Control Of Uncertain Nonlinear Systems Research Articles

Improved Command Filtered Backstepping Control for Uncertain Nonlinear Systems with Time-Delay

This paper presents an alternative method to solve the control problem of an uncertain nonlinear system in strict-feedback form with a time delay. Instead of using Lyapunov–Krasovskii functionals, ordinary Lyapunov functionals are used to design the controllers. In order to address the completely unknown uncertainties of the system, including the unmodeled dynamics, time-delay nonlinearities, and external disturbances, command filters are applied to reconstruct the estimations of such uncertainties, and the negative feedback of these estimations can be used to reduce the influence of such uncertainties on the system. With the help of the backstepping technique and the Lyapunov stability criterion, it is proved that the system output tracks the target signal with a small error, and contrastive simulation results verify our method’s effectiveness.

Adaptive fuzzy asymptotic predefined-time tracking control of uncertain nonlinear systems based on event-trigger

This paper proposes an event-triggered adaptive fuzzy asymptotic predefined-time controller for uncertain nonlinear systems (UNS) subject to external disturbances. By introducing a set of well-designed asymptotic performance adjustment (APA) functions, we establish a general framework for analyzing asymptotic predefined-time stability (APDTS). Under the control scheme based on the established framework, the system state is guaranteed to converge to a controllable area around zero within a user-defined time and eventually asymptotically converge to zero. Finally, numerical simulations of a robotic arm system verify the effectiveness and superiority of control approaches.

Neural network adaptive switched fault-tolerant control of uncertain nonlinear systems with full state constraints

This paper studies the neural network adaptive fault-tolerant control (NNAFTC) for a class of uncertain nonlinear systems with full state constraints. It is the first time to introduce switched adaptive fault compensation strategy for the controller design process. On the one hand, the proposed method overcomes the limitation needed to be given a prescribed local restriction region of the traditional state constraint schemes, such as log-type, tan-type and integral-type. On the other hand, the full-state constraint and switched fault-tolerant problem is effectively solved even if the existence of actuator failures. Concomitantly, the novel switched tuning functions, the NN approximation technique and the integral barrier Lyapunov functions (IBLF) are combined to construct the backstepping controllers and adaptation laws. It can be proved that all the closed-loop states are restricted in the proper compact sets for any given initial values. Finally, A simulation is shown to demonstrate the validity and advantages of the presented control approach.

Robust adaptive safety control of uncertain nonlinear systems and its application to differential robots

AbstractThis article focuses on the problem of robust adaptive safety control of a class of nonlinear systems with parametric uncertainties. Two novel definitions, that is, robust adaptive control Lyapunov function (RACLF) and robust adaptive control barrier function (RACBF) are introduced in this article. Also, an estimation of unknown parameters is obtained based on multiple identification models, state predictors and a logic switching mechanism. The switching mechanism plays a vital role in enhancing the transient properties of nonlinear systems. Meanwhile, a safe motion framework for differential robots is provided based on the existence of parametric uncertainties in RACLF and RACBF, and a safe and stable controller is obtained by solving quadratic programming. Finally, simulation results of differential robot capable of safe motion in space are presented to verify the validity of the design method.

Adaptive fixed-time PID-based control of uncertain nonlinear systems and its application to unmanned surface vehicles

This article shows that the PID control, applied in linear systems, is introduced to handle the adaptive fixed-time PID-based control issue of uncertain nonlinear systems. For handling smooth complex unknown nonlinearities existing in the considered system, neural networks will be introduced to estimate these functions. Furthermore, by integrating the self-tuning gain PID controller, an actual controller is proposed. The stability analysis and the simulations all demonstrate the utilisability of the given scheme.

Self-Organizing Type-2 Fuzzy Double Loop Recurrent Neural Network for Uncertain Nonlinear System Control.

Nonlinear systems, such as robotic systems, play an increasingly important role in our modern daily life and have become more dominant in many industries; however, robotic control still faces various challenges due to diverse and unstructured work environments. This article proposes a double-loop recurrent neural network (DLRNN) with the support of a Type-2 fuzzy system and a self-organizing mechanism for improved performance in nonlinear dynamic robot control. The proposed network has a double-loop recurrent structure, which enables better dynamic mapping. In addition, the network combines a Type-2 fuzzy system with a double-loop recurrent structure to improve the ability to deal with uncertain environments. To achieve an efficient system response, a self-organizing mechanism is proposed to adaptively adjust the number of layers in a DLRNN. This work integrates the proposed network into a conventional sliding mode control (SMC) system to theoretically and empirically prove its stability. The proposed system is applied to a three-joint robot manipulator, leading to a comparative study that considers several existing control approaches. The experimental results confirm the superiority of the proposed system and its effectiveness and robustness in response to various external system disturbances.

