Tube-based Model Predictive Control Research Articles

Integrated Motion Control Strategy Considering Parameter Robustness for Distributed Vehicle by Wire

<div>To address the issues of functional conflicts in execution subsystems and the deterioration of control performance due to model parameter uncertainties in the motion control of distributed vehicle by wire, this article proposes an integrated control strategy considering parameter robustness. This strategy aims to compensate for model mismatch, resolve functional conflicts, and achieve motion coordination. Based on the over-actuation characteristics of distributed vehicle by wire, this article constructs the dynamic model and utilizes the tire cornering properties along with phase portraits to delineate the working regions of the execution subsystems. To deal with model parameter uncertainties and mismatch, tube-based model predictive control (tube-based MPC) is applied to the control strategy design, which compensates for model deviations through state feedback and constructs a robust positively invariant set (RPI) to constrain the system state. Correspondingly, the weights of control inputs are adjusted adaptively, according to the working regions, to optimize the coordination logic of integrated control. In order to verify the effectiveness and feasibility of the strategy, extreme driving condition tests are executed on hardware-in-the-loop (HIL) and real vehicle test platforms. The test results indicate that the strategy proposed in this article is able to reduce the sideslip angle and tracking error of yaw rate, improve driving stability under extreme conditions through integrated control, and especially, it can still maintain precise stability control performance under severe model mismatch, exhibiting strong robustness facing parameter uncertainties.</div>

Adaptive Tube-Based Model Predictive Control for the Receiving-Side DC–DC of Dynamic Wireless Power Transfer System

Adaptive Tube-Based Model Predictive Control for the Receiving-Side DC–DC of Dynamic Wireless Power Transfer System

Cooperative control of virtually coupled trains considering train-to-train communication cycle: a tube-based model predictive control approach

In this paper, a distributed tube-based model predictive control (TMPC) method is proposed to address the cooperative control of virtually coupled high-speed train (HSTs), which consists of an optimisation control part and a feedback control part. The novelty of this work lies in its pioneering consideration of the inconsistency between the train-to-train (T2T) communication cycle and the train operation control cycle in the cooperative control of virtually coupled trains. Firstly, for the optimisation control part, a distributed MPC scheme is designed based on the nominal train dynamics model to address the cooperative control of trains with different initial states, state constraints and control input constraints. By solving the optimisation control problem of the MPC, the optimal control input sequence and operating state sequence of the train for the next T2T communication cycle can be obtained. Secondly, the recursive feasibility and convergence of the MPC are analysed theoretically. Thirdly, for the feedback control part, an adaptive feedback control law is designed based on the actual train dynamics model, auxiliary dynamic system (ADS) and neural network techniques. In the train operation control cycle, the feedback control part utilises the optimal state sequence from the MPC as a reference for feedback control to deal with the external disturbance and train dynamics modelling inaccuracy. Fourthly, it is theoretically proved that the actual operating state of the train can converge to a small region around the optimal state of the MPC in a finite time. Finally, the effectiveness of the proposed distributed cooperative control scheme is verified by simulations.

Tube-based MPC strategy for load frequency control of multi-area interconnected power system with HESS

With the rapid development of power generation technology and the increasing demand from power users, multi-area interconnected power systems have become a development trend. This article proposes a new robust tube-based model predictive control strategy (MPC) for multi-area interconnected power systems with hybrid energy storage systems (HESS), based on the application of HESS to optimize the performance of load frequency control in power systems. The proposed strategy is mainly based on a new robustness constraint, which effectively handles uncertain disturbances within interconnected power system by compressing the disturbance invariant set. This strategy effectively alleviates the problems caused by inconsistency in multi-area interconnection modes. In addition, a sufficient stability criterion is derived to ensure the robust stability of the system, even under uncertain disturbances. By modeling a four-area interconnected power system with HESS, the frequency fluctuations of different methods are compared and discussed in each area. Based on the constructed software-in-the-loop setup, the effectiveness and feasibility of the proposed strategy are verified by experiments.

