Class Of High-order Nonlinear Systems Research Articles

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.

Distributed Adaptive Control for Asymptotically Consensus Tracking of Uncertain Nonlinear Systems With Intermittent Actuator Faults and Directed Communication Topology.

In this article, we investigate the output consensus tracking problem for a class of high-order nonlinear systems with unknown parameters, uncertain external disturbances, and intermittent actuator faults. Under the directed topology conditions, a novel distributed adaptive controller is proposed. The common time-varying trajectory is allowed to be totally unknown by part of subsystems. Therefore, the assumption on the linearly parameterized trajectory signal in most literature is no longer needed. To achieve the relaxation, extra distributed parameter estimators are introduced in all subsystems. Besides, to handle the actuator faults occurring at possibly infinite times, a new adaptive compensation technique is adopted. It is shown that with the proposed scheme, all closed-loop signals are globally uniformly bounded and asymptotically output consensus tracking can be achieved.

Global regulation of high-order feedforward and non-feedforward systems with unknown time-varying delays in states and input

In this paper, the global regulation problem is considered for a class of high-order nonlinear systems with unknown time-varying delays. More specifically, the considered systems consist of a chain of power integrators with high-order nonlinearity and there are unknown input and state delays. From the system structural point of view, the high-order feedforward nonlinearity is further extended to include non-feedforward terms. In our controller design, our controller is a memoryless one which does not use any past input values such that any a priori information on time-varying delays is not needed. The global regulation of the controlled system is analyzed by using the Razumikhin theorem and adding a power integrator method.

Fast finite-time partial state feedback stabilization of high-order nonlinear systems with output constraint and dynamic uncertainties

This paper focuses on the problem of finite-time stabilization for a class of high-order nonlinear systems with output constraint and zero dynamics. The systems under investigation possess two remarkable features: the output is restricted in a pre-specified region arising from the demand of practical operation, and inherent nonlinearities include nonlinear growth rate of high-order and low-order together with unmeasurable dynamic uncertainties. This paper proposes a continuous controller by means of a new tangent function and a serial of nonnegative integral functions with sign functions, and the controller ensures the adjustability of convergent speed of system state, which is faster than the counterpart of traditional finite-time stabilizers. The novelty is attributed to a perspective to applying the fast finite-time stability in partial state feedback control design in the case when the output is restricted. Finally, a numerical example is presented to demonstrate the effectiveness of the theoretical result.

Global finite-time stabilisation of high-order nonlinear systems: a dynamic gain-based approach

ABSTRACTThis paper deals with finite-time stabilisation problem for a class of high-order nonlinear systems. By generalising a dynamic gain design method and adding a power integrator technique, a new state feedback controller is constructed by choosing an appropriate Lyapunov function. It is proved that the corresponding closed-loop system is globally finite-time stable by the constructed controller, and the proposed method can accelerate the convergent speed and decrease the settling time. Finally, a simulation example is given to verify the effectiveness of the proposed scheme.

Robust output feedback tracking control for a class of high-order time-delay nonlinear systems with input dead-zone and disturbances

This paper is concerned with the tracking control problem for a class of high-order nonlinear systems. Different from the related studies, the considered systems allow the existence of input dead-zone, external disturbances and polynomial growing conditions with time-varying delays. A new Lyapunov–Krasovskii functional is skillfully constructed and a robust output feedback tracking controller is designed by using a modified homogeneous domination method. It is guaranteed that all signals of the closed-loop system are bounded and the tracking error can converge to a compact domain which can be tuned sufficiently small. A simulation example is provided to show the validity of our control strategy.

Global fast finite-time partial state feedback stabilization of high-order nonlinear systems with dynamic uncertainties

This paper is concerned with the problem of finite-time stabilization for a class of high-order nonlinear systems with zero dynamic. As a significant feature, the systems considered suffer from both the unmeasurable dynamic uncertainties and inherent nonlinearities, including high-order and low-order nonlinear growth rates. On the basis of integral Lyapunov functions equipped with sign functions and the notion of input-to-state stability, a partial state feedback stabilizer is proposed to provide a faster finite-time state convergence compared to traditional finite-time one. The novelty of this paper lies in a distinct perspective to applying the concept of fast finite-time stability developed recently in partial state feedback control design, which has been previously regarded as a rather difficult problem.

