Managing and unlocking the flexibility hidden in electric vehicles (EVs) has emerged as a critical yet challenging task towards low-carbon power and energy systems. This paper focuses on the online bidding and dispatch strategies for an EV aggregator (EVA) in a joint energy-regulation market, considering EVs' flexibility contributions and compensations. A method for quantifying EV flexibility as a tradable commodity is proposed, allowing the EVA to set flexibility prices based on bid-in supply curves. An EVA bidding model in the joint market incorporate flexibility procurement is formulated. The stochastic model predictive control technique is employed to solve the bidding problem online and address the uncertainties from the electricity markets and the EVs. A power dispatch protocol that ensures a profitable and feasible allocation based on EV flexibility contribution is proposed. An affine mapping control strategy can be derived based on parametric linear programming, enables online indexing of optimal solutions given the regulation signals to avoid repeatedly solving the problem. Numerical experiments show the effectiveness of the proposed scheme, and the solution methodology can be applied in real-time.
Combining data-driven models that adapt online and model predictive control (MPC) has enabled effective control of nonlinear systems. However, when deployed on unstable systems, online adaptation may not be fast enough to ensure reliable simultaneous learning and control. For example, controllers on a vehicle executing highly dynamic maneuvers may push the tires to their friction limits, destabilizing the vehicle and allowing modeling errors to quickly compound and cause a loss of control. In this work, we present a Bayesian meta-learning MPC framework. We propose an expressive vehicle dynamics model that leverages Bayesian last-layer meta-learning to enable rapid online adaptation. The model's uncertainty estimates are used to guide informative data collection and quickly improve the model prior to deployment. Experiments on a Toyota Supra show that (i) the framework enables reliable control in dynamic drifting maneuvers, (ii) online adaptation alone may not suffice for zero-shot control of a vehicle at the edge of stability, and (iii) active data collection helps achieve reliable performance.
Uncrewed aerial systems have tightly coupled energy and motion dynamics which must be accounted for by onboard planning algorithms. This work proposes a strategy for coupled motion and energy planning using model predictive control (MPC). A reduced-order linear time-invariant model of coupled energy and motion dynamics is presented. Constrained zonotopes are used to represent state and input constraints, and hybrid zonotopes are used to represent non-convex constraints tied to a map of the environment. The structures of these constraint representations are exploited within a mixed-integer quadratic program solver tailored to MPC motion planning problems. Results apply the proposed methodology to coupled motion and energy utilization planning problems for 1) a hybrid-electric vehicle that must restrict engine usage when flying over regions with noise restrictions, and 2) an electric package delivery drone that must track waysets with both position and battery state of charge requirements. By leveraging the structure-exploiting solver, the proposed mixed-integer MPC formulations can be implemented in real time.
Autonomous vehicle (AV) motion planning problems often involve non-convex constraints, which present a major barrier to applying model predictive control (MPC) in real time on embedded hardware. This paper presents an approach for efficiently solving mixed-integer MPC motion planning problems using a hybrid zonotope representation of the obstacle-free space. The MPC optimization problem is formulated as a multi-stage mixed-integer quadratic program (MIQP) using a hybrid zonotope representation of the non-convex constraints. Risk-aware planning is supported by assigning costs to different regions of the obstacle-free space within the MPC cost function. A multi-stage MIQP solver is presented that exploits the structure of the hybrid zonotope constraints. For some hybrid zonotope representations, it is shown that the convex relaxation is tight, i.e., equal to the convex hull. In conjunction with logical constraints derived from the AV motion planning context, this property is leveraged to generate tight quadratic program (QP) sub-problems within a branch-and-bound mixed-integer solver. The hybrid zonotope structure is further leveraged to reduce the number of matrix factorizations that need to be computed within the QP sub-problems. Simulation studies are presented for obstacle-avoidance and risk-aware motion planning problems using polytopic maps and occupancy grids. In most cases, the proposed solver finds the optimal solution an order of magnitude faster than a state-of-the-art commercial solver. Processor-in-the-loop studies demonstrate the utility of the solver for real-time implementations on embedded hardware.
