Control Of High-order Nonlinear Systems Research Articles

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.

Neuroadaptive control of saturated nonlinear systems with disturbance compensation

Extended state observer acting as a popular tool can estimate the system states and total disturbances simultaneously. However, for extended-state-observer-based control of high-order nonlinear systems, there are still some difficult issues to solve, such as how to simultaneously reject matched and mismatched model uncertainties with strict theoretical proof, especially in the case of output feedback, “explosion of complexity” and so on. Motivated by these reasons, different control schemes in full-state feedback and output feedback conditions respectively will be integrated via the filter-based backstepping approach for saturated nonlinear systems. For the full-state feedback condition, adaptive neural network and extended state observer will be combined for each dynamic to handle the unknown nonlinear dynamics and external disturbances, respectively. For the output feedback condition, nonlinear disturbance observer design will be incorporated into the neural-network-based extended state observer scheme to handle mismatched disturbances at the same time. In particular, an auxiliary system will be constructed to compensate for the saturation influence. Moreover, the anticipate control effects of the developed controllers have been demonstrated by contrastive results for a hydraulic servo system.

Adaptive tracking control of high-order nonlinear systems under asymmetric output constraint

This paper addresses the tracking control problem of a class of high-order uncertain nonlinear systems under time-varying asymmetric output constraints. Most relevant results in the literature have two main restrictions: R1) some constraints need to be imposed on powers and growth conditions have to be established for the nonlinear functions of the system; R2) nonlinear bounding functions must be derived based on repeated derivations of virtual control variables during the design process. By integrating an improved technique of adding a power integrator with a dynamic surface control (DSC) method, we develop a systematic tracking control scheme that eliminates both of the above restrictions. Moreover, with an improved time-varying nonlinear transformed function introduced for high-order systems, the proposed scheme can be regarded as a unified tool in the sense that it works no matter whether the constraint is symmetric, asymmetric, or even without a constraint. The above results are also extended to systems with uncertain gain functions, and the proposed scheme estimates only one adaptive parameter. The simulation results of two deterministic practical applications show that the proposed control scheme is effective not only for high-order systems, but also for high-order-free systems.

Robust control of high-order nonlinear systems with unknown measurement sensitivity

Robust control of high-order nonlinear systems with unknown measurement sensitivity

Practically Finite-Time Control for Nonlinear Systems With Mismatching Conditions and Application to a Robot System

This paper is concerned with the practically finite-time (PFT) control problem for a class of more general nonlinear systems subject to mismatching time-varying disturbances. Without any extra assumptions on system nonlinearities, a composite controller is developed by introducing a disturbance observer and finite-time control technique. Based on the designed controller and Lyapunov stability theory, the PFT stability of the closed-loop system is strictly verified and proven to be a better convergence performance. Furthermore, as a byproduct of the proposed design method, the disturbance observer-based PFT control for high-order nonlinear systems is also shown to be possible. To the best of the authors’ knowledge, it is the first PFT control result for high-order nonlinear systems with external disturbances. Finally, an application example of a single-link robot system with disturbances and a numerical example are presented to demonstrate the effectiveness of the proposed scheme, respectively.

Adaptive Finite-Time Control for High-Order Nonlinear Systems With Multiple Uncertainties and its Application

The globally finite-time control issue is concerned in this note for high-order nonlinearly parameterized systems with unknown control gain and external disturbances. A novel control strategy combining adaptive control technique with sign function can well deal with serious uncertainties and unknown control gain. Without any nonlinear growth assumptions, a unified and systematic design procedure is employed to derive an adaptive state-feedback controller with the help of the adding a power integrator method and backstepping technique. Then, by finite-time stability analysis and Lyapunov functions, the proposed controller ensures that the closed-loop system is globally practically finite-time stable (PFTS). Two simulation examples, including a mass-spring mechanical system and a numerical example, are applied to verify the performance and effectiveness of the designed schemes.

Output tracking control of high-order nonlinear systems with dynamic uncertainties

This paper investigates the output tracking control problem for a class of nonlinear systems with zero dynamic. On the basis of adding a power integrator method and approximation technique, an appropriate controller is proposed to guarantee that the tracking error turns to a preassigned neighborhood of the origin. The systems under investigation allow unmeasurable dynamic uncertainties, unknown nonlinear functions and unknown high-order terms. As an application, two examples are provided to illustrate the effectiveness of a control strategy.

Adaptive terminal sliding mode control of high-order nonlinear systems

In recent decades, controller design has been attracted a great deal of interest of many researchers in control community which can make the job of many other researchers in different area of research easier. The present study aims to design a finite time adaptive control input for a high-order nonlinear system in presence of a variety of mismatched uncertainties and external disturbances. Adaptive terminal sliding mode control (ATSMC) method is used to design robust controller in a finite time. Also, adaptive concept is employed in ATSMC to estimate the upper bound of mismatched uncertainties and external disturbances and their estimations are used in control input. The finite time stability proof is performed by defining a proper candidate Lyapunov function. Numerical simulation results are carried out in Simulink/MATLAB to reveal the correctness of proposed design in this research. Finally, the performance criterion, integral of the square value (ISV), is defined to provide a numerical comparison between the proposed adaptive controller and non-adaptive controller.