Safety-Guaranteed Ship Berthing Using Cascade Tube-Based Model Predictive Control

Safety-Guaranteed Ship Berthing Using Cascade Tube-Based Model Predictive Control

A tube-based model predictive control method for intelligent vehicles path tracking

A tube-based model predictive control method for intelligent vehicles path tracking

A Tube-Based Model Predictive Control for Path Tracking of Autonomous Articulated Vehicle

This paper presents tube-based Model Predictive Control (MPC) for the path and velocity tracking of an autonomous articulated vehicle. The target platform of this study is an autonomous articulated vehicle with a non-steerable axle. Consequently, the articulation angle and wheel torque input are determined by the tube-based MPC. The proposed MPC aims to achieve two objectives: minimizing path tracking error and enhancing robustness to disturbances. Furthermore, the lateral stability of the autonomous articulated vehicle is considered to reflect its dynamic characteristics. The vehicle model for the MPC is formulated using local linearization to minimize modeling errors. The reference state is determined using a virtual controller based on the linear quadratic regulator to provide the optimal reference for the MPC solver. The proposed algorithm was evaluated through a simulation study with base algorithms under noise injection into the sensor signal. Simulation results demonstrate that the proposed algorithm achieved the smallest path tracking error, compared to the base algorithms. Additionally, the proposed algorithm demonstrated robustness to external noise for multiple signals.

A robust model predictive control unified framework for autonomous rendezvous and docking with a tumbling target

During autonomous rendezvous and docking (AR&D) with a tumbling target, multiple unfavorable engineering constraints exist, such as constraints on the control, velocity, or collision avoidance. Meanwhile, many sources of uncertainty exist, including incomplete and inaccurate measurements, control deviation, dynamic uncertainty, and inertial parameter uncertainty of the tumbling target, which significantly complicate the design of the guidance and control algorithm. Considering these challenges, this paper proposes a robust identification, planning, and control unified framework for AR&D with a tumbling target, which incorporates an extended Kalman filter (EKF) with a robust tube-based model predictive control for tracking (TMPT) controller. First, the EKF is designed to estimate the system state and inertial parameters of the target and then predict the future behavior of the tumbling target. Additionally, the prediction information of the target is transmitted to the designed TMPT controller as a reference signal. This TMPT controller unites trajectory planning and control in a single layer that can ensure the stability and recursive feasibility of the algorithm with a short prediction horizon. Moreover, it can guarantee that the closed-loop system is robustly and asymptotically convergent to the reachable set whose center is the optimal reachable periodic trajectory concerning the docking port of the tumbling target. The unified framework represents a robustness-to-optimality control strategy that can accomplish the AR&D mission efficiently while considering multiple engineering constraints and uncertainties. Finally, the efficiency of the proposed control framework is verified through a numerical simulation.

Tube-based model predictive control for linear systems with bounded disturbances and input delay

This paper proposes a tube-based model predictive control strategy for linear systems with bounded disturbances and input delay to ensure input-to-state stability. Firstly, the actual disturbed system is decomposed into a nominal system without disturbances and an error system. For the nominal system, solving an optimization problem, where the delayed control input is set as an optimization variable, yields a nominal control law that enables the nominal state signal to approach to zero. Then, for the error system, the Razumikhin approach is used to identify a robust control invariant set. Using the set invariance theorem, an ancillary control law is developed to confine the error state signal in the invariant set. Combining the two results, we obtain a control law that enables the state signal to remain within a robustly invariant tube. Finally, the effectiveness of the developed control strategy is validated by simulations.