This paper formalizes Hamiltonian-Informed Optimal Neural (Hion) controllers, a novel class of neural network-based controllers for dynamical systems and explicit non-linear model predictive control. Hion controllers estimate future states and compute optimal control inputs using Pontryagin's Maximum Principle. The proposed framework allows for customization of transient behavior, addressing limitations of existing methods. The Taylored Multi-Faceted Approach for Neural ODE and Optimal Control (T-mano) architecture facilitates training and ensures accurate state estimation. Optimal control strategies are demonstrated for both linear and non-linear dynamical systems.
This paper presents a comprehensive framework aimed at enhancing education in modeling, optimal control, and nonlinear Model Predictive Control~(MPC) through a practical greenhouse climate control model. The framework includes a detailed mathematical model of lettuce growth and greenhouse, which are influenced by real-time external weather conditions obtained via an application programming interface~(API). Using this data, the MPC-based approach dynamically adjusts greenhouse conditions, optimizing plant growth and energy consumption and minimizing the social cost of CO\textsubscript{2}. The presented results demonstrate the effectiveness of this approach in balancing energy use with crop yield and reducing CO\textsubscript{2} emissions, contributing to economic efficiency and environmental sustainability. Besides optimizing lettuce production, the framework also provides a valuable resource for making control systems education more engaging and effective. The main aim is to provide students with a hands-on platform to understand the principles of modeling, the complexity of MPC and the trade-offs between profitability and sustainability in agricultural systems. This framework provides students with hands-on experience, helping them to understand the control theory better, connecting it to the practical implementation, and developing their problem-solving skills. The framework can be accessed at \url{ecompc4greenhouse.streamlit.app}.
In order to address the nonlinear multi-agent formation tracking control problem with input constraints and unknown communication faults, a novel adaptive distributed observer-based distributed model predictive control method is developed in this paper. This design employs adaptive distributed observers in local control systems to estimate the leader's state, dynamics, and relative positioning with respect to the leader. Utilizing the estimated data as local references, the original formation tracking control problem can be decomposed into several fully localized tracking control problems, which can be efficiently solved by the local predictive controller. Through the incorporation of adaptive distributed observers, this proposed design not only enhances the resilience of distributed formation tracking against communication faults but also simplifies the distributed model predictive control formulation.
PC-Gym is an open-source tool for developing and evaluating reinforcement learning (RL) algorithms in chemical process control. It features environments that simulate various chemical processes, incorporating nonlinear dynamics, disturbances, and constraints. The tool includes customizable constraint handling, disturbance generation, reward function design, and enables comparison of RL algorithms against Nonlinear Model Predictive Control (NMPC) across different scenarios. Case studies demonstrate the framework's effectiveness in evaluating RL approaches for systems like continuously stirred tank reactors, multistage extraction processes, and crystallization reactors. The results reveal performance gaps between RL algorithms and NMPC oracles, highlighting areas for improvement and enabling benchmarking. By providing a standardized platform, PC-Gym aims to accelerate research at the intersection of machine learning, control, and process systems engineering. By connecting theoretical RL advances with practical industrial process control applications, offering researchers a tool for exploring data-driven control solutions.
Model predictive control (MPC) has established itself as the primary methodology for constrained control, enabling general-purpose robot autonomy in diverse real-world scenarios. However, for most problems of interest, MPC relies on the recursive solution of highly non-convex trajectory optimization problems, leading to high computational complexity and strong dependency on initialization. In this work, we present a unified framework to combine the main strengths of optimization-based and learning-based methods for MPC. Our approach entails embedding high-capacity, transformer-based neural network models within the optimization process for trajectory generation, whereby the transformer provides a near-optimal initial guess, or target plan, to a non-convex optimization problem. Our experiments, performed in simulation and the real world onboard a free flyer platform, demonstrate the capabilities of our framework to improve MPC convergence and runtime. Compared to purely optimization-based approaches, results show that our approach can improve trajectory generation performance by up to 75%, reduce the number of solver iterations by up to 45%, and improve overall MPC runtime by 7x without loss in performance.