Adaptive terminal sliding mode control of high-order nonlinear systems

In recent decades, controller design has been attracted a great deal of interest of many researchers in control community which can make the job of many other researchers in different area of research easier. The present study aims to design a finite time adaptive control input for a high-order nonlinear system in presence of a variety of mismatched uncertainties and external disturbances. Adaptive terminal sliding mode control (ATSMC) method is used to design robust controller in a finite time. Also, adaptive concept is employed in ATSMC to estimate the upper bound of mismatched uncertainties and external disturbances and their estimations are used in control input. The finite time stability proof is performed by defining a proper candidate Lyapunov function. Numerical simulation results are carried out in Simulink/MATLAB to reveal the correctness of proposed design in this research. Finally, the performance criterion, integral of the square value (ISV), is defined to provide a numerical comparison between the proposed adaptive controller and non-adaptive controller.

Cooperative control of high-order nonlinear systems with unknown control directions

In this paper, we investigate output synchronization problem of nonlinear systems that can be transformed into strict feedback form with unknown control direction. To this end, an augmented Laplacian potential function is introduced to construct local level distributed adaptive controllers such that outputs of networked agents can be synchronized while all other states maintain bounded. Moreover, tuning functions are designed to reduce the order of the parameter updater. In contrast to conventional adaptive backstepping procedure, both the parameter updating law and tuning function of the proposed scheme take advantage of information flow among networked agents and thus distributive in nature. It is proved that output synchronization of the entire network can be achieved by properly choosing Nussbaum functions, provided the information graph is undirected and connected. Furthermore, we also proposed a way to define a proper Nussbaum function. Simulation results are presented to verify the effectiveness of the proposed schemes.

Sufficient Condition for the Existence of the Compact Set in the RBF Neural Network Control.

In this brief, sufficient conditions are proposed for the existence of the compact sets in the neural network controls. First, we point out that the existence of the compact set in a classical neural network control scheme is unsolved and its result is incomplete. Next, as a simple case, we derive the sufficient condition of the existence of the compact set for the neural network control of first-order systems. Finally, we propose the sufficient condition of the existence of the compact set for the neural-network-based backstepping control of high-order nonlinear systems. The theoretic result is illustrated through a simulation example.

Uncertainty observer-based robust tracking control for high-order nonlinear systems using forwarding technique

ABSTRACTBased on uncertainty observers, we develop a robust tracking control approach for high-order nonlinear systems subject to uncertainties satisfying mismatched condition. In this study, by combining with forwarding technique, uncertainty observers are designed to estimate uncertainties including parameter perturbations and external disturbances in a bottom-up way; at the same time, the convergence rate of estimate error of uncertainty observers is analysed in detail. The insensitivity to uncertainties for each manifold, no need of a prior knowledge on the bound of the uncertainty and the feasibility of practical implementation are three advantages of the proposed scheme. Moreover, approximate error of uncertainty observer can be made sufficiently small by tuning the parameters. The design procedures are elaborated and the boundedness of all trajectories of the closed-loop systems is guaranteed. Two examples are illustrated, highlighting the superiority of the proposed methodology via comparison with other control strategies.

Quasi-finite-time control for high-order nonlinear systems with mismatched disturbances via mapping filtered forwarding technique

ABSTRACTIn this study, a quasi-finite-time control method for designing stabilising control laws is developed for high-order strict-feedback nonlinear systems with mismatched disturbances. By using mapping filtered forwarding technique, a virtual control is designed to force the off-the-manifold coordinate to converge to zero in quasi-finite time at each step of the design; at the same time, the manifold is rendered insensitive to time-varying, bounded and unknown disturbances. In terms of standard forwarding methodology, the algorithm proposed here not only does not require the Lyapunov function for controller design, but also avoids to calculate the derivative of sign function. As far as the dynamic performance of closed-loop systems is concerned, we essentially obtain the finite-time performances, which is typically reflected in the following aspects: fast and accurate responses, high tracking precision, and robust disturbance rejection. Spring, mass, and damper system and flexible joints robot are tested to demonstrate the proposed controller performance.

A new robust observer-based adaptive type-2 fuzzy control for a class of nonlinear systems

In this paper, a novel robust observer-based adaptive controller is presented using a proposed simplified type-2 fuzzy neural network (ST2FNN) and a new three dimensional type-2 membership function is presented. Proposed controller can be applied to the control of high-order nonlinear systems and adaptation of the consequent parameters and stability analysis are carried out using Lyapunov theorem. Moreover, a new adaptive compensator is presented to eliminate the effect of the external disturbance, unknown nonlinear functions approximation errors and sate estimation errors. In the proposed scheme, using the Lyapunov and Barbalat's theorem it is shown that the system is stable and the tracking error of the system converges to zero asymptotically. The proposed method is simulated on a flexible joint robot, two-link robot manipulator and inverted double pendulums system. Simulation results confirm that in contrast to other robust techniques, our proposed method is simple, give better performance in the presence of noise, external disturbance and uncertainties, and has less computational cost.

Discrete-time adaptive iterative learning control for high-order nonlinear systems with unknown control directions

An adaptive iterative learning control method is proposed for a class of nonlinear strict-feedback discrete-time systems with random initial conditions and iteration-varying desired trajectories. An n-step ahead predictor approach is employed to estimate the future states in the control design. Discrete Nussbaum gain method is utilised to deal with the lack of a priori knowledge of control directions. The proposed control algorithm guarantees the boundedness of all the signals in the controlled system. The tracking error converges to zero asymptotically along the iterative learning axis except for beginning states affected by random initial conditions. The effectiveness of the proposed control scheme is verified through numerical simulation.