Model Predictive Tracking Control Research Articles

A Provably Convergent Control Closure Scheme for the Method of Moments of the Chemical Master Equation.

In this article, we introduce a novel moment closure scheme based on concepts from model predictive control (MPC) to accurately describe the time evolution of the statistical moments of the solution of the chemical master equation (CME). The method of moments, a set of ordinary differential equations frequently used to calculate the first nm moments, is generally not closed since lower-order moments depend on higher-order moments. To overcome this limitation, we interpret the moment equations as a nonlinear dynamical system, where the first nm moments serve as states, and the closing moments serve as the control input. We demonstrate the efficacy of our approach using three example systems and show that it outperforms existing closure schemes. For polynomial systems, which encompass all mass-action systems, we provide probability bounds for the error between true and estimated moment trajectories. We achieve this by combining the convergence properties of a priori moment estimates from stochastic simulations with guarantees for nonlinear reference tracking MPC. Our proposed method offers an effective solution to accurately predict the time evolution of moments of the CME, which has wide-ranging implications for many fields, including biology, chemistry, and engineering.

Distributed Sensor-Tolerant MPC for Formation Tracking of Networked Multicopters With Input/State Constraints

This brief presents a novel model predictive control (MPC) algorithm to achieve formation tracking of networked multicopters (nodes) with sensor faults and physical constraints. The algorithm can be used to asymptotically form and maintain a user-defined three-dimensional pattern for the multicopters formation. Another concern lies on how to deal with the usual sensor faults caused by the failure of the Global Positioning System (GPS) or the Inertial Navigation System (INS), in the above-mentioned control process. To this end, we embed the residual generators and auxiliary variable observers into the algorithm for the detection and estimation of the multicopters faults. Multicopters only accept the information related to their neighbors for real-time online rolling optimization. By using the sum of local cost functions to construct a Lyapunov candidate, it is proved that the asymptotic stability of such a distributed MPC (DMPC) is guaranteed under the condition that the weight requirements are satisfied. Simulation results demonstrate the rationality and effectiveness of the proposed algorithm.

Robust Laguerre‐based model predictive control for trajectory tracking of a mobile robot using an linear matrix inequality (LMI)‐based approach

AbstractThis paper studies the trajectory tracking of a constrained mobile robot under slippery conditions. The goal is to propose a controller for real‐time operations of time‐varying dynamics with insignificant execution time. Therefore, a Laguerre‐based model predictive control (LMPC) is designed, and robustness is provided with an linear matrix inequality (LMI)‐feedback controller. Moreover, a recursive least square (RLS) algorithm with a forgetting factor is utilized to identify the required parameters of the LMI‐based controller. LMPC and LMI‐based controller stability is achieved with suboptimal theory and Lyapunov function, respectively. This algorithm separates the nominal system and introduces new dynamics containing uncertainties. Furthermore, LMPC is removed from the online calculation, which dramatically reduces computation burden and time; consequently, online computation is dedicated to determining the LMI feedback. Simulations are provided to compare the proposed robust controller to its not robust counterpart. Finally, it is demonstrated that this controller diminishes the execution time considerably, making it incomparable to previous robust MPC strategies.

Lexicographic optimization for economic model predictive control with zone tracking

Tracking model predictive control (MPC) and economic model predictive control (EMPC) are essential techniques in process control. Economic model predictive control with zone tracking offers an effective means of concurrently addressing both tracking MPC and EMPC objectives. However, the aggregated conflicting objectives do not always align with the prioritization of critical tasks, such as safety, stability, quality, and economy. To address this issue, this study introduces a lexicographic approach for EMPC with zone tracking, which aims at balancing the competing zone tracking and economic objectives. The work also explores a generalized lexicographic multi-objective MPC (MoMPC) formulation and presents lexicographic zone economic model predictive control to accommodate multiple tracking and economic objectives. The advantages, disadvantages, and effectiveness of the proposed approach are validated and showcased through extensive simulation experiments.

