Class Of Uncertain Nonlinear Systems Research Articles

Adaptive fuzzy performance control based on a triggering mechanism with decreasing function and internal dynamic variable

The problem of fuzzy adaptive prescribed performance control with dynamic event-triggered input for a class of uncertain nonlinear systems is investigated in this article. A dynamic event-triggered scheme is proposed that integrates an internal dynamic variable and an exponentially decreasing function, effectively reducing unnecessary trigger events and minimizing the system of communication resources. Subsequently, a fuzzy estimator is designed to estimate the unmeasurable states of the system, while fuzzy logic systems are employed to approximate the uncertain nonlinear terms. The proposed scheme ensures semi-globally uniformly ultimately bounded (SGUUB) of the closed-loop system and converges the tracking error to a prescribed performance range based on a barrier Lyapunov function. Finally, a simulation example is given to justify the rationality of the proposed strategy.

Fault tolerant control of uncertain hydraulic system against actuator fault based on redesign Lyapunov approach

The design of stabilizing controller for uncertain nonlinear systems with control constraints is a challenging problem. This paper proposes the design of fault tolerant control for a class of uncertain nonlinear systems with actuator faults based on Lyapunov redesign principle. First, an assumption is introduced to design the control of the nominal system. Then, a new control law has been introduced to handle the difficulty caused by actuator failures. It is shown that the actuator faults can be completely compensated by the proposed nonlinear controller. Finally, the method will be applied to a hydraulic system to show its effectiveness.

Finite-time adaptive fuzzy event-triggered control for nonlinear time-delay system with input quantization via command filter

This paper investigates the problem of finite-time adaptive fuzzy event-triggered control for a class of uncertain nonlinear systems with input quantization. The nonlinear systems under consideration contain unmodeled dynamics and time-varying delays. Fuzzy logic systems are used to handle unknown nonlinear terms. Additionally, finite-time filters are introduced to solve the problem of “explosion of complexity” as well as to ensure that the derivative of the virtual controller can be approximated in finite time. The Lyapunov–Krasovskii function is used to handle time-varying delays. The hysteresis quantizer is used to ensure adequate precision when there is a low transmission rate requirement. The control strategy combines event-triggered mechanisms and quantization technology to ensure that all signals of the closed-loop system remain bounded in finite time. Finally, two examples are included to demonstrate the effectiveness of the proposed controller.

Practical prescribed time tracking control for a class of nonlinear systems with event triggering and output constraints

AbstractThis paper investigates the practical prescribed time tracking for a class of uncertain nonlinear systems based on neural networks and event‐triggered control. Introducing a time‐varying constraint function transforms the original practical prescribed time‐tracking control issue into a tracking error constraint problem. An event‐triggered adaptive control has been proposed, which can effectively reduce the communication burden between the controller and the actuator. Using neural networks to approximate unknown nonlinear functions avoids the differentiation of virtual controllers, thereby reducing the computational burden. In addition, users can independently choose preset time and tracking accuracy without changing the control structure, which remains independent of the initial conditions and any design parameters. Finally, the effectiveness of this method is verified through simulation examples.

Logic-Based Fixed-Time Control for Uncertain Nonlinear Systems With Unknown Control Directions.

The fixed-time control problem is investigated for a class of uncertain nonlinear systems subjected to multiple unknown control directions. The control coefficients of nonlinear systems under consideration are time varying and their signs are not required to be identical. To tackle this challenge, a switching mechanism along with a novel dynamic boundary function is proposed. Utilizing the devised dynamic boundary function, adaptive parameters are introduced into the controller to effectively handle system uncertainties. It is proved that the system output converges to a small neighborhood of the origin in fixed time and the boundedness of all system signals is maintained. Finally, two simulation examples are used to show the validity of the presented switching control strategy.

Robust control design of uncertain nonlinear systems: a self-compensating and self-tuning approach

ABSTRACT The problem of robust stabilisation is considered for a class of uncertain nonlinear systems with linear control term. It is not required that the unforced nominal (nonlinear) system has to be stable and/or has to be known, which means that its Lyapunov function need not be known and/or found for designing a stabilising control scheme to compensate the effect of uncertainty on the systems like some traditional control design approaches. For such a class of uncertain nonlinear systems, a design approach, called a self-compensating and self-tuning one, is presented whereby some robust state feedback control schemes can be easily synthesised. The proposed design approach can result in a linear state feedback control scheme with a time-varying control gain for such a class of uncertain nonlinear systems, which implies the simplicity of the design approach and control results. In addition, the system uncertainty is also not required to have to satisfy the matching conditions.

Adaptive prescribed-time parameter estimation and control for a class of uncertain nonlinear systems

This paper presents a prescribed-time (PT) parameter estimation and control algorithm for a class of uncertain nonlinear systems. Using a time-varying forgetting factor and a normalization technique, a two-filter-based parameter estimation error reconstruction mechanism is developed. On the basis of this, a novel PT parameter estimation method is proposed, under the sufficient excitation condition, which is less conservative than the persistency of excitation condition. Furthermore, by combining the proposed PT parameter estimation method and the sliding mode control method, an adaptive PT control law is designed, which makes both the tracking error and the parameter estimation error converge to zero in a prescribed time, while all the closed-loop signals remain bounded. Moreover, a modified adaptive PT control scheme is proposed to avoid any numerical problems that may arise in the implementation of the adaptive PT control method due to the use of the infinity gain function. Finally, the effectiveness of the proposed algorithm is illustrated by two simulation examples.

