This paper investigates the distributed model predictive control for an asynchronous nonlinear multi-agent system with external interference via a self-triggered generator and a prediction horizon regulator. First, a shrinking constraint related to the error between the actual state and the predicted state is introduced into the optimal control problem to enable the robustness of the system. Then, the trigger interval and the corresponding prediction horizon are determined by altering the expression of the Lyapunov function, thus achieving a trade-off between control performance and energy loss. By implementing the proposed algorithm, the coordination objective of the multi-agent system is achieved under asynchronous communication. Finally, the recursive feasibility and stability are proven successively. An illustrative example is conducted to demonstrate the merits of the presented approach.
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.
Used water treatment plays a pivotal role in advancing environmental sustainability. Economic model predictive control holds the promise of enhancing the overall operational performance of the water treatment facilities. In this study, we propose a data-driven economic predictive control approach within the Koopman modeling framework. First, we propose a deep learning-enabled input-output Koopman modeling approach, which predicts the overall economic operational cost of the wastewater treatment process based on input data and available output measurements that are directly linked to the operational costs. Subsequently, by leveraging this learned input-output Koopman model, a convex economic predictive control scheme is developed. The resulting predictive control problem can be efficiently solved by leveraging quadratic programming solvers, and complex non-convex optimization problems are bypassed. The proposed method is applied to a benchmark wastewater treatment process. The proposed method significantly improves the overall economic operational performance of the water treatment process. Additionally, the computational efficiency of the proposed method is significantly enhanced as compared to benchmark control solutions.
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 investigates an aperiodic distributed model predictive control approach for multi-agent systems (MASs) in which parameterized synchronization constraints is considered and an innovative self-triggered criterion is constructed. Different from existing coordination methodology, the proposed strategy achieves the cooperation of agents through the synchronization of one-dimensional parameters related to the control inputs. At each asynchronous sampling instant, each agent exchanges the one-dimensional synchronization parameters, solves the optimal control problem (OCP) and then determines the open-loop phase. The incorporation of the selftriggered scheme and the synchronization parameter constraints relieves the computational and communication usage. Sufficient conditions guaranteeing the recursive feasibility of the OCP and the stability of the closed-loop system are proven. Simulation results illustrate the validity of the proposed control algorithm.
In this paper, we focus on the problem of shrinking-horizon Model Predictive Control (MPC) in uncertain dynamic environments. We consider controlling a deterministic autonomous system that interacts with uncontrollable stochastic agents during its mission. Employing tools from conformal prediction, existing works derive high-confidence prediction regions for the unknown agent trajectories, and integrate these regions in the design of suitable safety constraints for MPC. Despite guaranteeing probabilistic safety of the closed-loop trajectories, these constraints do not ensure feasibility of the respective MPC schemes for the entire duration of the mission. We propose a shrinking-horizon MPC that guarantees recursive feasibility via a gradual relaxation of the safety constraints as new prediction regions become available online. This relaxation enforces the safety constraints to hold over the least restrictive prediction region from the set of all available prediction regions. In a comparative case study with the state of the art, we empirically show that our approach results in tighter prediction regions and verify recursive feasibility of our MPC scheme.
This paper presents a model predictive control (MPC) for dynamic systems whose nonlinearity and uncertainty are modelled by deep neural networks (NNs), under input and state constraints. Since the NN output contains a high-order complex nonlinearity of the system state and control input, the MPC problem is nonlinear and challenging to solve for real-time control. This paper proposes two types of methods for solving the MPC problem: the mixed integer programming (MIP) method which produces an exact solution to the nonlinear MPC, and linear relaxation (LR) methods which generally give suboptimal solutions but are much computationally cheaper. Extensive numerical simulation for an inverted pendulum system modelled by ReLU NNs of various sizes is used to demonstrate and compare performance of the MIP and LR methods.