Set-point tracking MPC with avoidance features

This work proposes a finite-horizon optimal control strategy to solve the tracking problem while providing avoidance features to the closed-loop system. Inspired by the set-point tracking model predictive control (MPC) framework, the central idea of including artificial variables into the optimal control problem is considered. This approach allows us to add avoidance features into the set-point tracking MPC strategy without losing the properties of an enlarged domain of attraction and feasibility insurances in the face of any changing reference. Besides, the artificial variables are considered together with an avoidance cost functional to establish the basis of the strategy, maintaining the recursive feasibility property in the presence of a previously unknown number of regions to be avoided. It is shown that the closed-loop system is recursively feasible and input-to-state-stable under the mild assumption that the avoidance cost is uniformly bounded over time. Finally, two numerical examples illustrate the controller behavior.

Event-triggered model predictive tracking control of aero-engine with varying prediction horizon

Aero-engine is a complex thermal-mechanical system with strong nonlinearity, uncertainty, and time variation. Thus, it is crucial to design an effective controller for such a complex system to obtain the desired performances of the aero-engine. In recent years, model predictive control (MPC) has shown great potential in dealing with control problems with complex constraints of multi-variable systems, which has been applied to aero-engine control, achieving good results. Furthermore, the MPC strategy using an event-driven mechanism is good at balancing system resources and ensuring system control performances. In this paper, the problem of event-triggered MPC for aero-engine systems with bounded disturbances is studied. Firstly, an event-triggered strategy with a dynamic forced-trigger mechanism is proposed. Then, an MPC algorithm based on an event-triggered mechanism is designed. Finally, an application to the JT9D aero-engine model provided by T-MATS verifies the effectiveness of the designed algorithm. It is shown that the calculation load is significantly reduced, which proves the superiority of this method.

Hybrid Layer of Improved Interfered Fluid Dynamic System and Nonlinear Model Predictive Control for Navigation and Control of Autonomous Underwater Vehicles

This study introduces a hybrid control structure called Improved Interfered Fluid Dynamic System Nonlinear Model Predictive Control (IIFDS-NMPC) for the path planning and trajectory tracking of autonomous underwater vehicles (AUVs). The system consists of two layers; the upper layer utilizes the Improved Interfered Fluid Dynamic System (IIFDS) for path planning, while the lower layer employs Nonlinear Model Predictive Control (NMPC) for trajectory tracking. Extensive simulation experiments are conducted to determine optimal parameters for both static and dynamic obstacle scenarios. Additionally, real-world testing is performed using the BlueRov2 platform, incorporating multiple dynamic and static obstacles. The proposed approach achieves real-time control at a frequency of 100 Hz and exhibits impressive path tracking accuracy, with a root mean square (RMS) of 0.02 m. This research provides a valuable framework for navigation and control in practical applications.

Improved SSA‐RBF neural network‐based dynamic 3‐D trajectory tracking model predictive control of autonomous underwater vehicles with external disturbances

AbstractThis paper studies the three‐dimensional (3‐D) dynamic trajectory tracking control of an autonomous underwater vehicle (AUV). As AUV is a typical nonlinear system, each degree of freedom is strongly coupled, so the traditional control method based on the nominal model of AUV cannot guarantee the accuracy of the control system. To solve this problem, we first propose a prediction model based on a radial basis function neural network (RBF‐NN). The nonlinearity of AUV is learned and modeled offline by RBF‐NN based on previous data. This model can reflect the time sequence state and control variables of AUV. Secondly, to avoid the overfitting problem in network training based on the traditional gradient descent method, a new adaptive chaotic sparrow search algorithm (ACSSA) is proposed to optimize the network parameters, to improve the full approximation ability of RBF‐NN to nonlinear systems. To eliminate the steady‐state error caused by external interference during AUV trajectory tracking, a nonlinear optimizer is designed by updating the deviation of the NN model output layer. In each sampling period, the predictive control law is calculated online according to the deviation between the predicted value and the actual value. In addition, the stability analysis based on the Lyapunov method proves the asymptotic stability of the controller. Finally, the 3‐D dynamic trajectory tracking the performance of AUV under different external disturbances is verified by MATLAB/Simulink, and the results show that the proposed controller is more efficient and robust than the standard model predictive controller (MPC) controller and the standard NN model predictive controller (NNPC).