Trajectory Tracking Control of Autonomous Underwater Vehicles Using Improved Tube-Based Model Predictive Control Approach

Trajectory Tracking Control of Autonomous Underwater Vehicles Using Improved Tube-Based Model Predictive Control Approach

Tube-Based Model Predictive Control for Constrained Unmanned Marine Vehicles With Thruster Faults

Tube-Based Model Predictive Control for Constrained Unmanned Marine Vehicles With Thruster Faults

An anti-disturbance lane-changing trajectory tracking control method combining extended Kalman filter and robust tube-based model predictive control

This paper proposes a trajectory tracking control method combining extended Kalman filter (EKF) and robust tube-based model predictive control (RTMPC) methods to improve the anti-disturbance capability during lane-changing maneuver of automated vehicles. A time-based quintic polynomial function is introduced for the implementation of trajectory planning to obtain the desired reference trajectory. The planned trajectory is input to the nominal system-oriented model predictive controller (MPC) in RTMPC for optimization to obtain the optimal control of the nominal system. The EKF collects the state measurements of the current instant and the optimal state estimates of the previous instant, and performs filtering to obtain the optimal state estimates of the current instant. The optimal estimate of the current state and the current state of the nominal system are input into the auxiliary control law of RTMPC to obtain the control of the actual system. Comparative numerical simulation experiments are conducted to analyze robustness and sensitivity of the proposed method. The results show that the control method combining EKF and RTMPC can optimize the trajectory tracking performance of the vehicle system, especially in the lateral displacement and the yaw-rate control. When the amplitude of measurement noise reaches the maximum, the optimization effect of lateral control is most significant in experiments. And the optimization effect in the control of lateral displacement and yaw angle continues to enhance with the increase of measurement disturbance. Therefore, this study can provide a reference for the anti-interference lane change trajectory tracking strategy of automated vehicles in the future.

Variable Tube-Based Model Predictive Trajectory Tracking Control Strategy with Adaptive Load for Automatic Truck

Variable Tube-Based Model Predictive Trajectory Tracking Control Strategy with Adaptive Load for Automatic Truck

Tube-Based Model Predictive Control Based on Constrained Zonotopes

Tube-Based Model Predictive Control Based on Constrained Zonotopes

Maximal Admissible Disturbance Constraint Set for Tube-Based Model Predictive Control

Tube-based model predictive control (TMPC) is an outstanding control technique in robust control realms. However, the existing works are generally based on <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a priori</i> known admissible sets of disturbances, i.e., disturbance constraint sets, the sizes of which are by default small enough such that the region of attraction is non-empty. If the size of the disturbance constraint set specified is too large, or even oversized in some particular direction, TMPC may not be capable of handling it and lose the feasibility of the optimization problem. Otherwise, a small disturbance constraint set may be inadequate to cover all realizations of the actual disturbances. This implies that an improper selection of the disturbance constraint set may lead to the invalidity of TMPC. To address this issue, this technical note proposes an optimization-based algorithm to determine the maximal admissible disturbance constraint set for classical TMPC [1], which evaluates the robustness of TMPC. The proposed algorithm is also applicable to other TMPC methods for linear systems with a slight modification.

The Stochastic Robustness of Nominal and Stochastic Model Predictive Control

In this work, we establish and compare the stochastic and deterministic robustness properties achieved by nominal model predictive control (MPC), stochastic MPC (SMPC), and a proposed constraint-tightened MPC (CMPC) formulation, which represents an idealized version of tube-based MPC. We consider three definitions of robustness for nonlinear systems and bounded disturbances: robust asymptotic stability (RAS), robust asymptotic stability in expectation (RASiE), and RASiE w.r.t. the stage cost <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\ell (\cdot)$</tex-math></inline-formula> used in these MPC formulations ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\ell$</tex-math></inline-formula> -RASiE). Via input-to-state stability (ISS) and stochastic ISS (SISS) Lyapunov functions, we establish that MPC, subject to sufficiently small disturbances, and CMPC ensure all three definitions of robustness without a stochastic objective function. While SMPC also ensures RASiE and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\ell$</tex-math></inline-formula> -RASiE, SMPC does not guarantee RAS for nonlinear systems. Through a few simple examples, we illustrate the implications of these results and demonstrate that, depending on the definition of robustness considered, SMPC is not necessarily more robust than nominal MPC even if the disturbance model is exact.

