Tracking Control Of Nonlinear Systems Research Articles

Data-driven Tracking Control of Nonlinear Systems under Deception Attacks and Packet Loss

Data-driven Tracking Control of Nonlinear Systems under Deception Attacks and Packet Loss

Dynamic Event-Triggered Adaptive Fixed-Time Practical Tracking Control for Nonlinear Systems Through Funnel Function

Dynamic Event-Triggered Adaptive Fixed-Time Practical Tracking Control for Nonlinear Systems Through Funnel Function

Backstepping-Based Tracking Control of Nonlinear Systems With Concurrent State-Triggering Mechanism

Backstepping-Based Tracking Control of Nonlinear Systems With Concurrent State-Triggering Mechanism

Safe Tracking Control of Nonlinear Systems Based on Optimal Control for Low-Fidelity Models

Safe Tracking Control of Nonlinear Systems Based on Optimal Control for Low-Fidelity Models

Event‐triggered adaptive tracking control for nonlinear systems with input saturation and unknown control directions

AbstractThis article is concerned with event‐triggered adaptive tracking control design of strict‐feedback nonlinear systems, which are subject to input saturation and unknown control directions. In the design procedure, a smooth nonlinear function is employed to approximate the saturation function so that the controller can be designed under the framework of backstepping. The Nussbaum gain technique is employed to address the issue of the unknown control directions. A predetermined time convergent performance function and a nonlinear mapping technique are introduced to guarantee that the tracking error can converge in the predetermined time with a fast convergence rate and a high accuracy. Then the event‐triggered adaptive prescribed performance tracking control strategy is proposed, which not only ensures the boundedness of all the closed‐loop signals and the convergence of tracking error but also reduces the communication burden from the controller to the actuator. At last, the simulation study further tests the availability of the proposed control strategy.

Adaptive Output Feedback Tracking Control for Nonlinear Systems with Unknown Growth Rate

Article Adaptive Output Feedback Tracking Control for Nonlinear Systems with Unknown Growth Rate Manman Yuan 1,2,*, and Wei Qian 1,2,* 1 School of Electrical Engineering and Automation, Henan Polytechnic University, Jiaozuo 454003, China 2 Henan Key Laboratory of Intelligent Detection and Control of Coal Mine Equipment, Jiaozuo 454003, China * Correspondence: ymmamhappy@163.com; qwei@hpu.edu.cn Received: 4 September 2023 Accepted: 7 November 2023 Abstract: In this paper, the problem of adaptive output feedback tracking is considered for a class of nonlinear systems with lower-triangular structures. A novel dynamic gain is introduced to deal with the unknown growth rate. By coupling the dynamic gain with the observer and the controller, an adaptive output tracking controller is developed, which can guarantee that all signals of the closed-loop system are globally bounded. Finally, the effectiveness of the presented control scheme is illustrated by a numerical example.

Fault-tolerant tracking control for nonlinear systems with multiplicative actuator faults in view of zero-sum differential games

In view of zero-sum differential games, this paper addresses the fault-tolerant tracking control (FTTC) problem for nonlinear systems with multiplicative actuator faults. By augmenting the nominal system, the trajectory tracking problem is transformed into an optimal regulation problem. A fault observer is designed to estimate the multiplicative actuator fault factor. In order to better reflect system performance, a comprehensive performance index function including the trajectory tracking error, the control input, and the multiplicative actuator fault is constructed. By considering the control input and the multiplicative actuator fault as two players in the zero-sum differential game (ZSDG), the FTTC problem is thus transformed into a ZSDG problem. Then, a fault-tolerant control based on ZSDG is designed by solving the Hamilton–Jacobi-Isaacs (HJI) equation. Since the HJI equation is difficult to solve, a critic neural network is constructed to obtain its approximation, which constitutes the Nash equilibrium of the ZSDG. The closed-loop faulty system is guaranteed to be uniformly ultimately bounded via the Lyapunov’s direct method. The effectiveness of the developed FTTC method is demonstrated by two simulation examples.

Event-based adaptive fuzzy tracking control for nonlinear systems with input magnitude and rate saturations

In this paper, an event-based adaptive fuzzy tracking control strategy for a class of uncertain nonlinear systems with limited control input and its rate of change is proposed. The unknown nonlinear function of the considered system is approximated by a fuzzy logic system (FLS). Furthermore, an event-triggered control method is developed to save the computing resources, in which the controller parameters are adaptively adjusted by a fuzzy controller. Moreover, it is proved by designing the Lyapunov function that the event-based controller can ensure that all signals of the controlled system are bounded. In addition, the tracking error can converge to a preset domain. Meanwhile, two practical simulations are given to demonstrate the effectiveness of the proposed method.