Model predictive current control for maximum power point tracking of voltage source inverter based grid connected photovoltaic system

<p>Due to the high demand of grid connected photovoltaic systems, there is a need to track the maximum power point of the PV system. As the output of PV system is dc, there should be a converter, acting as medium between PV system and dc bus capacitor to track maximum power at all the loads. Usually boost converter is acting as medium between PV system and dc link capacitor as the duty cycle of the insulated-gate bipolar transistor in boost converter is in between 0 to 1 for maximum loads during maximum power point tracking (MPPT). To make PV system stable, the balance point is dc bus. If the dc bus voltage is constant, the system will be stable. Then the transfer power will just depend on current. For this purpose, the active current reference signal is to be generated by setting up the reference voltage across dc bus. Here to generate active reference current, PI controller is used and the reference voltage is taken according to the peak voltage of the inverter output voltage. The proposed control strategy was evaluated on a three-phase inverter linked to the grid and supplied by the PV system, which is working under varying irradiation conditions.</p>

Model-Based Predictive Control and Reinforcement Learning for Planning Vehicle-Parking Trajectories for Vertical Parking Spaces.

This paper proposes a vehicle-parking trajectory planning method that addresses the issues of a long trajectory planning time and difficult training convergence during automatic parking. The process involves two stages: finding a parking space and parking planning. The first stage uses model predictive control (MPC) for trajectory tracking from the initial position of the vehicle to the starting point of the parking operation. The second stage employs the proximal policy optimization (PPO) algorithm to transform the parking behavior into a reinforcement learning process. A four-dimensional reward function is set to evaluate the strategy based on a formal reward, guiding the adjustment of neural network parameters and reducing the exploration of invalid actions. Finally, a simulation environment is built for the parking scene, and a network framework is designed. The proposed method is compared with the deep deterministic policy gradient and double-delay deep deterministic policy gradient algorithms in the same scene. Results confirm that the MPC controller accurately performs trajectory-tracking control with minimal steering wheel angle changes and smooth, continuous movement. The PPO-based reinforcement learning method achieves shorter learning times, totaling only 30% and 37.5% of the deep deterministic policy gradient (DDPG) and twin-delayed deep deterministic policy gradient (TD3), and the number of iterations to reach convergence for the PPO algorithm with the introduction of the four-dimensional evaluation metrics is 75% and 68% shorter compared to the DDPG and TD3 algorithms, respectively. This study demonstrates the effectiveness of the proposed method in addressing a slow convergence and long training times in parking trajectory planning, improving parking timeliness.

Tracking model predictive control and moving horizon estimation design of distributed parameter pipeline systems

This manuscript proposes moving horizon control and state/parameter estimation designs for pipeline networks modelled by partial differential equations (PDEs) with boundary actuation. The spatial–temporal pressure and velocity dynamics within the pipelines are described by a system of six coupled one-dimensional first-order nonlinear hyperbolic PDEs. To address the discrete-time modelling challenge and preserve the infinite-dimensional nature of the pipeline system, the Cayley–Tustin transformation is deployed for model time discretization without any spatial discretization or model reduction. Considering the lack of full state information across the entire pipeline manifold, unknown states and uncertain parameters are estimated using moving horizon estimation (MHE). Based on the estimated states and parameters, a tracking model predictive control (MPC) strategy for the discrete-time infinite-dimensional pipeline system is proposed, which enables specific operation while ensuring physical constraint satisfaction. The effectiveness of the proposed controller and estimator designs is demonstrated via numerical examples.

Research on the Model Predictive Trajectory Tracking Control of Unmanned Ground Tracked Vehicles

This article summarizes the research significance and the development status of the unmanned ground tracked vehicles (UGTVs). According to the speed and steering principle of the UGTVs in plane motion, the kinematic state space equation of the vehicle is established. Based on the model predictive control (MPC), the UGTVs trajectory tracking controller is also established. After introducing the overall control system solution, based on the vehicle model, the track speed on both sides is used as the control input to solve the predicted output of the system. After constraining the control amount, the model prediction controller is established by using S function. Several simulations with different preset speeds are performed under linear conditions, and the numerical simulation with different prediction time domains and control time domains are performed under continuous curves. The test validates the effectiveness of the controller, and the effects of speed and time domain parameters on the deviation are analyzed based on the results. Based on satellite positioning technology, trajectory tracking tests of the UGTVs are carried out. After analyzing the positioning principle and common errors, the real-time kinematic technology is used to improve the positioning accuracy of the vehicle prototype. The hardware of the test platform includes a data acquisition system, a control execution system and a walking execution system, and the software part includes data processing and optimization control. The trajectory tracking experiments under different driving conditions are conducted, and the results show that the navigation tracking system can achieve good tracking performance.

