Control Of High-order Nonlinear Systems Research Articles

Adaptive fuzzy control for high-order nonlinear systems with asymmetric time-varying full-state constraints and dead-zone input

The issue of adaptive fuzzy control for a category of high-order uncertain nonlinear systems is discussed in this paper. The time-varying full-state constraints are asymmetric, and the input is subjected to dead-zone. The asymmetric time-varying high-order barrier Lyapunov functions (BLFs) are constructed to depict the constraints characteristic and a controller design strategy is proposed. A dead-zone compensation mechanism is used to eliminate the influence of dead-zone input. Based on adding a power integrator technique and the adaptive control method, an adaptive state feedback controller is designed. As a consequence, all the constraints are not breached and the tracking error converges into a prescribed small region around the origin. Finally, a numerical example and a practical example are given to show the effectiveness of the proposed method.

Unified Fuzzy Control of High-Order Nonlinear Systems With Multitype State Constraints.

This article presents a unified adaptive fuzzy control approach for high-order nonlinear systems (HONSs) with multitype state constraints. Existing methods always require the upper and lower constraint boundaries are strictly positive and negative functions (or constants), respectively, which is often inconsistent with the actual constraints. In this article, "multitype state constraint" means that the upper and lower constraint boundaries include multiple types, such as both being strictly positive (or negative), sometime be positive or negative, and so on (cases ①-⑥). By designing a unified mapping function (UMF), the multitype state constraints are processed under removal the feasibility conditions (FCs). Furthermore, a technical design makes the proposed method also applicable to unconstrained HONSs without changing the control structure. By means of a fuzzy-logic system (FLS) and fixed-time stability theory (FTST), the proposed algorithm can ensure that the tracking error converges to a zero-centered neighborhood within a fixed time, and the singularity which often appears in the existing fixed-time control (FTC) methods of HONSs is effectively avoided. Simulation results demonstrate the scheme developed.

Practical Tracking Control for High-order Nonlinear Systems With Dynamic Uncertainties and Unknown Powers via Event-triggered Mechanism

Practical Tracking Control for High-order Nonlinear Systems With Dynamic Uncertainties and Unknown Powers via Event-triggered Mechanism

Adaptive fuzzy prescribed-time control of high-order nonlinear systems with actuator faults

This study concentrates on the adaptive prescribed-time control of high-order nonlinear systems with actuator faults. Since the actual control signal of high-order nonlinear systems has a non-affine form, the existing results require that the bounds of time-varying actuator fault parameters be known. To break through the above limitation, the non-affine form of the actual control signal is solved in a linear manner, and novel adaptive estimations are designed. Moreover, fuzzy logic systems are adopted to approximate uncertain terms in control design. It is proved theoretically that the system states converge to zero within the prescribed time which can be set in advance, and all signals in the closed-loop system are bounded. Finally, the effectiveness of the proposed control scheme is certificated by a numerical simulation and a practical simulation of the electromechanical system.

Adaptive Fixed-Time Control for High-Order Nonlinear Systems With Unknown Control Coefficients and Quantized Input

Adaptive Fixed-Time Control for High-Order Nonlinear Systems With Unknown Control Coefficients and Quantized Input

Neural network-based output tracking control of high-order nonlinear systems with DoS attacks and perturbations

This paper focuses on the output feedback tracking control of a high-order nonlinear system with denial-of-service (DoS) attacks and exogenous disturbances. A radial basis function neural network (RBFNN)-based state observer is employed to estimate the system states. A new nonlinear filter with adaptive regulation is developed to eliminate the impacts of perturbed factors such as RBFNN approximation errors and disturbances. Constituting with filtering operation and backstepping control technique, a RBFNN-based security controller is constructed to suppress the influences of perturbations and DoS attacks based on the observation signals. The uniformly ultimately bounded output tracking result is established by using the security control signals via Lyapunov criterion in the cases of DoS attacks, nonlinearities, and disturbances. Comparative results are provided to validate the efficiency of the developed RBFNN-based observation and security control strategies of a nonlinear system.

Adaptive guaranteed cost tracking control for high-order nonlinear systems based on fully actuated system approaches

This paper considers the adaptive guaranteed cost tracking (AGCT) control problems for two classes of high-order nonlinear systems with unknown parameters. A new local smooth nonlinear function (LSNF) is introduced first, which provides an important mathematical tool for our controller design. Then, based on the LSNF and the high-order fully actuated (HOFA) system approaches, the AGCT controller is designed for HOFA system with unknown parameter, which guarantees that all of the states of the closed-loop HOFA system are globally bounded, and the tracking error is asymptotically convergent. Moreover, the upper bound of cost function (UBCF) characterizing the tracking performance can be arbitrarily preseted, and is completely independent of the system initial value and the unknown parameter, which significantly improves the tracking performance, and is difficult to achieve by using existing guaranteed cost control (GCC). Furthermore, an extra result, the AGCT controller for a class of strict-feedback systems with high-order form and unknown parameters, is obtained in this paper, which also guarantees that the system tracking error is globally asymptotically convergent with the arbitrarily preseted UBCF characterizing the tracking performance. Three simulation examples, including an inverted pendulum, are presented to show the effect and the superiority of the proposed method.

