Class Of High-order Nonlinear Systems Research Articles

Computer simulation of tracking in high-order nonlinear systems with time delay

In this paper, we study the problem of global practical tracking of a class of high-order nonlinear systems with feedback. A feature of the system under consideration is that the degree of limitation of the upper boundary of the nonlinearity is taken on a continuous interval. We develop a tunable and delayindependent tracking controller that dominates the effect of delay time non-linearity by generating a Lyapunov function, respectively, using a generalized method of adding a signum function and a power integrator. The resulting controller ensures global boundedness of all states of the studied closed system and a sufficiently small control error over a finite time. In addition, in this work, priority was given to computer simulation of previously achieved results.

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.

Emerging robust and data‐driven control methods for uncertain learning systems

Emerging robust and data‐driven control methods for uncertain learning systems

A fixed-time distributed extended state observer for uncertain second-order nonlinear system

This paper investigates the fixed-time distributed estimation problem for a class of second-order nonlinear systems with uncertain input, unknown nonlinearity and matched perturbation. A fixed-time distributed extended state observer (FxTDESO) consisting of a group of local observer nodes under directed communication topology is proposed, and each node can reconstruct both the full state and unknown dynamics of the system. To achieve fixed-time stability, a Lyapunov function is elaborated, and based on this, sufficient conditions for the existence of the FxTDESO are established. Under time-invariant and time-varying disturbance, the observation errors can converge to the origin and a small region of the origin within a fixed time, respectively, where the upper bound of the settling time (UBST) is irrelevant to the initial conditions. Compared to the existing fixed-time distributed observers, the proposed observer can reconstruct both the unknown states and uncertain dynamics, and only the output of the leader and 1-dimensional output estimates from the neighboring nodes are needed in the observer design which effectively reduces the communication load. The paper also extends previous finite-time distributed extended state observer to the case of time-variant disturbance and eliminates the complex linear matrix equation assumption that guarantees the finite-time stability. Furthermore, the FxTDESO design for a class of high-order nonlinear systems is also discussed. Finally, simulation examples are conducted to demonstrate the effectiveness of the proposed observer.

Prescribed Performance Back-Stepping Tracking Control for a Class of High-Order Nonlinear Systems via a Disturbance Observer.

Due to the widespread presence of disturbances in practical engineering and widespread applications of high-order systems, this paper first pays attention to a class of high-order strict-feedback nonlinear systems subject to bounded disturbance and investigates the prescribed performance tracking control and anti-disturbance control problems. A novel composite control protocol using the technique of a disturbance observer-prescribed performance control-is designed using the back-stepping method. The disturbance observer is introduced for estimating and compensating for unknown disturbances in each step, and the prescribed performance specifications guarantee both transient and steady-state performance of the tracking error to improve the control performance and result in better disturbance rejection. Moreover, the technique of adding a power integrator is modified to tackle controller design problems for the high-order systems. The Lyapunov function method is utilized for rigorous stability analysis. It is revealed that while the control performance completely remains in the prescribed bound, all states in the closed-loop system are input-to-state stable, and the tracking error and the disturbances estimating error asymptotically converge to zero simultaneously. Then, the feasibility and effectiveness of the proposed control protocol are verified by a simulation result.

Finite-Time Robust Stabilization for a Class of High-Order Nonlinear Systems With Multiple Uncertainties and External Disturbances

Finite-Time Robust Stabilization for a Class of High-Order Nonlinear Systems With Multiple Uncertainties and External Disturbances

Asymptotical Control Strategy for a Class of High-Order Nonlinear Systems With Multiple Uncertainties

Asymptotical Control Strategy for a Class of High-Order Nonlinear Systems With Multiple Uncertainties

Adaptive Fuzzy Sliding Exact Tracking Control Based on High-Order Log-Type Time-Varying BLFs for High-Order Nonlinear Systems