Fixed‐time stabilisation for a class of high‐order non‐linear systems

The problem of fixed-time stabilisation for a class of high-order non-linear systems is studied. By introducing the manipulation of sign functions and revamping by adding a power integrator technique, a novel approach is proposed to construct a continuous stabiliser as well as a continuously differentiable Lyapunov function, which is crucial for proving fixed-time stability. The novelty of this study is the development of a systematic design method that provides a delicate solution to the problem of fixed-time stabilisation for high-order non-linear systems.

Global stabilization of high-order nonlinear systems under multi-rate sampled-data control

This paper studies the sampled-data control problem for a class of high-order nonlinear systems. Based on exact discrete-time equivalent model of the sampled-data system, a multi-rate sampled-data controller with the form of a power series expansion is designed to achieve the global asymptotic stability of the closed-loop system under some assumptions. Approximate solutions of the proposed controller are proved to be effective by a theoretical analysis. The results show that, compared with the emulated control scheme, the approximate controllers allow considering larger sampling periods and enlarge the domain of attraction for a given sampling period. Finally, a simulation example is given to show the effectiveness of the proposed control scheme.

A new approach to stabilisation of a class of nonlinear systems with an output constraint

ABSTRACTThis paper investigates the problem of state-feedback stabilisation for a class of high-order nonlinear systems with an output constraint. A novel tangent-type barrier Lyapunov function is first developed to cope with the output constraint. Then, by introducing the sign function and incorporating the developed tangent-type barrier Lyapunov function, the celebrated adding a power integrator technique is revamped to systematically design a continuous state feedback stabilising controller that prevents violation of the output constraint during operation. The novelty of this paper is the development of an unified design procedure, which can tackle the stabilisation task of the systems with/without the output constraint simultaneously.

Smooth control design for adaptive leader-following consensus control of a class of high-order nonlinear systems with time-varying reference and unknown control directions

In this paper, we investigate the distributed adaptive leader-following consensus control for high-order nonlinear multi-agent systems with a time-varying reference trajectory under directed topology, subjected to mismatched unknown parameters and unknown control directions. By introducing local estimators for the bounds of the reference trajectory and a filter for each agent, a new backstepping-based smooth distributed adaptive control protocol is proposed. Meanwhile, a Nussbaum-type function is applied to address the consensus control with unknown control directions. It is shown that global uniform boundedness of all the closed-loop signals and asymptotic output consensus tracking can be achieved. Simulation results are provided to verify the effectiveness of our scheme.

State feedback stabilization for nonlinear systems with more general high-order terms

This paper aims to solve the state feedback stabilization problem for a class of high-order nonlinear systems with more general high-order terms. Based on the backstepping design method and Lyapunov stability theorem, a state feedback controller is constructed to ensure that the origin of the closed-loop system is globally asymptotically stable. The efficiency of the state feedback controller is demonstrated by a simulation example.

Finite-time Stabilization with Output-constraints of A Class of High-order Nonlinear Systems

In this paper, the finite-time stabilization with output-constraint is investigated for a class of high-order nonlinear systems with the powers of positive odd rational numbers by constructing a Barrier Lyapunov function. First, sufficient conditions on characterizing the nonlinear functions of the considered systems are derived. Then, based on the technique of adding one power integrator, the global finite-time stabilizers of individual subsystems are systematically constructed to guarantee global finite-time stability with output constraints of the closed-loop nonlinear system. Finally, an example is provided to demonstrate the effectiveness of the proposed result.

