Tracking Control Design Research Articles

Event-triggered fuzzy adaptive control for a class of MIMO discrete-time nonlinear systems with uncertain control gains

ABSTRACT An event-triggered output control technique is devised for the output anticipated trajectory tracking controller design problem for a class of unknown multiple-input-multiple-output (MIMO) discrete-time nonlinear systems. A parameterized state observer is established to estimate the non-measurable states accurately by utilizing the filter states and the gradient-based fuzzy parameter updated laws. A series of fuzzy filters are proposed to evaluate the immeasurable states, and a filter state observer is constructed to overcome the state estimation that is triggered by the unknown control gains and the coupling of control input. One non-zero parameter is added to a fuzzy logic system (FLS) to reduce the computed burden of the controller with several updating laws. A FLS with one non-zero parameter is introduced to reduce the calculated burden of the controller with fewer updating laws. The proposed method reduces the computed burden and communication consumption while realizing the immeasurable state estimations, guaranteeing the ultimately uniformly bounded (UUB) of the closed-loop system, and achieving a good tracking impact. Finally, simulation analyses are used as a numerical example to confirm that the proposed control strategy is valid.

Control Design and Implementation of Autonomous Robotic Lawnmower

This paper presents the trajectory tracking control design and implementation of feedback linearization (FL) and robust feedback linearization (RFL), applicable to a robotic lawnmower with four mecanum driving wheels. The RFL control design additionally includes a robust control law. These two nonlinear control laws are developed to enable the controlled robotic lawnmower to accurately follow any specified trajectory. The simulation outcomes illustrate that the suggested control law based on RFL displays superior trajectory tracking accuracy and resilience compared to the FL control method in the case of a robotic lawnmower operating under demanding conditions. These conditions encompass environmental disturbances and uncertainties in modeling. The RFL control method also exhibits lower energy consumption compared to the FL control method. Finally, using the RFL controller derived from this study, the error in trajectory tracking in computer simulations and the actual mowing performance have demonstrated outstanding results.

Filter‐Based Average Dwell‐Time Tuning Approach for Adaptive Prescribed‐Time Tracking of Uncertain Switched Nonlinear Systems

ABSTRACTThis paper addresses neural‐network‐based adaptive prescribed‐time (PT) tracking for uncertain switched systems with unmatched nonlinearities. A continuously switched adaptive tuning mechanism for neural network learning is developed by applying the average dwell time (ADT). First, a neural‐network‐based PT tracking control design strategy using the ADT‐based adaptive tuning mechanism is established for switched nonlinear systems in strict‐feedback form. A novel adaptive dynamic surface controller is designed recursively using a practical finite‐time scaling function and continuously switched tuning parameters. The switched adaptive tuning laws for neural networks are structured to reduce the conservatism associated with common adaptive laws. Then, a filter‐based tuning approach is employed to ensure the continuity of switched adaptive parameters with ADT in the designed controller. The practical PT stability of the closed‐loop system is demonstrated based on the boundedness of the adaptive parameters. Building upon this foundation, the proposed PT design approach is extended to control switched pure‐feedback nonlinear systems, even in cases where control directions are unspecified. The unknown sign problem encountered with switched virtual and actual control coefficient functions is resolved in the PT control framework. It is shown that the PT performance bound of the tracking error can be reduced by selecting the design parameter of the scaling function. Finally, simulation results illustrate the merits of the proposed theoretical approach.