This article investigates the adaptive fuzzy sliding exact tracking control problem of a class of high-order nonlinear systems with full-state constraints and mismatched external disturbances. To achieve exact tracking control, the upper bound of a composite polynomial is estimated, which is composed of approximation error, mismatched disturbance, and virtual control law and its upper bound estimated information is employed in the controller design. In this way, once the tracking error deviates from the origin, the corresponding adaptive fuzzy sliding exact tracking control mechanism will be activated to force it to slide along the origin, and then exact tracking control is achieved. Meanwhile, high-order log-type time-varying barrier Lyapunov functions are introduced to ensure that the full-state constraint is not violated. A 2-D high-order nonlinear system and an underactuated nonlinear benchmark system with weak coupling are considered to illustrate the characteristics of the control mechanism in simulation.

Finite-Time Adaptive Neural Control Scheme for Uncertain High-Order Systems with Input Nonlinearities and Unmodeled Dynamics

This paper proposes a novel finite-time adaptive neural control method for a class of high-order nonlinear systems with high powers in the presence of dead zone input nonlinearities and unmodeled dynamics. By utilizing prescribed performance functions and radial basis function neural networks, the tracking error and state errors are limited within the preassigned range in a finite time, which can be specified by the designer in advance according to the chosen the parameters of the novel prescribed performance functions. Nonlinear transformed error surfaces are designed to counteract the effects of dead zone input nonlinearities in nonlinear high-order systems with unknown system nonlinearities and unmodeled dynamics. Based on the Lyapunov theorem, the tracking errors are proven to converge into a preassigned set in a finite time previously specified by the novel prescribed performance function. Finally, simulation results demonstrate the effectiveness of the proposed method.

Continuous global tracking of a class high-order time-delay nonlinear systems

This paper deals with the problem of global practical tracking for a class of high-order nonlinear systems with time delay. The peculiarity of the system under study is that the degree of restriction on the upper limit of nonlinearity can be obtained in a continuous interval. By introducing a sign (signum) function and adding a generalized method for enabling the power integrator, as well as selecting the corresponding Lyapunov function, we create an adjustable and time-independent tracking controller that will dominate the time-delayed nonlinearity. All the closed system states obtained as a result of the developed controller are widely limited and ensure that the tracking error after the set time is sufficiently small. A numerical example is given to demonstrate the effectiveness and validity of the proposed design.

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.

Output Feedback Stabilization for a Class of Uncertain High-Order Nonlinear Systems

We investigate output feedback stabilization for a class of high-order nonlinear systems whose output function and nonlinear terms are unknown. First, a smooth state feedback control law is designed by adding a power integrator technique. Next, we design a high-order observer to estimate the unmeasurable state, and allocate gains of the observer one by one in an iterative way. Finally, a dynamic output compensator is achieved such that the closed-loop system converges to the equilibrium point quick. Two examples are provided to demonstrate the effectiveness of the proposed method.

Fixed-time stabilization for interconnected high-order nonlinear systems with dead-zone input and output constraint

This paper deals with the problem of fixed-time stabilization for a class of high-order nonlinear systems with time-varying output constraint (also known as p-normal form systems). Compared with the existing results, the order of the systems can be less than 1, which is more relaxed. Moreover, each subsystem is with the dead-zone input and interconnected nonlinearity. We design a new decentralized fixed-time controller based on the recursive design method by revamping the technique of adding a power integrator and using the tan-type barrier Lyapunov function. The proposed controller is also effective for the systems with asymmetric output constraints. Based on Lyapunov stability theory, it is proved that the decentralized controller can realize that the outputs are strictly constrained within predefined boundaries and all state variables converge to zero in a fixed time, where the bound of reaching time is independent of the initial conditions. Finally, simulation examples are given to illustrate the effectiveness of the proposed method.

Robust Stabilization of High-Order Nonlinear Systems With Unknown Sensitivities and Applications in Humanoid Robot Manipulation

This article is concerned with the improvement of robust control methodology and its application in stabilizing a class of high-order nonlinear systems with multiple unknown time-varying sensitivities, and discusses how to use the proposed control strategy on humanoid robot manipulation. The novel design approach successfully breaks through the limitation of the neural network technique; that is, state variables must be located in some compact sets. The remarkable feature of the systems under investigation lies in the presence of measurement sensitivities and higher powers, which makes the nonlinear systems essentially different from the related works. By reductio and the introduction of a modified tuning function, an appropriate controller is constructed to render that all the state variables belong to a predetermined bounded set. Finally, an example is provided to illustrate 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.