Prescribed-time adaptive output feedback tracking control for nonlinear systems with quantized input

This study concentrates on the prescribed-time output feedback tracking problem for nonlinear systems with unknown control gains and quantized input. A modified observer with the first-order scale function handles the unmeasurable problem of states while achieving accurate observation in the prescribed time. A simple controller is constructed by a new function transformation in which the computation burden is greatly reduced. The resulting controller not only drives that tracking error converges to zero but also ensures that all signals in the closed-loop system are bounded. Finally, the effectiveness of the control scheme is demonstrated by a numerical simulation and a practical simulation.

Event-Triggered Prescribed-Time Tracking Control for Nonlinear Systems With Asynchronous Switching

Event-Triggered Prescribed-Time Tracking Control for Nonlinear Systems With Asynchronous Switching

Prescribed-time Tracking Control for Robotic Manipulator with Time-varying Output Constraints

This paper introduces prescribed-time tracking control of nonlinear systems for robotic manipulator under time-varying output constraints (TVOC). For the robotic manipulator driven by DC motor, we will design a controller to realize: one is to realize prescribed-time tracking control; the other is no violation of the time-varying output constraints (TVOC). First, sufficient conditions for prescribed-time tracking control for nonlinear systems with TVOC are presented. Secondly, relying on the backstepping technique, the recursive design algorithm is applied to construct the controller, which then realizes the prescribed-time tracking without the violation of TVOC. Finally, the applicability of this method in robot manipulator is verified by simulation.

Adaptive tracking control for nonlinear systems with uncertain control gains and its application to a TCP/AQM network

This paper is concerned with the adaptive tracking control problem for nonlinear systems with virtual control coefficients including known and unknown items. The known items are employed for controller design directly, such that more information is utilized to achieve better performance. To deal with the unknown items, a novel real control law is firstly constructed by introducing an auxiliary system. The proposed controller is designed and applied to an uncertain TCP/AQM network system, which guarantees the practical boundedness of all the signals in the closed-loop system. Finally, the effectiveness and practicability of the developed control strategy are validated by simulation results.

Adaptive critic learning for approximate optimal event-triggered tracking control of nonlinear systems with prescribed performances

This paper studies the approximate optimal event-triggered tracking control problem for a class of second-order nonlinear systems with prescribed performances. By employing a prescribed performances function, restrictions on tracking errors are removed for prescribed performances including convergence rate, maximum overshoot, and steady-state error. On this basis, a complex optimal tracking control problem can be transformed into an optimal stabilising control problem by constructing an augmented system. Subsequently, an event-triggered mechanism is introduced to reduce communication resources. Then, an adaptive critic learning algorithm is used to solve the Hamilton-Jacobi-Bellman equation, where the weights in the critic networks are tuned through the gradient descent approach and experience replay technology. Through the developed learning method, the persistence of excitation condition is released, and the data efficiency is improved. The Lyapunov stability theory is introduced to verify the stability of the close-loop system and the tracking errors are uniformly ultimately bounded. Finally, simulation results are presented to show the effectiveness of the proposed approach.

Adaptive Finite-Time Tracking Control of Nonlinear Systems With Dynamics Uncertainties

In this paper, the problem of adaptive backstepping finite-time tracking control is investigated for a class of strict-feedback nonlinear systems with unmodeled dynamics and dynamic disturbances. A modified finite-time dynamic signal is first introduced to dominate the dynamic disturbance. By using the adaptive control, backstepping technique, and finite-time stability theory, an adaptive finite-time tracking controller is developed. Under the proposed control scheme, the finite-time tracking performance and the boundedness property of all signals in the closed-loop system are ensured. Finally, simulation results check the effectiveness of the suggested approach.

Tracking control of nonlinear systems actuated by saturated oscillatory force generator

This research has been devoted to the construction of a permanent-stable algorithm for tracking control of a nonlinear 1-degree of freedom (DOF) mechanical system affected by a second-order vibratory constrained actuator. The dynamics of the actuator is involved in governing equation of the mechanical system, and using the two-step Adams-Bashforth and Adams-Moulton methods, the resultant continuous-time model is formulated in the discrete-time domain. The discrete-time model of the whole system is then employed in a discrete-time power reaching law-based controller architecture. Using the reaching law strategy and considering the saturation boundaries of the actuation system, various available bounds of position and velocity control signals can be determined with respect to the reaching law coefficients. Then, special optimization algorithms are employed to determine the optimal value of position and velocity power reaching law coefficients as well as the optimally modified trajectory references. The position and velocity control commands resulting from the concept of optimal trajectory reference, along with the optimal reaching law coefficient, ensure the permanent-stable tracking control of both position and velocity modes regarding the actuation constraint. In the next step, another concept, namely the optimal combined position-velocity controller, is taken into account, which is a Gaussian-weighted average of the position and velocity control commands to form the main control command of the proposed controller. Consequently, the designed controller will be a permanent-stable control approach that never violates the actuation constraint. Finally, numerical simulations are conducted to evaluate the performance of the proposed method for two types of desired inputs, including piecewise-step and harmonic trajectories. The results suggest the proposed controller efficiency in satisfying pre-determined characteristics.