Particle Swarm Optimization Algorithm Based Fuzzy PID Controller Design for Speed Tracking Control of Separately Excited DC Motor

Particle Swarm Optimization Algorithm Based Fuzzy <scp>PID</scp> Controller Design for Speed Tracking Control of Separately Excited <scp>DC</scp> Motor

Optimization design of unmanned mining truck path tracking controller based on road adhesion coefficient estimation

Abstract In response to the issues of inaccurate tracking precision caused by continuous turning and variable road adhesion coefficients on complex roads in mining areas for unmanned mining trucks, this paper adopts unscented Kalman filter (UKF) to estimate the road adhesion coefficient. Based on this, an adaptive preview feedforward linear quadratic regulator (LQR) control algorithm is designed using genetic algorithm, feedforward control, and linear quadratic optimal path tracking control methods. Firstly, a nine degree of freedom vehicle dynamics model and a two degree of freedom vehicle lateral dynamics model are established, and the Dugoff model to calculate tire forces is introduced; secondly, utilizing UKF to estimate the road adhesion coefficient, and leveraging active disturbance rejection control for rapid tracking of road curvature, an optimized design of the LQR controller is carried out. Then, the effectiveness of the designed controller was verified through Trucksim/Simulink joint simulation testing. Finally, the hardware in the loop test results showed that the designed controller had good tracking accuracy and strong adaptability in complex road and special working conditions in mining areas.

Tracking Control Design for a Bilinear Control System With Unstable and Uncertain Internal Dynamics Using Adaptive Backstepping

Tracking Control Design for a Bilinear Control System With Unstable and Uncertain Internal Dynamics Using Adaptive Backstepping

Lyapunov-based robust model predictive tracking controller design for discrete-time linear systems with ellipsoidal terminal constraint

In this article, a robust model predictive control (MPC) method is introduced based on Lyapunov-theory to control the discrete-time uncertain linear systems due to external disturbances. The structure of the proposed controller consists of two parts designed based on the offline/online schemes. In the offline-scheme, an H ∞ -based robust tracking controller is provided to satisfy the robust and tracking performance. Based on the H ∞ performance, a new linear matrix inequality problem is developed to calculate the offline-controller gains. By considering the Lyapunov-function of the offline-controller as the terminal cost of the MPC and the designed offline-controller, the online optimisation problem (OOP) is structured. This means, the MPC is designed based on the stabilised system to satisfy the physical limitations of the overall controller and the system states. Moreover, to improve the feasibility problem of the OOP, an ellipsoidal terminal constraint is added to the proposed MPC problem. Therefore, compared with the existing min–max MPC and tube MPC, the advantages of the overall controller are feasibility improvement and reducing the computational complexity with less conservatism while the robustness against parametric uncertainties and disturbances is achieved. Two simulation examples are employed to show the superiorities of the proposed robust MPC.

Observer-Based Finite-Time Prescribed Performance Sliding Mode Control of Dual-Motor Joints-Driven Robotic Manipulators with Uncertainties and Disturbances

Considering system uncertainties (e.g., gear backlash, unmodeled dynamics, nonlinear friction and parameters perturbation) coupling disturbances weaken the motion performance of robotic systems, an observer-based finite-time prescribed performance sliding mode control with faster reaching law is proposed for robotic manipulators equipped with dual-motor joints (DMJs). In the case where the backlash information is completely unknown, the backlash is maximally eliminated using a simple but efficient dual-motor adaptive anti-backlash strategy. Thus, the design of position tracking controllers for DMJs can be simplified. Then, to deal with the influence of disturbances and residual uncertainties (excluding backlash), a novel finite-time adaptive sliding mode disturbance observer (ASMDO) is proposed to practically estimate the lumped uncertainties where their upper bounds are assumed to be unknown. Finally, a finite-time composite fast non-singular terminal sliding mode (TSM) controller, integrated with the prescribed performance principle, is proposed in this paper. To enhance the convergence rate, a novel TSM-type reaching law has been developed. The controller ensures that the tracking error is not only stabilized within a finite-time convergence rate but also adheres to a predefined maximum transient-steady-state error. The proposed scheme is implemented through simulation and experimental results, demonstrating its superior performance.