Koopman operator theory is a kind of data-driven modelling approach that accurately captures the nonlinearities of mechatronic systems such as vehicles against physics-based methods. However, the infinite-dimensional Koopman operator is impossible to implement in real-world applications. To approximate the infinite-dimensional Koopman operator through collection dataset rather than manual trial and error, we adopt deep neural networks (DNNs) to extract basis functions by offline training and map the nonlinearities of vehicle planar dynamics into a linear form in the lifted space. Besides, the effects of the dimensions of basis functions on the model accuracy are explored. Further, the extended state observer (ESO) is introduced to online estimate the total disturbance in the lifted space and compensate for the modelling errors and residuals of the learned deep Koopman operator (DK) while also improving its generalization. Then, the proposed model is applied to predict vehicle states within prediction horizons and later formulates the constrained finite-time optimization problem of model predictive control (MPC), i.e., ESO-DKMPC. In terms of the trajectory tracking of autonomous vehicles, the ESO-DKMPC generates the wheel steering angle to govern lateral motions based on the decoupling control structure. The various conditions under the double-lane change scenarios are built on the CarSim/Simulink co-simulation platform, and extensive comparisons are conducted with the linear MPC (LMPC) and nonlinear MPC (NMPC) informed by the physics-based model. The results indicate that the proposed ESO-DKMPC has better tracking performance and moderate efficacy both within linear and nonlinear regions.
Model Predictive Control (MPC)-based trajectory planning has been widely used in robotics, and incorporating Control Barrier Function (CBF) constraints into MPC can greatly improve its obstacle avoidance efficiency. Unfortunately, traditional optimizers are resource-consuming and slow to solve such non-convex constrained optimization problems (COPs) while learning-based methods struggle to satisfy the non-convex constraints. In this paper, we propose SOMTP algorithm, a self-supervised learning-based optimizer for CBF-MPC trajectory planning. Specifically, first, SOMTP employs problem transcription to satisfy most of the constraints. Then the differentiable SLPG correction is proposed to move the solution closer to the safe set and is then converted as the guide policy in the following training process. After that, inspired by the Augmented Lagrangian Method (ALM), our training algorithm integrated with guide policy constraints is proposed to enable the optimizer network to converge to a feasible solution. Finally, experiments show that the proposed algorithm has better feasibility than other learning-based methods and can provide solutions much faster than traditional optimizers with similar optimality.
This paper presents a novel Koopman (composition) operator representation framework for control systems in reproducing kernel Hilbert spaces (RKHSs) that is free of explicit dictionary or input parametrizations. By establishing fundamental equivalences between different model representations, we are able to close the gap of control system operator learning and infinite-dimensional regression, enabling various empirical estimators and the connection to well-understood learning theory in RKHSs under one unified framework. As a consequence, our proposed framework allows for arbitrary accurate finite-rank approximations in infinite-dimensional spaces and leads to finite-dimensional predictors without apriori restrictions to a finite span of functions or inputs. To enable applications to high-dimensional control systems, we improve the scalability of our proposed control Koopman operator estimates by utilizing sketching techniques. Numerical experiments demonstrate superior prediction accuracy compared to bilinear EDMD, especially in high dimensions. Finally, we show that our learned models are readily interfaced with linear-parameter-varying techniques for model predictive control.
Personalization is crucial for the widespread adoption of advanced driver assistance system. To match up with each user's preference, the online evolution capability is a must. However, conventional evolution methods learn from naturalistic driving data, which requires a lot computing power and cannot be applied online. To address this challenge, this paper proposes a lesson learning approach: learning from driver's takeover interventions. By leveraging online takeover data, the driving zone is generated to ensure perceived safety using Gaussian discriminant analysis. Real-time corrections to trajectory planning rewards are enacted through apprenticeship learning. Guided by the objective of optimizing rewards within the constraints of the driving zone, this approach employs model predictive control for trajectory planning. This lesson learning framework is highlighted for its faster evolution capability, adeptness at experience accumulating, assurance of perceived safety, and computational efficiency. Simulation results demonstrate that the proposed system consistently achieves a successful customization without further takeover interventions. Accumulated experience yields a 24% enhancement in evolution efficiency. The average number of learning iterations is only 13.8. The average computation time is 0.08 seconds.
Facing the congestion challenges of mixed road networks comprising expressways and arterial road networks, traditional control solutions fall short. To effectively alleviate traffic congestion in mixed road networks, it is crucial to clear the interaction between expressways and arterial networks and achieve orderly coordination between them. This study employs the multi-class cell transmission model (CTM) combined with the macroscopic fundamental diagram (MFD) to model the traffic dynamics of expressway systems and arterial subregions, enabling vehicle path tracking across these two systems. Consequently, a comprehensive traffic transmission model suitable for mixed road networks has been integrated. Utilizing the SUMO software, a simulation platform for the mixed road network is established, and the average trip lengths within the model have been calibrated. Based on the proposed traffic model, this study constructs a route guidance model for mixed road networks and develops an integrated model predictive control (MPC) strategy that merges route guidance, perimeter control, and ramp metering to address the challenges of mixed road networks' traffic flow control. A case study of a scenario in which a bidirectional expressway connects two subregions is conducted, and the results validate the effectiveness of the proposed cooperative guidance and control (CGC) method in reducing overall congestion in mixed road networks.