Adaptive dynamic‐surface repetitive control for uncertain nonlinear systems with mismatched disturbances and input delay

AbstractBased on additive state decomposition technique, this article presents an adaptive dynamic‐surface repetitive control method for a class of uncertain nonlinear systems with mismatched disturbances and input delay. First, the original uncertain nonlinear system is decomposed into a linear time invariant (LTI) primary system responsible for the periodic signal tracing and rejection task, and a nonlinear secondary system with input time delay responsible for the robust stabilization task. A modified repetitive controller with a small correction to the delay constant is then independently designed for the LTI primary system, while an adaptive dynamic surface controller is designed for the nonlinear secondary system. Stability analysis is performed for each subsystem and the design procedure of the whole system is presented in detail. Finally, comparative simulations with other repetitive control and dynamic surface control methods show that the presented method not only relaxes the constraints on the reference inputs and exogenous disturbances, but also ensures that the system has better disturbance rejection and periodic‐signal tracking performance in both transient and steady states. As a result, this method broadens the application of both repetitive control and dynamic surface control.

Adaptive Anti-Disturbance Control for a Class of Uncertain Nonlinear Systems With Composite Disturbances.

High-precision and safety control in face of disturbances and uncertainties is a challenging issue of both theoretical and practical importance. In this article, new adaptive anti-disturbance control schemes are proposed for a class of uncertain nonlinear systems with composite disturbances, including additive disturbances, multiplicative actuator faults, and implicit disturbances deeply coupled with system states. Both the cases with known and unknown control/fault directions are investigated. By properly fusing the techniques of disturbance observers and adaptive compensation, it is shown that all closed-loop signals are globally uniformly bounded and the tracking error converges to zero asymptotically, no matter the control/fault directions are known or not. In the case of known directions, the proposed control scheme, for the first time, guarantees asymptotic tracking and L∞ tracking performance simultaneously in face of disturbances and actuator faults. Moreover, novel Nussbaum functions and a contradiction argument are introduced, which allow the system to have multiple unknown nonidentical control directions and unknown time-varying fault direction. Simulation results illustrate the effectiveness of the proposed control schemes.

Dynamic gain–based neural network backstepping control with its applications to a quad-rotor hover

In this paper, a novel neural network (NN) backstepping control method is proposed for a class of uncertain nonlinear systems with unknown control direction functions. To solve the control problems caused by unknown control direction functions, a method called “virtual control coefficient” is presented using equivalence transformations. However, to improve the flexibility of the control method, a function named “dynamic gain” is introduced to design the feedback gains of the NN backstepping controllers. Moreover, instead of using σ-modification, gradient descent algorithm is applied to train the weights of NNs such that the unknown nonlinearities of the system can be well approximated by NNs. With the help of Lyapunov stability criterion, it can be proved that the system tracking error is semi-global uniformly ultimately bounded. Finally, the effectiveness of the proposed control method is verified by the experimental results on a quad-rotor hover platform.

Adaptive nonlinear robust lead compensator design for a class of uncertain nonlinear systems

Adaptive nonlinear robust lead compensator design for a class of uncertain nonlinear systems

Event-triggered prescribed-time control for a class of uncertain nonlinear systems using finite time-varying gain

This paper addresses the event-triggered prescribed-time control problem for a class of high-order nonlinear systems based on finite time-varying gain. Due to the existence of unknown gain functions and system uncertainties, the resultant control with prescribed-time convergence performance becomes nontrivial. The problem becomes even more complex due to the use of event-based communication instead of continuous communication. To tackle the aforementioned challenges, this paper proposes an event-triggered prescribed-time stabilization approach with the following key steps. Firstly, we establish a new prescribed-time stability lemma to overcome the technical difficulty arising from the prescribed-time controller design, and stability analysis. Secondly, we give the controller design procedure upon using the backstepping technique. Thirdly, we redesign the event-triggering threshold condition based on time-varying functions, which allows the controller terminal jitter to be mitigated and the controller to be implemented straightforwardly in practice. Furthermore, the proposed control scheme avoids Zeno behavior. The numerical simulation confirms the effectiveness of the proposed control scheme.

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.

Event-Triggered Adaptive Neural Network Tracking Control for Uncertain Systems With Unknown Input Saturation Based on Command Filters.