Polynomial Iterative Learning Control (ILC) Tracking Control Design for Uncertain Repetitive Continuous-Time Linear Systems Applied to an Active Suspension of a Car Seat

Polynomial Iterative Learning Control (ILC) Tracking Control Design for Uncertain Repetitive Continuous-Time Linear Systems Applied to an Active Suspension of a Car Seat

Barrier Lyapunov Function-based Backstepping Controller Design for Path Tracking of Autonomous Vehicles

This research proposes a novel BLF-based backstepping controller for path tracking of Autonomous Vehicles (AVs) with unknown dynamics and unmeasurable states. The proposed framework includes: (1) forming geometric-dynamic model of the vehicle by combining the dynamics of the vehicle with the kinematics of the visual measurement system, (2) designing a fixed-time Extended-State Observer (ESO) to estimate the unknown dynamics and unmeasurable states, and (3) introducing a BLF-based controller for faster response and more accurate path tracking compared to previous BLF-based controllers. Besides the novelty of the BLF-based controller, by transforming the closed-loop error dynamics into a unified proportional-derivative (PD)-type structure, an intuitive criterion is proposed to provide a systematic procedure for comparing BLF-based controllers. A combined BLF is further proposed based on this performance criterion to eliminate the sensitivity of BLF-based controllers to the magnitude of the constraint. The stability analysis is performed for the fixed-time ESO and the closed-loop control system. MATLAB/CarSim co-simulation is conducted to evaluate the performance of the proposed control system. The outcomes of the work show that the closed-loop control system is exponentially stable. In addition, it can provide a faster response and result in more accurate path tracking compared to previous BLF-based control systems.

Design of an observer-based anti-disturbance speed tracking controller for integrated motor-transmission systems under uncertain parameters and road slope variation

Design of an observer-based anti-disturbance speed tracking controller for integrated motor-transmission systems under uncertain parameters and road slope variation

Multi-stage trajectory tracking control design under comprehensive constraints based on Generalized Udwadia–Kalaba theory

A novel control design based on Generalized Udwadia–Kalaba (GUK) theory is proposed to achieve the trajectory tracking under comprehensive constraints in this paper. To describe the complex task requirements, a constraint framework including equality and inequality constraints is constructed. Thus, the complex trajectory tracking problem is converted into a constraint-following problem. Based on the framework above, GUK equation is introduced to consider the equality and inequality constraints individually. Specifically, the equality constraints are transformed into second-order matrix form, while the inequality constraints are addressed via a diffeomorphism. Then, a novel control method including servo control term and high-order control term is proposed. Through these two control terms, the constraint forces for equality and inequality can be solved separately. The effectiveness of this control method is verified by the stability analysis based on Lyapunov minimax apprach and illustrative application of unmanned surface vehicle (USV). Meanwhile, the superiority of this method is demonstrated through a comparative analysis with Udwadia–Kalaba (UK) method, Linear Quadratic Regulator (LQR) method and sliding mode control (SMC) method.

Development of an Anti-rollover Warning and Active Intervention Controller for Wheeled Tractor

Background: Tractor rollover accidents are the most severe problem in agricultural production. According to the statistical analysis of the rollover incidents, some rollover accidents can be avoided by timely anti-rollover warning and active control. There are a few researches on the anti-rollover control for agricultural tractors, although great progress in the research on tractor security has been achieved, such as rollover protective structure design. Objective: The purpose of this patent study was to develop a controller with the function of warning as well as active anti-rollover control employing the power motor installed on the steering column to adjust the front wheel angle and control the rollover index within the safety range. Methodology: The structure block for the hardware of the controller was devised that included data obtaining, rollover risk estimation, rollover warning, and front-wheel steering control sections. The main circuits have been designed in detail by adopting module methods, such as motor control circuit, positioning and transmission circuit, etc. The control scheme has been demonstrated by designing an overview of the overall architecture, including rollover indicator calculation, load transfer ratio (LTR) controller design, and front-wheel steering angle tracking controller design. C language has been used to accomplish the software design. Results: The active anti-rollover controller can calculate and keep the LTR within the stable range by adjusting the front wheel angle in real-time. The fast response and smoothness of the results demonstrate that the controller can fulfill the designed function. Conclusion: The developed controller can meet the control requirement due to several advantageous aspects, such as reliability, effectiveness, and practicability. It is prospective for the developed controller to provide a valuable reference to reduce tractor rollover accidents.