Output Tracking Control for High-Order Nonlinear Systems with Time Delay via Output Feedback Design

Design approach of an output feedback tracking controller is proposed for a class of high-order nonlinear systems with time delay. To deal with the time delays, an appropriate Lyapunov–Krasovskii the tracking analysis is ingeniously constructed, and an output feedback tracking controller is designed by using a homogeneous domination method. It is shown that the proposed output controller independent of time delay can make the tracking error be adjusted to be sufficiently small and render all the trajectory of the closed-loop system as bounded. An example is given to illustrate the effectiveness of the proposed method.

Adaptive Approximation-Based Tracking Control for a Class of Unknown High-Order Nonlinear Systems With Unknown Powers.

In this article, the problem of adaptive tracking control is tackled for a class of high-order nonlinear systems. In contrast to existing results, the considered system contains not only unknown nonlinear functions but also unknown rational powers. By utilizing the fuzzy approximation approach together with the barrier Lyapunov functions (BLFs), we present a new adaptive tracking control strategy. Remarkably, the BLFs are employed to determine a priori the compact set for maintaining the validity of fuzzy approximation. The primary advantage of this article is that the developed controller is independent of the powers and can be capable of ensuring global stability. Finally, two illustrative examples are given to verify the effectiveness of the theoretical findings.

Fuzzy Adaptive Fixed-time Sliding Mode Control with State Observer for A Class of High-order Mismatched Uncertain Systems

Using state observer has attracted a notable interest of researchers in control community to provide an on-line state estimator for control systems instead of measuring them physically by sensors which is costly, inaccurate, and easy to contaminate by noise. Some challenges ahead to design state observer in control systems are using estimated data by observer in the designed controller as well as the system stability analysis by using controller and observer simultaneously. This paper proposes Fuzzy Adaptive Fixed-time Sliding Mode Control (FAFSMC) technique for trajectory tracking of a class of high-order nonlinear systems with mismatched external disturbances and uncertainties. Meanwhile, the fixed-time state observer is proposed to incorporate with the controller for estimating the unmeasured even states (velocity) and providing on-line data in the controller. A proper candidate Lyapunov function is defined to verify the system global fixed-time stability by considering designed control law, state observer term, and adaptive law, simultaneously. The simulation results of three simulation examples, ship course system, two-link robotic manipulator, and three-link robotic manipulator, are carried out in Simulink/MATLAB to reveal the effectiveness of the proposed FAFSMC scheme compared with the other three conventional methods for solving trajectory tracking problem. Two performance criteria, Integral of the Square Value (ISV) and Integral of the Absolute value of the Error (IAE), are used to make a comprehensive comparison among the proposed FAFSMC method with state observer and the other three methods.

Global output tracking by state feedback for high-order nonlinear systems with time-varying delays

This paper focuses on the problem of global practical output tracking for a class of high-order non-linear systems with time-varying delays (via state feedback). Under mild growth conditions on the...

A unified approach to finite-time stabilization of high-order nonlinear systems with an asymmetric output constraint

The problem of finite-time stabilization for a class of high-order nonlinear systems (also known as p-normal form systems) with an asymmetric output constraint is investigated in this paper. A novel design approach is proposed by delicately revamping the technique of adding a power integrator with the introduction of a distinctive asymmetric barrier Lyapunov function and performing a skillful manipulation of sign functions. By using the present method, a continuous state feedback finite-time stabilizer can be recursively constructed while achieving the requirement of the asymmetric output constraint. The novelty of the proposed approach is that it is a unified manner that enables us to simultaneously tackle the problem of finite-time stabilization for high-order nonlinear systems with and without asymmetric output constraints, without changing the controller structure.