Robust nonlinear MPC without terminal constraint for tracking changing setpoints in the presence of non‐additive unknown disturbance

AbstractThis paper develops a novel robust tracking model predictive control (MPC) without terminal constraint for discrete‐time nonlinear systems capable to deal with changing setpoints and unknown non‐additive bounded disturbances. The MPC scheme without terminal constraint avoids difficult computations for the terminal region and is thus simpler to design and implement. However, the existence of disturbances and/or sudden changes in a setpoint may lead to feasibility and stability issues in this method. In contrast to previous works that considered changing setpoints and/or additive slowly varying disturbance, the proposed method is able to deal with changing setpoints and non‐additive non‐slowly varying disturbance. The key idea is the addition of tightened input and state (tracking error) constraints as new constraints to the tracking MPC scheme without terminal constraints based on artificial references. In the proposed method, the optimal tracking error converges asymptotically to the invariant set for tracking, and the perturbed system tracking error remains in a variable size tube around the optimal tracking error. Closed‐loop input‐to‐state stability and recursive feasibility of the optimization problem for any piece‐wise constant setpoint and non‐additive disturbance are guaranteed by tightening input and state constraints as well as weighting the terminal cost function by an appropriate stabilizing weighting factor. The simulation results of the satellite attitude control system are provided to demonstrate the efficiency of the proposed predictive controller.

Additive-state-decomposition-based model predictive tracking control for PMSM servo system with multiple disturbances

This paper presents an additive-state-decomposition-based model predictive tracking control and disturbance rejection method for a permanent magnet synchronous motor (PMSM) servo system subject to unknown parameter perturbations, unmodeled dynamics, and time-varying load torque. The basic idea of this method is to equivalently decompose the original system into a primary system for handling the tracking control subproblem and a secondary system for dealing with the robust stabilization subproblem. A model predictive controller is designed for the primary system to achieve high-accuracy tracking of the reference speed. As for the secondary system, a novel high-order generalized extended state observer (HGESO) is constructed to estimate the multiple disturbances simultaneously, and a state feedback control law incorporating a disturbance compensator is developed to eliminate the adverse effect of the multiple disturbances on the system output. By combining the control inputs of the two subsystems together, the control objectives of the original system can be achieved. Both the stability criterion and design procedure of the closed-loop control system are developed. Finally, hardware-in-the-loop-based comparative experiments are conducted to demonstrate that the proposed method effectively suppresses the influence of the multiple disturbances on motor speed tracking accuracy and that the control system has both satisfactory dynamic performance and robustness.

Model Predictive Energy-Maximising Tracking Control for a Wavestar-Prototype Wave Energy Converter

To date, one of the main challenges in the wave energy field is to achieve energy-maximizing control in order to reduce the levelized cost of energy (LCOE). This paper presents a model predictive velocity tracking control method based on a hierarchical structure for a Wavestar-like deivce in the WEC-SIM benchmark. The first part of the system structure aims to estimate the wave excitation moment (WEM) by using a Kalman filter. Then, an extended Kalman filter (EKF) is chosen to obtain the amplitude and angular frequency of the WEM in order to compute the reference velocity. Following this, a low-level model predictive control (MPC) method is designed to ensure the wave energy converter (WEC) tracks the optimal reference velocity for maximum energy extraction from irregular waves. Two Gaussian Process (GP) models are considered to predict the future wave excitation moment and future reference velocity, which are needed in MPC design. The proposed strategy can give a new vision for energy-maximizing tracking control based on MPC.

Distributed robust model predictive control-based formation-containment tracking control for autonomous underwater vehicles

The autonomous underwater vehicle (AUV) formation may be carried out in a complex maritime environment. The formation-containment tracking problem is faced with challenges due to limited input saturation and maritime safety constraints. Based on communication-measurement union, a navigation control integration framework is proposed to solve the poor observability of underwater acoustic communication interactions. Moreover, a control protocol based on distributed robust model predictive control is designed to efficiently coordinate cooperation between AUVs. With the proof of the Lyapunov theory, the proposed control method can achieve formation-containment tracking even in the presence of external disturbances. Finally, a 7-AUV formation-containment tracking numerical simulation is designed to verify the effectiveness of the proposed method.

