Fixed-Time Adaptive Neural Network Tracking Control for Output-Constrained High-Order Systems Using Command Filtered Strategy

This paper proposes a fixed time adaptive neural command filtered controller for a category of high-order systems based on adding a power integrator technique. Different from existing research, the presented controller has the following distinguishing advantages: i) fixed-time control framework is extended to the tracking control problem of high-order systems. ii) the error compensation mechanism eliminates filter errors that arise from dynamic controllers. iii) growth assumptions about unknown functions are relaxed with the help of adaptive neural networks. iv) more general systems: the developed controller can apply to high-order systems subject to uncertain dynamics, unknown gain functions and asymmetric constraints. Stability analysis shows that all states are semi-globally bounded, and the convergence rate of tracking error is independent of initial conditions. The main innovation of our work is that the presented controller considers simultaneously filter errors, fixed-time convergence, growth conditions and asymmetric output constraint for the tracking control issue of high-order systems. Finally, the simulation results validate the advantages and efficacy of the developed control scheme.

Adaptive output feedback controller design for high-order stochastic nonlinear systems with uncertain output function and unknown growth rates

This paper concentrates on the adaptive output feedback controller design for a class of high-order stochastic nonlinear systems(SNSs) with uncertain output function. Firstly, a homogeneous output feedback controller for the nominal system is designed through the technique of adding a power integrator. Secondly, a well-designed dynamic gain is introduced into the controller to ensure the original SNSs globally asymptotically stable(GAS) in probability. Besides, the proposed control strategy can be also extended to upper-triangular SNSs. Finally, two numerical examples illustrate the effectiveness of the proposed method.

Nonsingular Global Fixed-Time Stabilization for Nonlinear Systems

Since existing results about fixed-time stabilization are only applied to strict feedback systems, this paper investigates the nonsingular fixed-time stabilization of more general high-order nonlinear systems. Based on a novel concept named coordinate mapping of time domain, a control method is first proposed to transform the nonsingular fixed-time convergence problem into the finite-time convergence problem of a transformed time-varying system. By extending the existing, adding a power integrator technique into the considered time-varying system, a periodic controller is constructed to stabilize the original system in fixed time. The results of simulations verify the effectiveness of the proposed method.

A State-scaling Design for Prescribed-time Stabilization of High-order Nonlinear Systems with Input Quantization

This article considers global stabilization problem for a kind of uncertain high-order nonlinear systems (HONSs). Two distinct characteristics of this study are that the considered system possesses the input-quantized actuator, and the prescribed time convergence of the system states is wanted. To address these, a novel state-scaling transformation (SST) is firstly introduced to convert the aboriginal prescribed-time stabilization (PTS) to the asymptotic stabilization of the transformed one. Then, under the new framework of equivalent transformation, a quantized state feedback controller that achieves of the performance requirements is developed with the aid of the technique of adding a power integrator (API). Finally, simulation results of a liquid-level system are provided to confirm the efficacy of the proposed approach.

Adaptive output feedback control for a class of uncertain stochastic nonlinear systems

This article concentrates on the output feedback controller design for a class of stochastic nonlinear systems with unknown homogeneous growth rates. First, a full-order observer is proposed coupling with a dynamic gain so as to obtain system state estimates. Then, an adaptive output feedback controller is put forward by the homogeneity theory and adding a power integrator technique. Combined with the stochastic Barbalat’s lemma, the signals of the closed-loop system are demonstrated to be bounded and all the system states are proved to converge to the origin in probability. Besides, the results are also expanded to the controller design of upper-triangular stochastic nonlinear system. Two simulation results indicate usefulness of the designed control algorithm.

Fixed-time trajectory tracking control for multiple nonholonomic mobile robots

This paper investigates the fixed-time trajectory tracking control for a group of nonholonomic mobile robots, where the desired trajectory is generated by a virtual leader, the leader’s information is available to only a subset of the followers, and the followers are assumed to have only local interaction. According to fixed-time control theory and adding a power integrator technique, distributed fixed-time tracking controllers are developed for each robot such that all states of each robot can reach the desired value in a fixed time. Moreover, the settling time is independent of the system initial conditions and only determined by the controller parameters. Simulation results illustrate and verify the effectiveness of the proposed schemes.

A Novel Approach to Fixed-Time Stabilization for a Class of Uncertain Second-Order Nonlinear Systems

This paper is concerned with the problem of fixed-time stabilization for a class of uncertain second-order nonlinear systems. By delicately introducing extra manipulations in the feedback domination and revamping the technique of adding a power integrator, a new approach is developed, by which a state feedback controller, together with a suitable Lyapunov function, which is critical for verifying fixed-time convergence, can be explicitly organized to render the closed-loop system fixed-time stable. The major novelty of this paper is attributed to a subtle strategy that offers a distinct perspective in controller design as well as stability analysis in the problem of fixed-time stabilization for nonlinear systems. Finally, the proposed approach is applied to the attitude stabilization of a spacecraft to demonstrate its merits and effectiveness.

Finite-time attitude stabilization of an output-constrained rigid spacecraft

This article concentrates on the study of finite-time attitude stabilization for a rigid spacecraft with output constraints. The dynamics of the spacecraft are expressed by modified Rodrigues parameters, so that the singularity of covariance matrix owing to quaternion’s redundancy is eliminated. Based on the backstepping technique in combination with adding a power integrator technique, the attitude stabilization control law is constructed. Rigorous mathematical proof shows that the closed-loop system is finite time stable and all the outputs remain bounded by using a barrier Lyapunov function technique. The effectiveness of the proposed finite-time stabilization scheme is verified by a simulation example.

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.

Distributed finite-time tracking for multiple uncertain mechanical systems with dead-zone input and external disturbances

This paper addresses the distributed finite-time tracking problem for multiple uncertain mechanical systems with dead-zone input and external disturbances. An observer-based adaptive finite-time consensus protocol is designed, which consists of two steps. Firstly, distributed observers are developed such that all the mechanical systems can obtain the leader’s state in finite settling time. Then, based on backstepping method and adding a power integrator technique, the finite-time consensus protocol and appropriate adaptive laws are designed to track the estimated leader’s state. Rigorous proofs show that the tracking errors between each mechanical system and the leader can converge to a small neighborhood of origin in finite time despite the presence of dead-zone nonlinearity and external disturbances. Finally, simulation example is provided to demonstrate the effectiveness of the proposed scheme.