Uncertainties and Output Feedback in Rollout Event-Triggered Control

The fact that event-triggered control (ETC) often exhibits an improved performance-communication tradeoff over time-triggered control renders it especially useful for Networked Control Systems (NCSs). However, it has proven difficult to characterize the traffic produced by ETC a priori. Rollout ETC addresses this issue by using a triggering and control law that is <i>implicitly</i> defined by the solution to an optimal control problem (OCP), instead of an explicit one as in classical ETC. This allows to directly incorporate predefined constraints on the transmission traffic as well as on states and inputs. In this article, we examine the practically relevant case when output instead of state measurements are available, and measurements as well as the LTI plant are subject to uncertainties. To address these challenges, we adapt methods from robust tube-based model predictive control and propose three different strategies to implement an error feedback in an NCSs setup, the applicability of which depends on the capabilities of the actuator. We establish recursive feasibility, robust constraint satisfaction and convergence. Finally, we illustrate our results in a numerical example.

All-in-One Control Framework for Distributed Drive Electric Buses Path Tracking Subject to Uncertain Crosswind and Varied Passenger Mass

This paper proposes an all-in-one control framework for distributed drive electric buses (DDEBs) that can effectively attenuate the effects of uncertain crosswind and varied passenger mass in path tracking, while minimizing the electricity consumption of battery. To track the desired path and ensure driving stability, a robust tube-based model predictive control method is proposed considering lateral, yaw and roll motions. Simultaneously, for the longitudinal motion, a robust sliding mode control method is designed to achieve accurate tracking of longitudinal velocity. Meanwhile, the uncertain crosswind and varied passenger mass faced by the DDEBs are decoupled into external disturbances and their effects on the system are eliminated in both controllers. Then, to cope with energy optimization problem in path tracking, a torque distribution controller is constructed by formulating the vehicle stability margin, tracking dynamic requirements and energy efficiency as constrained weighted least squares problem. Finally, a Trucksim-Simulink co-simulation is performed, where the simulation results demonstrated that the proposed control framework is robust and effective, and can achieve better energy saving effect compared to the original control methods.

Nonparameteric Event-Triggered Learning With Applications to Adaptive Model Predictive Control

In this paper, an event-triggered online learning problem for Lipschitz continuous systems with nonlinear model mismatch is considered, with the aim of building a data-efficient non-parametric estimation approach for learning-based control. The system considered is composed of known linear dynamics and unknown nonlinearity, and the main focus of this work includes the design and analysis of event-triggered learning mechanisms, and the application of the learning method to adaptive model predictive control (MPC). First, a sample grid-based event-triggering mechanism and a prediction uncertainty-based event-triggering mechanisms are designed on the basis of the lazily adapted constant kinky inference framework. Then, the properties of the designed event-triggered learning methods are analyzed, and it is proved that the proposed approach provides error-bounded predictions with limited computational complexity. Third, a tube-based adaptive MPC design approach is developed utilizing the proposed event-triggered learning approach, and the closed-loop stability of the adaptive MPC is analyzed and proved based on the properties of the event-triggered learning algorithms. Implementation issues are discussed, and the effectiveness of the results is illustrated by numerical examples and comparative simulations.

Energy saving and indoor temperature control for an office building using tube-based robust model predictive control

Actively controlling a building’s heating, ventilation, and air conditioning (HVAC) system can reduce costs and improve indoor comfort. Model predictive control (MPC) is an effective control algorithm that can facilitate the active control of complex systems such as the HVAC system. However, the uncertainty of the prediction model engenders many challenges in practical application. To address these issues, we propose a tube-based MPC strategy. First, a reduced-order thermal capacitance and thermal resistance model is established for the target system. Subsequently, a tube-based MPC scheme is designed to effectively handle uncertainties in real systems. The prediction uncertainty space is re-assumed in the tube, combined with the actual prediction error, to more closely correspond to the actual situation. The proposed model is tested and validated using the BOPTEST open-source testing framework. The results show that the proposed tube-based MPC can reduce the operating cost by at least 24%, compared with the traditional open-loop and closed-loop MPC, and can better control the indoor temperature when considering multiple uncertain predictions.