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.
In this work, we explore the efficacy of rectified linear unit artificial neural networks in addressing the intricate challenges of convoluted constraints arising from feedback linearization mapping. Our approach involves a comprehensive procedure, encompassing the approximation of constraints through a regression process. Subsequently, we transform these constraints into an equivalent representation of mixed-integer linear constraints, seamlessly integrating them into other stabilizing control architectures. The advantage resides in the compatibility with the linear control design and the constraint satisfaction in the model predictive control setup, even for forecasted trajectories. Simulations are provided to validate the proposed constraint reformulation.
Distributed energy resources (DERs) such as grid-responsive loads and batteries can be harnessed to provide ramping and regulation services across the grid. This paper concerns the problem of optimal allocation of different classes of DERs, where each class is an aggregation of similar DERs, to balance net-demand forecasts. The resulting resource allocation problem is solved using model-predictive control (MPC) that utilizes a rolling sequence of finite time-horizon constrained optimizations. This is based on the concept that we have more accurate estimates of the load forecast in the short term, so each optimization in the rolling sequence of optimization problems uses more accurate short term load forecasts while ensuring satisfaction of capacity and dynamical constraints. Simulations demonstrate that the MPC solution can indeed reduce the ramping required from bulk generation, while mitigating near-real time grid disturbances.
We propose a hybrid formulation of the linear inverted pendulum model for bipedal locomotion, where the foot switches are triggered based on the center of mass position, removing the need for pre-defined footstep timings. Using a concept similar to reference spreading, we define nontrivial tracking error coordinates induced by our hybrid model. These coordinates enjoy desirable linear flow dynamics and rather elegant jump dynamics perturbed by a suitable extended class ${\mathcal K}_\infty$ function of the position error. We stabilize this hybrid error dynamics using a saturated feedback controller, selecting its gains by solving a convex optimization problem. We prove local asymptotic stability of the tracking error and provide a certified estimate of the basin of attraction, comparing it with a numerical estimate obtained from the integration of the closed-loop dynamics. Simulations on a full-body model of a real robot show the practical applicability of the proposed framework and its advantages with respect to a standard model predictive control formulation.
Reference tracking and obstacle avoidance rank among the foremost challenging aspects of autonomous driving. This paper proposes control designs for solving reference tracking problems in autonomous driving tasks while considering static obstacles. We suggest a model predictive control (MPC) strategy that evades the computational burden of nonlinear nonconvex optimization methods after embedding the nonlinear model equivalently to a linear parameter-varying (LPV) formulation using the so-called scheduling parameter. This allows optimal and fast solutions of the underlying convex optimization scheme as a quadratic program (QP) at the expense of losing some performance due to the uncertainty of the future scheduling trajectory over the MPC horizon. Also, to ensure that the modeling error due to the application of the scheduling parameter predictions does not become significant, we propose the concept of scheduling trust region by enforcing further soft constraints on the states and inputs. A consequence of using the new constraints in the MPC is that we construct a region in which the scheduling parameter updates in two consecutive time instants are trusted for computing the system matrices, and therefore, the feasibility of the MPC optimization problem is retained. We test the method in different scenarios and compare the results to standard LPVMPC as well as nonlinear MPC (NMPC) schemes.
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.
Learning-based techniques have become popular in both model predictive control (MPC) and reinforcement learning (RL). Probabilistic ensemble (PE) models offer a promising approach for modelling system dynamics, showcasing the ability to capture uncertainty and scalability in high-dimensional control scenarios. However, PE models are susceptible to mode collapse, resulting in non-robust control when faced with environments slightly different from the training set. In this paper, we introduce the $\textbf{u}$ncertainty-$\textbf{d}$riven rob$\textbf{u}$st $\textbf{c}$ontrol (UDUC) loss as an alternative objective for training PE models, drawing inspiration from contrastive learning. We analyze the robustness of UDUC loss through the lens of robust optimization and evaluate its performance on the challenging Real-world Reinforcement Learning (RWRL) benchmark, which involves significant environmental mismatches between the training and testing environments.