Adaptive Fuzzy Fixed-Time Control for Uncertain Nonlinear Systems with Mismatched Disturbances

This paper focuses on addressing the adaptive fuzzy fixed-time issue for a class of nonlinear systems with uncertainty functions and mismatched disturbances. Fuzzy logical systems are utilized for identifying unknown functions. Additionally, to tackle challenges posed by mismatched disturbances, disturbance observers are constructed based on the backstepping method. Utilizing the adding one power integrator approach and the fixed-time control method, this paper introduces a fixed-time adaptive fuzzy control algorithm. Notably, this algorithm accommodates the presence of unknown mismatched disturbances and nonlinear functions. The paper establishes, through the application of the Lyapunov stability theory, that the designed adaptive fixed-time fuzzy control algorithm ensures practical fixed-time stability for the resulting closed-loop systems. Finally, the effectiveness of the derived strategy is demonstrated through an illustrative example involving two cases.

A Simple Controller Design for a Class of Uncertain Nonlinear Control Systems Guaranteed to Achieve Arbitrary Exponential Convergence Rates

This paper first proposes the concepts of high-efficiency stabilizable systems and high-efficiency controller. Then, using the time-domain analysis methodology, it is proved that a class of uncertain nonlinear systems can indeed become high-efficiency stabilizable systems under certain conditions; at the same time, we also provide its corresponding high-efficiency controller. Finally, some numerical simulation results are offered to illustrate and demonstrate the correctness of the main theorem and the design process of such a high-efficiency controller

Fixed-Time Fuzzy Control for Uncertain Nonlinear Systems With Prescribed Performance and Event-Triggered Communication

Fixed-Time Fuzzy Control for Uncertain Nonlinear Systems With Prescribed Performance and Event-Triggered Communication

Adaptive Fuzzy Asymptotic Tracking Control of Uncertain Nonlinear Systems With Full State Constraints

Adaptive Fuzzy Asymptotic Tracking Control of Uncertain Nonlinear Systems With Full State Constraints

Event-Triggered Adaptive Sliding Mode Control of Uncertain Nonlinear Systems Based on Fully Actuated System Approach

Event-Triggered Adaptive Sliding Mode Control of Uncertain Nonlinear Systems Based on Fully Actuated System Approach

Dynamic output feedback control of uncertain nonlinear systems based on co-design adaptive event-triggered scheme

This paper presents a framework to design a robust dynamic output feedback (DOF) controller for a class of nonlinear systems, based on the adaptive event-triggered control (AETC) method. The considered system contains parametric uncertainty and to design the event-triggered mechanism (ETM) Finite-gain L2 stability criteria are used. In this paper, a robust adaptive event-triggered mechanism (AETM) is first designed using a pre-designed controller. Then, in a co-design approach, the AETM and the DOF controller are designed together to increase the closed-loop performance. Indeed, the matrices of the DOF controller and the sufficient conditions for the AETM are obtained simultaneously. These conditions are represented as linear matrix inequalities (LMIs) and lead to a significant increase in the update interval. Moreover, the proposed design method guarantees the stability of the closed-loop system in the presence of the proposed triggering event. Finally, to illustrate the performance of the controller three examples are simulated.

Improved Command-Filtering-Based Fixed-Time Fuzzy Adaptive Control for Uncertain Nonlinear Systems With Full State Constraints

Improved Command-Filtering-Based Fixed-Time Fuzzy Adaptive Control for Uncertain Nonlinear Systems With Full State Constraints

Supervisory adaptive safety control for uncertain nonlinear systems

This paper investigates the supervisory adaptive safety control problem for uncertain nonlinear systems with unmeasurable states. In order to estimate unknown parameters and unmeasurable states, a supervisory observer framework consisting of a multi-observer bank and a supervisor unit, is proposed based on a dividing rectangles (DIRECT) algorithm. Under a desired accuracy, the parameter estimates converge to near the true parameters within finite-time while the estimation error of the system state converges to a small neighborhood near the origin. Also, an observer robust adaptive control barrier function is constructed to ensure safety for uncertain nonlinear systems by guaranteeing controlled invariance of a time-varying auxiliary set. By adjusting some parameters in the DIRECT algorithm, the time-varying auxiliary set approaches the original safe set, which reduces the conservatism generated by the compression of the safe set. Finally, two examples, including an adaptive cruise control system, are given to demonstrate the effectiveness of the proposed method.