This paper investigates distributed computing and cooperative control of connected and automated vehicles (CAVs) in ramp merging scenario under transportation cyber-physical system. Firstly, a centralized cooperative trajectory planning problem is formulated subject to the safely constraints and traffic performance in ramp merging scenario, where the trajectories of all vehicles are jointly optimized. To get rid of the reliance on a central controller and reduce computation time, a distributed solution to this problem implemented among CAVs through Vehicles-to-Everything (V2X) communication is proposed. Unlike existing method, our method can distribute the computational task among CAVs and carry out parallel solving through V2X communication. Then, a multi-vehicles model predictive control (MPC) problem aimed at maximizing system stability and minimizing control input is formulated based on the solution of the first problem subject to strict safety constants and input limits. Due to these complex constraints, this problem becomes high-dimensional, centralized, and non-convex. To solve it in a short time, a decomposition and convex reformulation method, namely distributed cooperative iterative model predictive control (DCIMPC), is proposed. This method leverages the communication capability of CAVs to decompose the problem, making full use of the computational resources on vehicles to achieve fast solutions and distributed control. The two above problems with their corresponding solving methods form the systemic framework of the V2X assisted distributed computing and control. Simulations have been conducted to evaluate the framework's convergence, safety, and solving speed. Additionally, extra experiments are conducted to validate the performance of DCIMPC. The results show that our method can greatly improve computation speed without sacrificing system performance.
This paper presents a novel learning-based approach for online estimation of maximal safe sets for local trajectory planning in unknown static environments. The neural representation of a set is used as the terminal set constraint for a model predictive control (MPC) local planner, resulting in improved recursive feasibility and safety. To achieve real-time performance and desired generalization properties, we employ the idea of hypernetworks. We use the Hamilton-Jacobi (HJ) reachability analysis as the source of supervision during the training process, allowing us to consider general nonlinear dynamics and arbitrary constraints. The proposed method is extensively evaluated against relevant baselines in simulations for different environments and robot dynamics. The results show a success rate increase of up to 52 \% compared to the best baseline while maintaining comparable execution speed. Additionally, we deploy our proposed method, NTC-MPC, on a physical robot and demonstrate its ability to safely avoid obstacles in scenarios where the baselines fail.
We present the implementation of a novel economic model predictive control (E-MPC) strategy for froth flotation, the largest tonnage mineral separation process. A previously calibrated and validated dynamic model incorporating froth physics was used, which overcomes the limitations of previous simplified models reported in the literature. The E-MPC's optimal control problem was solved using full discretization with orthogonal collocation over finite elements, employing automatic differentiation via CasADi. This approach was applied in a 30-litre laboratory-scale flotation cell, significantly improving mineral recovery from 9% to 29% under feed flowrate disturbances while maintaining a minimum concentrate grade of 20%.
Nonlinear Model Predictive Control (NMPC) is a general and flexible control approach, used in many industrial contexts, and is based on the online solution of a nonlinear optimization problem. This operation requires in general a high computational cost, which may compromise the NMPC implementation in ``fast'' applications, especially if a large number variables is involved. To overcome this issue, we propose a quantum computing approach for the solution of the NMPC optimization problem. Assuming the availability of an efficient quantum computer, the approach has the potential to considerably decrease the computational time and/or enhance the solution quality compared to classical algorithms.
Model Predictive Control (MPC) is a successful control methodology, which is applied to increasingly complex systems. However, real-time feasibility of MPC can be challenging for complex systems, certainly when an (extremely) large number of constraints have to be adhered to. For such scenarios with a large number of state constraints, this paper proposes two novel MPC schemes for general nonlinear systems, which we call constraint-adaptive MPC. These novel schemes dynamically select at each time step a (varying) set of constraints that are included in the on-line optimization problem. Carefully selecting the included constraints can significantly reduce, as we will demonstrate, the computational complexity with often only a slight impact on the closed-loop performance. Although not all (state) constraints are imposed in the on-line optimization, the schemes still guarantee recursive feasibility and constraint satisfaction. A numerical case study illustrates the proposed MPC schemes and demonstrates the achieved computation time improvements exceeding two orders of magnitude without loss of performance.
Autonomous driving is a complex and highly dynamic process that ensures controlling the coupled longitudinal and lateral vehicle dynamics. Model predictive control, distinguished by its predictive feature, optimal performance, and ability to handle constraints, makes it one of the most promising tools for this type of control application. The content of this article handles the problem of autonomous driving by proposing an adaptive linear parameter varying model predictive controller (LPV-MPC), where the controller's prediction model is adaptive by means of a recurrent neural network. The proposed LPV-MPC is further optimised by a hybrid Genetic and Particle Swarm Optimization Algorithm (GA-PSO). The developed controller is tested and evaluated on a challenging track under variable wind disturbance.
