Tube-based Model Predictive Control Research Articles

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.

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.

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

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

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

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.

An Improved Model Predictive Control-Based Trajectory Planning Method for Automated Driving Vehicles Under Uncertainty Environments

For automated driving vehicles, trajectory planning is responsible for obtaining feasible trajectories with velocity profiles according to driving environments. From the perspective of trajectory planning, multiple uncertainties of environments and tracking deviations are two significant factors affecting driving safety. The former disturbs the judgment of trajectory planning on the environments, and the latter reduces the tracking accuracy of planned trajectories. To solve these problems, an improved model predictive control (MPC) trajectory planning method is proposed in this paper. Firstly, a Kalman filter fusion method is carried out to predict obstacle trajectory and their uncertainty, which combines model-based and data-based prediction methods. Based on the prediction results, a tube-based MPC trajectory planning method is applied to plan a reference trajectory with a small tracking deviation. The tube-based MPC is composed of two parts. One is the MPC with tightened constraints that is used to plan a feasible trajectory according to a nominal vehicle system and driving environment. The other is a state feedback control that is proposed to adjust the above planned trajectory to reduce the tracking deviations. To our knowledge, this paper proposes Kalman filter fusion and tube-based MPC planning method for the first time to consider the uncertainties of trajectory prediction and tracking control meanwhile in the planning. The planning method is verified by simulations and experiments in multiple scenes. Results show that the method is suitable for both static and dynamic scenes. Compared with applying the basic prediction method, the lateral deviation of the proposed method from the ideal trajectory is decreased by 46.5%. Compared with the nominal MPC method, the lateral tracking deviations of the proposed method are decreased by 77.42%.

Autonomous Spacecraft Rendezvous Using Tube-Based Model Predictive Control: Design and Application

As the concentration of large space debris increases, how rendezvous maneuvers involving these typically non-cooperative, freely tumbling bodies are planned and executed is evolving. The rendezvous must be carefully planned, employing up-to-date in situ data to identify the inertial and motion parameters of the target body, and executed in a manner that accounts for the remaining uncertainty in these parameters. This paper presents an extension of the Tumbling Rendezvous via Autonomous Characterization and Execution (TRACE) pipeline used in the ROAM/TumbleDock Astrobee experiment campaign, which sequences the target state estimation, motion planning, controller design, and maneuver execution tasks while additionally providing logical loop-back avenues to previous tasks, increasing the chances of a successful maneuver. The pipeline’s performance is analyzed in simulation, utilizing target state estimates generated in a previous activity on a dedicated on-ground test bed; online motion planning, based on nonlinear programming and warm-started using a trajectory library generated offline with a novel graphics-processing-unit-based method; and tube-based model predictive control to robustly track the planned trajectory. Tube-based model predictive control is an actively evolving subject, distributed over multiple publications and various research interests. The necessary theory and considerations for practical implementation of the method are consolidated; its use, features, and limitations in the proposed task are demonstrated.

Asynchronous Computation of Tube-based Model Predictive Control

Tube-based model predictive control (MPC) methods bound deviations from a nominal trajectory due to uncertainties in order to ensure constraint satisfaction. While techniques that compute the tubes online reduce conservativeness and increase performance, they suffer from high and potentially prohibitive computational complexity. This paper presents an asynchronous computation mechanism for system level tube-MPC (SLTMPC), a recently proposed tube-based MPC method which optimizes over both the nominal trajectory and the tubes. Computations are split into a primary and a secondary process, computing the nominal trajectory and the tubes, respectively. This enables running the primary process at a high frequency and moving the computationally complex tube computations to the secondary process. We show that the secondary process can continuously update the tubes, while retaining recursive feasibility of the primary process.

Tube-based MPC of hierarchical distribution network for voltage regulation considering uncertainties of renewable energy

• A novel model for low-voltage distribution areas based on genetic algorithm is developed, which simplifies the complexity of online computation and suppresses the inner voltage deviations in a safe section. • The coordination of PVs and ESs at different voltage levels is promoted to improve the voltage regulation while short of the reactive power capacity of PVs. • A tube-based MPC controller is proposed for voltage fluctuation under uncertainties introduced by power disturbance and a genetic-algorithm-based equivalent model of low-voltage areas, with which a distribution network can work in common conditions under variable operations of PVs. With the ever-growing penetration of distributed generators (DGs), voltage deviation caused by randomness and fluctuation has become increasingly prominent in distribution networks. Conventional voltage control cannot sufficiently utilize the rapid and flexible characteristics of DGs. In this paper, a tube-based model predictive control (TMPC) method is proposed to address voltage violation and fluctuation difficulties considering the uncertainties of renewable energy. Firstly, a simplified model approach based on a genetic algorithm (GA) is proposed to unify numerous DGs in low-voltage distribution areas. Then, based on this simplified model combined with the voltage sensitivity model, the TMPC controller is designed for the whole distribution network, which consists of two subsidiary controllers to suppress voltage deviation caused by uncertainties. The former is used to generate a central path for different operating points of the grid, and the latter is designed to track the path in a bound tube. The proposed method can cope with the uncertainties caused by external disturbances such as drastic power fluctuations. Finally, the numerical simulation in the case studies demonstrates the effectiveness of the proposed method in accuracy and efficiency.

Tube-based coalitional MPC with plug-and-play features

This paper presents a distributed setting of model predictive control (MPC) to manage linear multi-agent systems consisting of coupled subsystems. Specifically, local controllers can work in coalitions to improve performance and handle plug-and-play events. This study provides insight into a coalitional MPC strategy based on optimized tubes that handles plug-in and plug-out subsystems. Moreover, we explore an inherent robustness gap to absorb disturbances not covered by the tubes without having to group local controllers. A comparison of our approach with centralized and decentralized MPC is reported using an illustrative example.

Tube-Based Robust MPC for Two-Timescale Systems Using Reduced-Order Models

A tube-based robust Model Predictive Control (MPC) formulation is presented for systems with slow and fast timescale dynamics. The controller uses a reduced-order model that approximates the slow timescale dynamics and is implemented with a relatively large time step size. By analyzing the error between the full- and reduced-order models, the MPC optimization problem is proven to be recursively feasible and to produce closed-loop trajectories that satisfy state and input constraints. By relating bounds on all model errors to bounds on the change of the input in time, input change bounds are included as decision variables in the MPC problem to achieve a time-varying balance between fast transients with large model error and steady-state operation with zero model error. Zonotopes are used to make the approach practical and a numerical example demonstrates the benefits of optimizing time-varying input change bounds as part of the MPC formulation.