Prescribed-Time Output Feedback Control for High-Order Nonlinear Systems

In this article, a novel prescribed-time output feedback control strategy is developed for high-order nonlinear systems. To begin with, a new coordinate transformation method is proposed, under which a time-varying gain that goes to infinity towards the terminal time and a constant scaling gain are simultaneously introduced into the system. Then, the reduced-order observer and output feedback controller are successfully constructed by using the homogeneous domination approach. Unlike many existing results, our proposed control strategy can ensure that the convergence time is independent of both the initial conditions and design parameters, and the convergence rate of the system is adjustable. Moreover, the design process is simplified and the control scheme can operate even after the prescribed-time. Finally, a simulation example is used to verify the validity of the proposed control strategy.

Finite-time adaptive practical tracking control for high-order nonlinear systems with full-state constraints and input saturation

This paper focuses on finite-time adaptive practical tracking control for a class of high-order nonlinear systems with full-state constraints and input saturation. The state constraints are handled by applying nonlinear transformed functions (NTFs) and the input saturation is estimated by an auxiliary hyperbolic tangent function. On the basis of adding a power integrator technique and adaptive control method, an adaptive state feedback controller is designed for the closed-loop system. With the aid of finite-time stability theory, the tracking error converges to a bounded neighbourhood of the origin in a finite time, and all the signals in the closed-loop system are bounded. At last, a simulation example and a practical example are presented to show the effectiveness of the proposed control procedure.

Adaptive Event-triggered Control for High-order Nonlinear Systems with Deferred Asymmetric Full-state Constraints

Adaptive Event-triggered Control for High-order Nonlinear Systems with Deferred Asymmetric Full-state Constraints

Fixed-time tracking control for high-order nonlinear systems with unknown time-varying input delay

Fixed time tracking control for nonstrict feedback high-order nonlinear systems with unknown time-varying external disturbance and unknown time-varying input delay has been studied in this research. Firstly, the obstacle caused by unknown time-varying input delay has been tackled by introducing a compensation signal. The unknown nonlinear functions are identified by neural networks and the algebraic loop problem for nonstrict feedback systems has been overcome by using the properties of neural networks. Further, a bound estimation mechanism is employed to estimate the identify error and unknown time-varying external disturbance without using the priori knowledge of the boundary. Regarding the obstacle caused by high-order terms and the singularity problem have been tackled by using adding a power integrator mechanism and the inequality transformation technique, respectively. The boundedness of all the signals in the closed-loop systems has been proved by using the Lyapunov stability theorem, and the convergence time is independent of the initial value of the system state. Finally, the simulation results show the effectiveness of the proposed method.

Adaptive Fault-tolerant Control for High-order Nonlinear Systems with Supervisory Controllers and Command Filters

Adaptive Fault-tolerant Control for High-order Nonlinear Systems with Supervisory Controllers and Command Filters

Fuzzy approximation-based adaptive tracking control for high-order nonlinear systems with asymmetric full-state constraints

This paper studies the adaptive tracking control for a class of constrained high-order nonlinear systems with uncertainties. First, a type of improved asymmetric log-type barrier Lyapunov functions (LBLFs) is constructed to handle the full-state constraints. Second, fuzzy systems are built to approximate the unknown functions in the control system. An adaptive controller is designed on the basis of adding a power integrator technique. Consequently, the designed controller can ensure that the constraints are not breached, while the tracking error approaches an arbitrarily small neighborhood of the origin. The designed controller’s performance can be guaranteed with the disappearance of the constraints. The computational burden of fuzzy approximation is mitigated by the adaptive gain-update law. A numerical example and a practical example are presented to verify the effectiveness of the proposed method.

Adaptive Fuzzy Event-Triggered Control for High-Order Nonlinear Systems With Prescribed Performance.

This article focuses on the design of a novel adaptive fuzzy event-triggered tracking control approach for a category of high-order uncertain nonlinear systems with prescribed performance requirements, in which a high-order tan-type barrier Lyapunov function (BLF) is employed to handle and analyze the output tracking error, fuzzy systems are adopted to identify the totally unknown nonlinear functions, and only one gain function rather than parameter estimation functions is designed to cancel out all unknowns appearing in fuzzy systems. As a result, complicated calculations are avoided and a structured simple control is achieved. The proposed controller not only ensures that the tracking error is always within a predefined region but also reduces the communication burden from the controller to the actuator. Finally, comparison simulations are presented to verify the effectiveness of the proposed control schemes.