This paper addresses autonomous racing by introducing a real-time nonlinear model predictive controller (NMPC) coupled with a moving horizon estimator (MHE). The racing problem is solved by an NMPC-based off-line trajectory planner that computes the best trajectory while considering the physical limits of the vehicle and circuit constraints. The developed controller is further enhanced with a learning extension based on Gaussian process regression that improves model predictions. The proposed control, estimation, and planning schemes are evaluated on two different race tracks.
Optimization-based controllers, such as Model Predictive Control (MPC), have attracted significant research interest due to their intuitive concept, constraint handling capabilities, and natural application to multi-input multi-output systems. However, the computational complexity of solving a receding horizon problem at each time step remains a challenge for the deployment of MPC. This is particularly the case for systems constrained by many inequalities. Recently, we introduced the concept of constraint-adaptive MPC (ca-MPC) to address this challenge for linear systems with hard constraints. In ca-MPC, at each time step, a subset of the constraints is removed from the optimization problem, thereby accelerating the optimization procedure, while resulting in identical closed-loop behavior. The present paper extends this framework to soft-constrained MPC by detecting and removing constraints based on sub-optimal predicted input sequences, which is rather easy for soft-constrained MPC due to the receding horizon principle and the inclusion of slack variables. We will translate these new ideas explicitly to an offset-free output tracking problem. The effectiveness of these ideas is demonstrated on a two-dimensional thermal transport model, showing a three order of magnitude improvement in online computational time of the MPC scheme.
Model predictive control (MPC) is an optimization-based control strategy with broad industrial adoption. Unfortunately, the required computation time to solve the receding-horizon MPC optimization problem can become prohibitively large for many applications with a large number of state constraints. This large number of state constraints can, for instance, originate from spatially discretizing a partial differential equation of which the solution has to satisfy constraints over the full spatial domain. This is particularly the case in MPC for RF-based hyperthermia cancer treatments, which forms a strong motivation for this study. To address this problem, we propose a novel constraint-adaptive MPC framework for linear discrete-time systems. In this framework, we select at each time-step a subset of the state constraints that are included in the optimization problem, thereby reducing the online computational burden. Critically, our framework guarantees the same closed-loop performance, recursive feasibility, and constraint satisfaction properties as the original (non-reduced) MPC scheme. We achieve this result by efficiently exploiting reachable set computations and the MPC cost function. We will demonstrate our novel method using a hyperthermia cancer treatment case study showing a two-orders of magnitude improvement in computation time, with identical closed-loop performance as the original (non-reduced) MPC scheme.
Large Language Models have demonstrated remarkable abilities in reasoning and planning by breaking down complex problems into sequential steps. Despite their success in various domains like mathematical problem-solving and coding, LLMs face challenges in ensuring reliable and optimal planning due to their inherent myopic nature of autoregressive decoding. This paper revisits LLM reasoning from an optimal-control perspective, proposing a novel method, Predictive-Decoding, that leverages Model Predictive Control to enhance planning accuracy. By re-weighting LLM distributions based on foresight trajectories, Predictive-Decoding aims to mitigate early errors and promote non-myopic planning. Our experiments show significant improvements in a wide range of tasks for math, coding, and agents. Furthermore, Predictive-Decoding demonstrates computational efficiency, outperforming search baselines with reduced computational resources. This study provides insights into optimizing LLM planning capabilities.
At the forefront of control techniques is Model Predictive Control (MPC). While MPCs are effective, their requisite to recompute an optimal control given a new state leads to sparse response to the system and may make their implementation infeasible in small systems with low computational resources. To address these limitations in stability control, this research presents a small deterministic Physics-Informed MPC Surrogate model (PI-MPCS). PI-MPCS was developed to approximate the control by an MPC while encouraging stability and robustness through the integration of the system dynamics and the formation of a Lyapunov stability profile. Empirical results are presented on the task of 2D quadcopter landing. They demonstrate a rapid and precise MPC approximation on a non-linear system along with an estimated two times speed up on the computational requirements when compared against an MPC. PI-MPCS, in addition, displays a level of stable control for in- and out-of-distribution states as encouraged by the discrete dynamics residual and Lyapunov stability loss functions. PI-MPCS is meant to serve as a surrogate to MPC on situations in which the computational resources are limited.