery capacity of the fleet can be used to restore critical electric loads. We develop a dispatch policy that balances the need to continue serving passengers (especially critical workers) and the ability to transfer energy across the network. The model predictive control policy tracks both passenger and energy flows and provides maximum passenger throughput if any policy can. The resulting mixed integer linear programming problem is difficult to solve for large-scale problems, so a distributed solution approach is developed to improve scalability, privacy, and resilience. We demonstrate that the proposed heuristic, based on the alternating direction method of multipliers, is effective in achieving near-optimal solutions quickly. The dispatch policy is examined in simulation to demonstrate the ability of vehicles to balance these competing objectives with benefits to both systems. Finally, we compare several dispatch behaviors, demonstrating the importance of including operational constraints and objectives from both the transportation and electric systems in the model.
This paper considers the application of Model Predictive Control (MPC) to a weighted coverage path planning (WCPP) problem. The problem appears in a wide range of practical applications, such as search and rescue (SAR) missions. The basic setup is that one (or multiple) agents can move around a given search space and collect rewards from a given spatial distribution. Unlike an artificial potential field, each reward can only be collected once. In contrast to a Traveling Salesman Problem (TSP), the agent moves in a continuous space. Moreover, he is not obliged to cover all locations and/or may return to previously visited locations. The WCPP problem is tackled by a new Model Predictive Control (MPC) formulation with so-called Coverage Constraints (CCs). It is shown that the solution becomes more effective if the solver is initialized with a TSP-based heuristic. With and without this initialization, the proposed MPC approach clearly outperforms a naive MPC formulation, as demonstrated in a small simulation study.
In this paper we analyze the equilibrium points of a collaborative transportation task, composed of two unmanned aerial vehicles and a payload - in this case, a bar. Moreover, centralized and decentralized linear model predictive controllers are designed, where the nonlinear dynamics are linearized around the equilibrium points previously analyzed. A comparison between the centralized and decentralized formulations is provided, based on experimental results for both setups, and considering the time to solution and performance of each controller. Our findings provide new operational equilibrium points that can be paired with predictive model-based controllers for efficient operation.
This paper presents a stochastic model predictive control (SMPC) algorithm for linear systems subject to additive Gaussian mixture disturbances, with the goal of satisfying chance constraints. We focus on a special case where each Gaussian mixture component has a similar variance. To solve the SMPC problem, we formulate a branch model predictive control (BMPC) problem on simplified dynamics and leverage stochastic simulation relations (SSR). Our contribution is an extension of the SMPC literature to accommodate Gaussian mixture disturbances while retaining recursive feasibility and closed-loop guarantees. We illustrate the retention of guarantees with a case study of vehicle control on an ill-maintained road.
Model predictive control (MPC) is an industry standard control technique that iteratively solves an open-loop optimization problem to guide a system towards a desired state or trajectory. Consequently, an accurate forward model of system dynamics is critical for the efficacy of MPC and much recent work has been aimed at the use of neural networks to act as data-driven surrogate models to enable MPC. Perhaps the most common network architecture applied to this task is the recurrent neural network (RNN) due to its natural interpretation as a dynamical system. In this work, we assess the ability of RNN variants to both learn the dynamics of benchmark control systems and serve as surrogate models for MPC. We find that echo state networks (ESNs) have a variety of benefits over competing architectures, namely reductions in computational complexity, longer valid prediction times, and reductions in cost of the MPC objective function.
This paper presents a data-driven min-max model predictive control (MPC) scheme for linear parameter-varying (LPV) systems. Contrary to existing data-driven LPV control approaches, we assume that the scheduling signal is unknown during offline data collection and online system operation. Assuming a quadratic matrix inequality (QMI) description for the scheduling signal, we develop a novel data-driven characterization of the consistent system matrices using only input-state data. The proposed data-driven min-max MPC minimizes a tractable upper bound on the worst-case cost over the consistent system matrices set and over all scheduling signals satisfying the QMI. The proposed approach guarantees recursive feasibility, closed-loop exponential stability and constraint satisfaction if it is feasible at the initial time. We demonstrate the effectiveness of the proposed method in simulation.
Effective power and thermal management are essential for ensuring battery efficiency, safety, and longevity in Connected and Automated Electric Vehicles (CAEVs). However, real-time implementation is challenging due to the multi-timescale dynamics and complex trade-offs between energy consumption, battery degradation, traffic efficiency, and thermal regulation. This paper proposes a novel integrated power and thermal management strategy based on the Multi-Horizon Model Predictive Control (MH-MPC) framework to enhance energy efficiency, optimize battery temperature, ensure traffic safety and efficiency, and reduce battery degradation for CAEVs. The proposed strategy is formulated with a focus on the aging term, allowing it to more effectively manage the trade-offs between energy consumption, battery degradation, and temperature regulation. Moreover, the proposed strategy leverages multi-horizon optimization to achieve substantial improvements, reducing computation time by 7.18%, cooling energy by 14.22%, traction energy by 8.26%, battery degradation loss by over 22%, and battery degradation inconsistency by 36.57% compared to the benchmark strategy. Furthermore, sensitivity analyses of key parameters, including weighting factors, sampling time, and prediction horizons, demonstrate the robustness of the strategy and underscore its potential for practical applications in extending battery lifespan while ensuring safety and efficiency.
In this paper, we investigate a secure communication architecture based on unmanned aerial vehicle (UAV), which enhances the security performance of the communication system through UAV trajectory optimization. We formulate a control problem of minimizing the UAV flight path and power consumption while maximizing secure communication rate over infinite horizon by jointly optimizing UAV trajectory, transmit beamforming vector, and artificial noise (AN) vector. Given the non-uniqueness of optimization objective and significant coupling of the optimization variables, the problem is a non-convex optimization problem which is difficult to solve directly. To address this complex issue, an alternating-iteration technique is employed to decouple the optimization variables. Specifically, the problem is divided into three subproblems, i.e., UAV trajectory, transmit beamforming vector, and AN vector, which are solved alternately. Additionally, considering the susceptibility of UAV trajectory to disturbances, the model predictive control (MPC) approach is applied to obtain UAV trajectory and enhance the system robustness. Numerical results demonstrate the superiority of the proposed optimization algorithm in maintaining accurate UAV trajectory and high secure communication rate compared with other benchmark schemes.
A model predictive control scheme to stabilize desired configurations of collinear Coulomb spacecraft formations is derived in this paper. The nonlinearities of the dynamics with respect to the input make this problem difficult to solve, computationally. It is shown that the nonlinearities in the input lead to a finite horizon optimization problem which is a nonconvex quadratically-constrained quadratic program (QCQP). A convex relaxation of the nonconvex QCQP is therefore derived which can be solved quickly using a convex optimization solver. A simulation of a four spacecraft formation is provided which demonstrates why optimizing over a prediction horizon is a prudent approach to Coulomb spacecraft formation control.