Adaptive iterative learning control for high-order nonlinear systems with random initial state shifts

Aiming at the tracking problem for a class of high-order nonlinear systems with arbitrary initial state, this paper proposes different initial state shifts rectifying schemes for systems with different orders from the perspective of solving differential equations to ensure that the systems achieve complete tracking over the specified interval. This method relaxes the requirement of initial positioning in iterative learning control, and solves the problem of iterative learning control for high-order nonlinear systems with arbitrary initial state error. The theoretical analysis shows that the proposed schemes can make all signals in the system bounded, and ensure that the tracking error in the preset interval tends to zero as the number of iterations increases. When designing the controller, the arctangent function is used to avoid flutter of the control signal and related variables. The final simulations verify the effectiveness of the proposed algorithms.

Nonsingular recursive-structure sliding mode control for high-order nonlinear systems and an application in a wheeled mobile robot

This work investigates the problem of fast tracking control for a class of high-order nonlinear systems subject to the matched disturbances. More particularly, a novel practical fixed-time disturbance observer is first presented by using a smooth hyperbolic tangent function. Then, a new nonsingular recursive-structure sliding mode surface is proposed based on the terminal sliding mode surface. With the reconstructed information deriving from the designed disturbance observer, a nonsingular recursive-structure sliding mode based finite-time tracking control approach incorporating with a new adaptive law is proposed to ensure the tracking errors converge to a small region of the origin in finite time. The finite-time stability of the closed-loop tracking control system driven by the proposed control scheme is analyzed and proved utilizing Lyapunov theory. And also, the proposed generalized control approach is applied to a mobile robotic experimental platform to achieve accurate trajectory tracking on the uneven ground. Finally, the numerical simulation and comparative experiment results demonstrate the effectiveness and superiority of the proposed approach.

Adaptive Control of Full-State Constrained High-Order Nonlinear Systems With Time-Varying Powers

This article studies full-state constrained control for high-order nonlinear systems with unknown multiple time-varying powers and serious parameter unknowns. Due to the simultaneous existence of unknown powers and full-state constraints, we construct a log-type quadratic barrier Lyapunov function (BLF) rather than a quadratic Lyapunov function. By skillfully combining the log-type BLF, adding a power integrator technique and adaptive technique, an adaptive state feedback controller is developed. Under feasibility conditions, which are provided as sufficient conditions for the existence of proposed full-state constrained control, it is proved that all the signals of the closed-loop system are bounded, original system states converge to zero and full-state constraints are not violated.

Adaptive Fixed-Time Control of Strict-Feedback High-Order Nonlinear Systems.

This paper examines the adaptive control of high-order nonlinear systems with strict-feedback form. An adaptive fixed-time control scheme is designed for nonlinear systems with unknown uncertainties. In the design process of a backstepping controller, the Lyapunov function, an effective controller, and adaptive law are constructed. Combined with the fixed-time Lyapunov stability criterion, it is proved that the proposed control scheme can ensure the stability of the error system in finite time, and the convergence time is independent of the initial condition. Finally, simulation results verify the effectiveness of the proposed control strategy.

Control of high-order nonlinear systems under error-to-actuator based event-triggered framework

This paper solves the finite-time tracking problem of a class of high-order nonlinear systems under event-triggered input. Unlike existing event-triggered frameworks based on signal transmission channels from the sensor to the controller or from the controller to the actuator, these developed trigger mechanisms only compare the difference between the signal to be transmitted and the holding signal. By introducing internal trigger conditions and external trigger conditions, a novel error-to-actuator based event-triggered framework is proposed. It further considers the response of the trigger mechanism to system control performance such that the tracking performance of the system can be guaranteed while reducing the number of signal transmissions. In addition, filter-based techniques (such as the dynamic surface control method), for the first time, are utilised to eliminate some strong constraints that exist in the literature for most high-order nonlinear systems. The effectiveness of the proposed approach is evaluated on simulation examples including comparative studies and a practical example.

Adaptive neural tracking control of high-order nonlinear systems with quantized input

In this paper, adaptive neural tracking control problem is considered for non-strict-feedback high-order nonlinear systems with quantized input signal. Compared with the logarithmic quantizer, the quantizer introduced in this paper can avoid chattering problem. The dynamic surface control (DSC) technique is introduced to solve the problem of ‘explosion of complexity’, which is appeared in the classic adaptive backstepping control of high-order nonlinear systems. The structural properties of radial basis function neural networks (RBF NNs) are used to simplify the design difficulty from the functions of whole state variables. According to the classic adaptive backstepping technique and neural network algorithm, an output tracking controller is designed, which can guarantee that all the signals of the closed-loop system are semiglobally uniformly bounded and the output of the system can track the reference signal. Finally, a numerical example is presented to verify the effectiveness of the proposed method.