A fully actuated system approach: Desired compensation adaptive robust control for uncertain nonlinear systems

A desired compensation adaptive robust control (DCARC) framework is presented for two types of fully actuated systems (FASs) subject to both parametric and nonlinear uncertainties based on the Lyapunov theory. The designed controller consists of three parts: (i) a fundamental linear state error feedback term; (ii) an adaptive feedforward compensation term; (iii) a robust compensation term. Different from the existing FAS approaches, the adaptive compensation in the proposed controller relies on the noise-free desired trajectory and online parameter estimate only. A better overall tracking performance with an accelerated transient response is expected, arising from significantly reducing interaction between the robustness part and the adaptation part. Through theoretical analysis, the proposed controller ensures that the estimation error of the unknown parameter vector and the tracking error finally converge to a bounded ellipsoid. The comparative simulation of a permanent magnet (PM) stepper motor demonstrates the effectiveness of the presented approach.

Adaptive prescribed performance tracking control for uncertain nonlinear systems with unknown backlash-like hysteresis

In this paper, an adaptive prescribed performance tracking control(PPTC) problem of uncertain nonlinear systems with unknown hysteresis input is investigated. For the purpose of implementing the PPTC, a performance function and an error conversion function are introduced. Moreover, a backlash-like hysteresis model is adopted to describe the hysteresis nonlinearity, which makes the controller design feasible. Additionally, by converting the backlash-like hysteresis model into a linear model with bounded error, the difficulties caused by hysteresis behavior on controller design are settled. Thus, integrating multi-dimensional Taylor network(MTN) approximation technique into adaptive backstepping method, an adaptive control scheme for uncertain nonlinear systems is proposed. Apart from ensuring that all signals of the closed-loop system keep bounded, the proposed control scheme not only makes the tracking error converge to an arbitrarily small neighborhood around the origin, but also guarantees the tracking error trajectory within the limits set by PPTC. Ultimately, two simulations are applied to verify the validity of the proposed control scheme.

Event‐triggered adaptive estimated inverse neural network control of uncertain nonlinear systems with unknown hysteresis effects

AbstractThis article investigates an event‐triggered adaptive estimated inverse control scheme for uncertain nonlinear systems with hysteresis effects, parametric uncertainties, and unknown disturbances. An online estimated inverse hysteresis compensation mechanism is developed, in which an adaptive technique is designed to obtain the value of unknown hysteresis parameters. Compared with common approaches, its biggest advantage lies in the fact that it eliminates the need for experimental determination of hysteresis parameters, thereby reducing time‐consuming offline identification work and enhance the compatibility of the proposed method. Additionally, an adaptive radial basis functions neural network is applied to approximate the unknown disturbances, and its weight coefficients, along with unknown system parameters, are estimated by means of the adaptive method. Furthermore, the introduction of relative threshold event‐triggered control significantly reduces communication costs resulting from the hysteresis compensation. Through Lyapunov analysis, the proposed controller guarantees all signals are bounded and the errors are convergent. Numerical simulation results demonstrate the superiority of the developed controller.

Efficient learning control of uncertain nonlinear systems with input constraints: a disturbance observer-based neural network approach

Efficient learning control of uncertain nonlinear systems with input constraints: a disturbance observer-based neural network approach

Actor–Critic-Based Predefined-Time Fuzzy Adaptive Optimal Control for Uncertain Nonlinear Systems With Input Saturation

Actor–Critic-Based Predefined-Time Fuzzy Adaptive Optimal Control for Uncertain Nonlinear Systems With Input Saturation

Hierarchical Self-Organizing Fuzzy Control for Uncertain Nonlinear Systems

Hierarchical Self-Organizing Fuzzy Control for Uncertain Nonlinear Systems