Event-Triggered Tracking Control of Nonlinear Systems Under Sparse Attacks and its Application to Rigid Aircraft

This study is aimed at addressing the event-based state estimation and tracking control problems for a class of nonlinear systems, the output of which is measured by multiple sensors, but the adversary can manipulate nearly half of the measurements simultaneously. First, a sampled-data-based event-triggered strategy is developed to reduce unnecessary data transmissions under sparse sensor attacks, and the transmitted data are filtered by a data selector to obtain reliable data. Subsequently, an output-prediction-based continuous-discrete observer is improved so that it can estimate continuous-time system states from the event-triggered output, rather than being limited to time-triggered sampled output. Further, to design a tracking controller with the segmentally differentiable estimated states, a backstepping method incorporating tracking differentiators is proposed. Finally, the effectiveness of the proposed method is demonstrated by applying it in the simulation of a rigid aircraft.

Self-Triggered and State-Triggered Sampling Adaptive Fuzzy Design for Full State Constrained Nonlinear Systems

In this paper, the problems of state-triggered sampling and self-triggered tracking control for nonlinear systems with constraints are studied. Firstly, the fuzzy observer is designed for the unknown state. In the presence of state-triggered sampling error, the cooperative design of constraint controller is a key problem to be solved. The median value theorem provides help to solve this problem and an asymmetric state-triggering strategy is presented. In addition, it is proved that the closed-loop signals are input-to-state stable, and the sampling error and tracking error are bounded. Then, a general self-triggered tracking control scheme is presented. In order to compare the control performance of different triggering mechanisms, fuzzy observer and logarithmic barrier Lyapunov function are selected also, and the scheme is designed under the framework of backstepping method. Co-designing controllers and scheduling functions is a key issue, so that the physical implementation benefits from not requiring constant monitoring of the state. Finally, the effectiveness of the proposed method is verified by case study, and the control performance of different triggering mechanisms is compared.

Neuroadaptive Asymptotic Tracking Control of Nonlinear Systems with Multiple Uncertainties

In this work, several innovative robust neuroadaptive control algorithms are integrated via the command filtered backstepping approach for a class of mismatched uncertain nonlinear systems. They utilize neural network adaptive control to achieve an enhanced model compensation effect. In addition, different robust terms with a positive time-varying integral expression are synthesized for each of the algorithms to address external disturbances. Each of the synthesized control algorithms has a continuous control input and cannot only remove the adverse effects of the “explosion of complexity” inherent in the traditional backstepping technology but also produce an asymptotic tracking result for the closed-loop system via strict theoretical analysis. Comparative simulation verifications are implemented to check the feasibility and practicability of the presented controllers.

Predictor-Based Neural Dynamic Surface Control for Strict-Feedback Nonlinear Systems With Unknown Control Gains.

Neural dynamic surface control (NDSC) is an effective technique for the tracking control of nonlinear systems. The objective of this article is to improve closed-loop transient performance and reduce the number of learning parameters for a strict-feedback nonlinear system with unknown control gains. For this purpose, a predictor-based NDSC (PNDSC) approach is presented. It introduces Nussbaum functions and predictors into the traditional NDSC for nonlinear systems with unknown control gains. Unlike NDSC that uses surface errors to update the learning parameters of neural networks (NNs), the PNDSC employs prediction errors for the same purpose, leading to improved transient performance of closed-loop control systems. To reduce the number of learning parameters, the PNDSC is further embedded with the technique of the minimal number of learning parameters (MNLPs). This avoids the problem of the ``explosion of learning parameters'' as the order of the system increases. A Lyapunov-based stability analysis shows that all signals are bounded in the closed-loop systems under PNDSC embedded with MNLPs. Simulations are conducted to demonstrate the effectiveness of the PNDSC approach presented in this article.

Adaptive asymptotic tracking control for nonlinear systems with actuator fault and prescribed performance based on event‐triggered mechanism

AbstractIn this article, the event‐triggered adaptive neural networks tracking control problem for nonlinear systems with prescribed performance and actuator fault is investigated. Meanwhile, bias faults and loss of effectiveness in actuators are taken into consideration, and the effectiveness factor is unknown. In the process of controller design under the framework of backstepping technology, neural networks are implemented to model the unknown terms of systems, and the tracking error is limited to a predefined boundary by using an error transformation. To economize communication resources, an adaptive neural networks event‐triggered control (ETC) strategy is developed, which can ensure that all the closed‐loop signals are bounded, and the tracking error not only confines to a prescribed function but also asymptotically converges to zero. Finally, two simulation examples are presented to further confirm the effectiveness of the proposed control strategy.