Fault reconstruction‐based robust tracking control design for periodic piecewise polynomial systems with disturbances

AbstractIn this article, we address the topics of fault reconstruction and robust fault‐tolerant tracking control for periodic piecewise polynomial uncertain systems with time‐varying delays, faults and external disturbances. In detail, the periodic piecewise polynomial learning observer system is configured with the intent to concurrently reconstruct the faults and immeasurable states of the system that is being considered. Precisely, the key intent of this study centers around in devising a robust fault‐tolerant tracking control to achieve the tracking performance of the system as intended with mixed and passivity performance. To this end, a robust fault‐tolerant tracking control is designed by incorporating the reconstructed faults and error feedback, which aids in vouching for the outcomes that were desired. Besides, by building the periodic piecewise polynomial Lyapunov–Krasovskii functional and making use of the matrix polynomial lemma and Wirtinger's inequality, certain adequate conditions are procured in the frame of linear matrix inequalities. Subsequently, the required gain values for the devised controller and the configured observer are found by using the established linear matrix inequalities. Ultimately, in order to attest the controller's intrinsic potential and relevance, numerical example along with the simulation results is supplied.

Path Tracking Controller Design of Automated Parking Systems via NMPC with an Instructible Solution

Parking difficulties have become a social issue that people have to solve. Automated parking system is practicable for quick par operations without a driver which can also greatly reduces the probability of parking accidents. The paper proposes a Lyapunov-based nonlinear model predictive controller embedding an instructable solution which is generated by the modified rear-wheel feedback method (RF-LNMPC) in order to improve the overall path tracking accuracy in parking conditions. Firstly, A discrete-time RF-LNMPC considering the position and attitude of the parking vehicle is proposed to increase the success rate of automated parking effectively. Secondly, the RF-LNMPC problem with a multi-objective cost function is solved by the Interior-Point Optimization, of which the iterative initial values are described as the instructable solutions calculated by combining modified rear-wheel feedback to improve the performance of local optimal solution. Thirdly, the details on the computation of the terminal constraint and terminal cost for the linear time-varying case is presented. The closed-loop stability is verified via Lyapunov techniques by considering the terminal constraint and terminal cost theoretically. Finally, the proposed RF-LNMPC is implemented on a self-driving Lincoln MKZ platform and the experiment results have shown improved performance in parallel and vertical parking conditions. The Monte Carlo analysis also demonstrates good stability and repeatability of the proposed method which can be applied in practical use in the near future.

Non-fragile tracking controller design for fractional order systems against active disturbance rejection

Non-fragile tracking controller design for fractional order systems against active disturbance rejection

RL-based adaptive control for a class of non-affine uncertain stochastic systems with mismatched disturbances

This paper investigates the reinforcement learning (RL) adaptive tracking control design problem for a class of mismatched stochastic nonlinear systems with non-affine structure. The stochastic system studied in this paper is more generally representative due to the presence of non-affine inputs, internal uncertainties, and mismatched external disturbances. Firstly, in order to solve the non-affine structure of stochastic systems, an extended stochastic differential equation is constructed. Based on the actor–critic framework, by generating reinforcement signals, the network is stimulated to evolve more quickly towards the desired direction, while compensating internal uncertainties and induced uncertainties in the stochastic system. Furthermore, aiming at the approximation errors and external disturbances, while satisfying stochastic stability, the adaptive laws for disturbances boundary estimator are established with the usage of higher powers of tracking errors. As a result, a novel non-affine adaptive tracking controller has been proposed by integrating RL, disturbances boundary estimation, and dynamic surface method. Through the stability analysis, it is proved that all closed-loop signals are bounded in probability, and the system output converges to a small neighborhood near the desired trajectory. Numerical simulations demonstrate the effectiveness and superiority of the proposed controller.