This brief presents a modified event-triggered command filter backstepping tracking control scheme for a class of uncertain nonlinear systems with unknown input saturation based on the adaptive neural network (NN) technique. First, the virtual control functions are reconstructed to address the uncertainties in subsystems by using command filters. A piecewise continuous function is employed to deal with the unknown input saturation problem. Next, an event-triggered tracking controller is developed by utilizing the adaptive NN technique. Compared with standard NN control schemes based on multiple-function-approximators, our controller only requires a single NN. The closed-loop system stability is analyzed based on the Lyapunov stability theorem, and it is shown that the Zeno behavior is also avoided under the designed event-triggering mechanism. Simulation studies are performed to validate the effectiveness of our controller.

Asymptotic tracking control for a class of uncertain nonlinear systems with output constraint

In this paper, we investigate the asymptotic tracking control for a class of strict-feedback nonlinear systems with unknown nonlinear functions and output constraint. The nonlinear transformation function-based system transformation approach is employed to convert the initial constrained system into an unconstrained one. To achieve the objective of asymptotic tracking, the tracking error is scaled by an exponential proportional function. Furthermore, to address the challenge of repetitive derivation of virtual control laws that occurs in the traditional design process of high-order backstepping methods, a first-order filter is applied. The designed control scheme guarantees that the system output will asymptotically track a predefined reference tracking trajectory while ensuring that the output constraint is not violated. Moreover, it is shown that the filter error will converge asymptotically to the origin. The effectiveness of the developed control strategy is verified through simulation results.

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

Practical Finite-Time Command-Filtered Adaptive Backstepping With Its Applications to Quadrotor Hovers.

In this article, a practical finite-time command-filtered adaptive backstepping (PFTCFAB) control method is presented for a class of uncertain nonlinear systems with nonparametric unknown nonlinearities and external disturbances. Unlike PFTCFAB control techniques that use neural networks (NNs) or fuzzy-logic systems (FLSs) to deal with system uncertainties, the proposed method is capable of handling such uncertainties without the need for NNs or FLSs, thus reducing complexity and increasing reliability. In the proposed approach, novel function adaptive laws are designed to directly estimate unknown nonparametric nonlinearities and external disturbances by means of command filter techniques, and a type of practical finite-time command filters is proposed to obtain such laws. Moreover, the PFTCFAB controllers and finite-time command filters are designed with practical finite-time Lyapunov stability, which ensures finite-time stability of system tracking and filter estimation errors. Experimental results with a quadrotor hover system are presented and discussed to demonstrate the advantages and effectiveness of the proposed control strategy.

Robust tracking and model following of uncertain nonlinear systems with some uncertainties and dead-zone inputs

The problem of robust tracking and model following is reconsidered for a class of uncertain nonlinear systems with some uncertainties and dead-zone input constraints. In this paper, the system uncertainties are regarded as some nonlinear functions which are not required to must satisfy the matching conditions. That is, being different from traditional robust control theory, the matched structures of uncertainties are sufficient, but not necessary, for being able always to design some types of robust tracking control schemes. In addition, the external disturbances of dynamical systems are assumed to be any bounded functions which is not also required to satisfy the matching condition. By making use of the integral inequality, instead of Lyapunov function, a class of robust tracking control schemes is constructed to guarantee the uniform exponential boundedness of the model tracking errors. Moreover, the upper bounds of nonlinear uncertainties are not required to be known, and it is also unnecessary to know or estimate the characteristic parameters of dead-zone functions. Therefore, the resulting robust tracking control schemes have a simple structure. Actually, the resulting robust tracking control scheme is a linear feedback control one with a self-tuning control gain. Finally, an illustrative numerical example is provided to demonstrate the validity of the presented theoretical results.

Sliding mode disturbance observer based control with arbitrary convergence time

In this study, an arbitrary finite-time backstepping control method for a class of uncertain nonlinear systems in the presence of external disturbance is proposed based on disturbance observer. Motivated by the desire to attain external disturbance compensation, a sliding mode disturbance observer with arbitrary convergence time is presented to estimate the disturbance. This arbitrary prespecified time is independent of initial conditions and system parameters. The designed observer is very simple with only one tuning parameter used to tune the convergence rate. Only the upper bound of the first derivative of the disturbance is necessary. Then, based on the proposed disturbance observer, a backstepping control technique is developed in which the convergence time can be chosen arbitrarily. Utilizing the Lyapunov stability criterion, it is proven that the system states, as well as the disturbance observer error converge to the origin in arbitrarily chosen time. Finally, some numerical examples are presented to demonstrate the validity and applicability of the proposed disturbance observer-based controller.

Adaptive output-feedback global stabilisation for a class of more general nonlinear systems

ABSTRACT This article investigates the global stabilisation problem via adaptive output feedback for a class of uncertain nonlinear systems. It is worth emphasising that the system under investigation possesses function control coefficients, input matching uncertainty and the polynomial-of-output growth rate, which is essentially different from the existing related literature, and hence brings some technical difficulties to the control design. To solve this problem, an adaptive output-feedback controller with dynamic high-gain and extended state observer is proposed. Remarkably, only one dynamic gain is introduced to overcome the function control coefficients, the serious uncertainty and the polynomial-of-output in the system growth rate. Moreover, under the designed controller, the states of the original system globally converge to zero. Two simulation examples are given to demonstrate the effectiveness of the proposed approach.