Adaptive stabilization for a class of uncertain $${\textit{p}}$$ p -normal nonlinear systems via a generalized homogeneous domination technique

This paper investigates a generalized homogeneous adaptive stabilization method for a class of high-order nonlinear systems without controllable/observable linearizations. Based on a general approximated homogeneous function restraining hypothesis, a series of quasi-homogeneous adaptive virtual controllers are built. By modifying the homogenous domination approach, an inductive stability analysis as well as the guideline of update laws is carried out in an explicit way. Furthermore, based on the proposed design framework, the asymptotical and finite-time stabilization with the flexibility of tuning homogeneous degree are investigated. Numerical simulations and a real example are presented to demonstrate the effectiveness of the proposed method.

Fully Distributed Adaptive Consensus Control of a Class of High-Order Nonlinear Systems With a Directed Topology and Unknown Control Directions.

In this paper, we investigate the adaptive consensus control for a class of high-order nonlinear systems with different unknown control directions where communications among the agents are represented by a directed graph. Based on backstepping technique, a fully distributed adaptive control approach is proposed without using global information of the topology. Meanwhile, a novel Nussbaum-type function is proposed to address the consensus control with unknown control directions. It is proved that boundedness of all closed-loop signals and asymptotically consensus tracking for all the agents' outputs are ensured. In simulation studies, a numerical example is illustrated to show the effectiveness of the control scheme.

A Novel Error-Compensation Control for a Class of High-Order Nonlinear Systems With Input Delay.

A novel tracking error-compensation-based adaptive neural control scheme is proposed for a class of high-order nonlinear systems with completely unknown nonlinearities and input delay. In the tracking errors of existing papers, there exist the following difficulties: first, output curve always lags behind the desired trajectory, second, some big peak errors cause a decrease in tracking precision, and third, a big initial value of the modified tracking error can make the closed-loop system unstable. To tackle them, three corresponding error-compensation terms are constructed, including a prediction and compensation term, an auxiliary signal produced by the constructed auxiliary system, and a damping term. However, inequality amplification caused by high order will weaken the effectiveness of the proposed error-compensation scheme, and the control precision will decrease under an assumption that the lower bounds of the unknown control coefficients should be exactly known. To overcome aforementioned difficulties, in the derivation of the first virtual control law, the radial basis function neural network is used to approximate a hybrid term online constructed by unknown nonlinearities, a lumped control coefficient achieved by state transformation, and the dynamic of the proposed error-compensation terms and desired signal. Meanwhile, input delay is coped with a robust compensation signal constructed based on a finite integral of the past control values. Finally, it is proven that all the closed-loop signals are semiglobally uniformly ultimately bounded. Simulation results demonstrate the effectiveness of the proposed method.

A combined NN and dynamic gain-based approach to further stabilize nonlinear time-delay systems

This paper focuses on the state-feedback control problem for a class of high-order nonlinear systems with unknown time delay and control coefficients. Based on a novel dynamic gain-based backstepping technique and radial basis function neural network (RBF NN) approximation approach, the restrictions on high-order and nonlinearities are removed or further relaxed. Under these weaker conditions, a smooth state-feedback controller is skillfully constructed with only one adaptive parameter. In addition, the knowledge of time delay, NN nodes and weights is not necessary to be known a priori. It is proven that the designed controller can render the closed-loop system be semi-globally uniformly ultimately bounded. Finally, both practical and numerical examples are shown to demonstrate the effectiveness of the proposed scheme.

Adaptive stabilization control for high-order nonlinear time-delay systems with its application

This paper investigates the state-feedback stabilization problem in the smooth case for a class of high-order nonlinear systems with time delays. By generalizing a novel radial basis function neural network (RBF NN) approximation approach to high-order nonlinear systems, we successfully remove the power order restriction and the growth conditions on system nonlinearities. It should be pointed out that the knowledge of NN nodes and weights does not need to be known a priori and operate on-line, and the adaptive parameter is only one. Furthermore, without imposing any growth assumptions on system nonlinearities, we construct a smooth adaptive state-feedback controller which guarantees the closed-loop system to be semi-globally uniformly ultimately bounded (SGUUB). Finally, we apply the proposed scheme to a single-link robot system and a numerical example to demonstrate the effectiveness of the controller.