Event-triggered learning-based robust tracking control for robotic manipulators with uncertain dynamics and non-zero equilibrium

This paper presents a novel optimal tracking control method for robotic manipulators (RMs) with system uncertainties and non-zero equilibrium points. The existing tracking control methods typically require the precise system dynamics and assume the existence of a zero equilibrium point, which may not always be true in practice. To overcome this issue, a new cost function with respect to the first derivative of system states and a known upper bound on the system’s mismatched disturbances is designed, and then an optimal control problem of RMs is formulated. Furthermore, to solve this optimization, an event-triggered critic learning control framework is proposed to estimate the solution of Hamilton–Jacobi–Bellman equation, reducing the computational burden. In the critic learning control designs, novel weight updating laws related to system stability information are proposed to train the critic neural networks, which eliminates the initial stabilization requirement. Theoretical analysis shows that the stability of the closed-loop system in the sense of uniform ultimate boundedness is ensured. It should be emphasized that the proposed control method offers a simplification of the tracking controller design process and removes the restriction on system dynamics. Finally, simulation results are given to demonstrate the effectiveness of the proposed method.

Neural Robust Control for a Mobile Agent Leader–Follower System

A controller employing a combined new strategy of output feedback linearization and a recurrent high-order neural network (RHONN) adaptive approach for a mobile agent leader–follower system is presented. The controller structure is based on feedback linearization; then, a scheme of lumping uncertainties which are estimated via the RHONN is incorporated; with this estimate, the controller is able to produce a robust control action for mobile agents so they track a prescribed reference trajectory. Moreover, the nonlinear system part is transformed into a linearizable one; then, a specific function lumps all the nonlinearities, uncertain parameters, and unmodeled dynamics of the system; this overall function is estimated via the RHONN. Thus, both parametric uncertainties and unmodeled dynamics between agents can be compensated via the controller, and, subsequently, follower agents track the reference provided by the leader. The obtained controller is such that the estimation scheme is not based on high-gain controllers. Here, it is underlined that the main contribution consists of designing a nonlinear controller and combining it with an RHONN to estimate the nonlinear uncertainties in the leader–follower system. This control action includes robust features provided by the online recurrence and the nonlinear base of the neural network in which not general but specific parametric disturbances and unmodeled discrepancies are identified or compensated. For this control scheme, only nominal values of the system parameters are required, as well as the velocities of the agents. Numeric simulation of the model and designed tracking control are carried out in which the control law is applied to a two-wheeled differential mobile robot model, obtaining satisfactory results for tracking angular velocities of the wheels.

Improved Model Predictive Control Path Tracking Approach Based on Online Updated Algorithm with Fuzzy Control and Variable Prediction Time Domain for Autonomous Vehicles

The design of trajectory tracking controllers for smart driving cars still faces problems, such as uncertain parameters and it being time-consuming. To improve the tracking performance of the trajectory tracking controller and reduce the computation of the controller, this paper proposes an improved model predictive control (MPC) method based on fuzzy control and an online update algorithm. First, a vehicle dynamics model is constructed and a feedforward MPC controller is designed; second, a real-time updating method of the time domain parameters is proposed to replace the previous method of empirically selecting the time domain parameters; lastly, a fuzzy controller is proposed for the real-time adjustment of the weight coefficient matrix of the model predictive controller according to the lateral and heading errors of the vehicle, and a state matrix-based cosine similarity updating mechanism is developed for determining the updating nodes of the state matrix to reduce the controller computation caused by the continuous updating of the state matrix when the longitudinal vehicle speed changes. Finally, the controller is compared with the traditional model prediction controller through the co-simulation of CARSIM and MATLAB/Simulink, and the results show that the controller has great improvement in terms of tracking accuracy and controller computational load.