Model Predictive Trajectory Tracking Control of 2 DoFs SCARA Robot under External Force Acting to the Tip along the Trajectory

The robot arms often follow a certain trajectory depending on the type of end effector with functions of spray-painting, arc welding, bonding or machining etc. Therefore, trajectory-tracking control is a very important issue in robot arm applications. Also, the robot must be able to follow the determined trajectory stably under the influence of external forces or machining forces it encounters in its operations. In this study, a Model Predictive Control (MPC) for trajectory tracking control of a 2 Degrees of Freedom (DoFs) Selective Compliant Assembly Robot Arm (SCARA) under an external force acting to the tip of the robot along the trajectory was performed. The effectiveness of the MPC method used has been demonstrated by simulation applications. According to simulation studies, successful results were obtained.

Robust adaptive tube tracking model predictive control for piece‐wise constant reference signals

AbstractRobust tracking of piece‐wise constant reference signals for constrained systems with parametric plant uncertainty and additive disturbances is addressed in this paper. The parametric uncertainty is decreased online by set‐membership estimation and a nominal model is updated for improving set‐point tracking. The online estimated parametric uncertainty is used for an online‐determined terminal set which enlarges the set of reachable references close to the system constraints when compared to an offline worst‐case consideration. An artificial target state is introduced which can deviate from the nominal target state. This new target state is used to ensure recursive feasibility for unreachable references and changes in the reference signal. Moreover, a novel “recovery mode” is specified which is deployed in case the new nominal model yields an infeasible control problem. Control algorithms are developed for time‐invariant systems and systems with arbitrarily fast changing plants but known relative bounds. Constraint satisfaction and ‐stability are guaranteed for the proposed algorithms. Controlling the engine load of a self‐propelled work machine is used as a practical example.

Integrated path tracking control based on the dimension reduction model for improving real-time performance

In limit conditions, autonomous vehicles face the risk of lateral instability. The integrated control of steering and braking, an important measure for improving the stability of autonomous vehicles, has been extensively studied. A novel steering and braking integrated model predictive path tracking control (PTC) based on a dimension reduction model is proposed in this study. This method aims at the dilemma of the real-time limitation of the current integrated model predictive PTC based on nonlinear vehicle dynamics in practical applications and the unsatisfactory control effect of the integrated model predictive PTC based on the linearised vehicle dynamics in limit conditions. The core concept of this study is to reduce the input dimension of the integrated controller model by designing a model dimension reduction method, thereby reducing the decision variables of the optimisation problem and improving the real-time performance. The model dimension reduction method is designed based on the optimal utilisation of tire force to ensure the control performance of the proposed integrated control method in limit conditions. The integrated control method based on the dimension reduction model is compared with several existing integrated control methods in limit conditions to demonstrate its validity and superiority. The simulation tests with Simulink and CarSim indicate that the proposed method can reduce the calculation time by more than 40 % on the premise of ensuring path tracking accuracy and vehicle stability in limit conditions. Moreover, the hardware-in-the-loop tests prove the practicability of the presented method.

Collision-Free Model Predictive Trajectory Tracking Control for UAVs in Obstacle Environment

In this paper, we propose a collision-free model predictive trajectory tracking control algorithm for unmanned aerial vehicles (UAVs) in environments with both static obstacles and dynamic obstacles. Collision avoidance is ensured by obtaining outer polyhedral approximations of each interval of the dynamic obstacles trajectories based on MINVO basis, and then optimizing a plane to separate the polyhedra and the trajectory of the UAV. By incorporating the resulting computationally efficient collisionfree constraints and divers physical constraints, a model predictive control (MPC) optimization problem is formulated with a tailored terminal constraint set, which can be solved by a standard nonlinear programming solver. Moreover, the control theoretic properties are established, including recursive feasibility, the guarantee of collision avoidance, as well as closed-loop stability. Finally, the efficacy of the proposed algorithm is successfully evaluated by a simulation in a multi-obstacle environment.