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.

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.

Finite-time control of uncertain time-varying systems in p-normal form

This paper addresses a finite-time regulation problem for time-varying nonlinear systems in p-normal form. This class of time-varying systems includes a well-known lower-triangular system and a chain of power integrator systems as special cases. No growth condition on time-varying uncertainties is imposed. The control law can guarantee that all closed-loop trajectories are bounded and well defined. Furthermore, all states converge to zero in finite time.

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.

Global State-Feedback Control for Switched Nonlinear Time-Delay Systems via Dynamic Gains

In this paper, the problem of global state-feedback control is investigated for a class of switched nonlinear time-delay systems. In order to obtain a less-conservative common dynamic gain update law across subsystems, we construct different dynamic gain update laws for individual subsystems. Based on multiple Lyapunov function approach and adding one power integrator technique, the delay-independent controllers for all subsystems and a proper switching law are designed to guarantee that the states of the switched nonlinear time-delay systems can be globally asymptotically to the origin; meanwhile, all the signals of the closed-loop system are bounded. Finally, an example is provided to demonstrate the effectiveness of the proposed method.

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.