Yuqiang Wu

Finite-time tracking controller design for nonholonomic systems with extended chained form

A design scheme of the finite-time tracking controller is given for the nonholonomic systems with extended chained form. The relay switching technique and the terminal sliding mode control scheme with finite-time convergence are used to the design of the controller. The global stability is guaranteed and the system states accurately track the states of the reference model in finite time. The simulation results for two physical models of a knife-edge and a wheeled mobile robot have demonstrated the effectiveness of the proposed algorithm.

Global asymptotic stability controller of uncertain nonholonomic systems

Abstract This paper proposes a global asymptotic stability controller for a class of nonholonomic systems with nonlinear uncertainties. Different from the existing results, we construct a new nonlinear switching law employing the full states feedback, which renders the origin to be a solution of the closed-loop system. With this switching control scheme, the finite time escape phenomenon is avoided. We apply the definition of Lyapunov stability to the stability analysis of the discontinuous closed-loop system, and achieve the global asymptotic stability for the system in our class. The simulation results testify to the effectiveness and the robust features of the developed control approach.

Global finite-time stabilisation for a class of stochastic high-order time-varying nonlinear systems

ABSTRACT In this paper, the problem of global finite-time stabilisation by state feedback is investigated for a class of stochastic high-order nonlinear systems with time-varying nonlinearities. Based on the generalised stochastic Lyapunov theorem on finite-time stability, and by skillfully using the method of adding a power integrator, a continuous state feedback controller is successfully constructed to guarantee that the closed-loop system is globally finite-time stable in probability. Finally, several simulation examples are provided to illustrate the effectiveness of the proposed method.

Further results on global stabilisation and tracking control for underactuated surface vessels with non-diagonal inertia and damping matrices

This paper studies the global uniform stabilisation and exponential tracking problems for an underactuated ship with non-diagonal inertia and damping matrices. For the synthesis of the controller, first, the underactuated ship in question is converted into two cascade connected subsystems by using state and input transformations. Two constructive backstepping design schemes are developed, respectively, to get around the stabilisation burden and tracking burden. Along the way of proving stability analysis, it is shown that the designed control strategies can guarantee the global uniform asymptotic convergence of the state to the origin and global exponential convergence to the desired reference trajectory. Simulation results are provided to demonstrate the effectiveness of the proposed control methodologies.

Global stabilisation for a class of more general high-order time-delay nonlinear systems by output feedback

This paper addresses the problem of global stabilisation by output feedback for a class of high-order time-delay nonlinear systems with more general uncertainties, which cover both high-order and low-order nonlinearities. By introducing sign function and necessarily modifying the homogeneous domination approach, an output feedback controller is successfully constructed to guarantee the global asymptotic stability of the resulting closed-loop system. Due to the versatility of the homogeneous domination approach and homogeneous properties, the proposed method is also utilised to the control design of upper-triangular systems.

Fixed-time regulation control of uncertain nonholonomic systems and its applications

ABSTRACT Stabilisation of nonholonomic systems is of great practical importance to the industry. Moreover, fixed-time control is more comfortable than finite-time control since the upper bound of the settling time is independent on the initial system states in a fixed-time control issue and therefore can be estimated in advance. Inspired by the aforementioned two points, we consider the fixed-time stabilisation for a kind of uncertain nonholonomic systems subject to perturbations in this paper. A globally fixed-time stabilisation strategy is proposed by taking advantage of adding one power integrator technique and switching ideal. Under the designed controllers, all states can be regulated to zero before a fixed time and kept zero afterwards. As an application, the fixed-time stabilisation for a class of dynamic nonholonomic systems is also addressed by the combined method of adding one power integrator and terminal sliding-mode control. Three mechanical and academic examples are provided to show the flexibility and effectiveness of the assumptions and control algorithms.

Partial-state feedback control of high-order cascade systems with unknown control direction

Without a priori knowledge of the signs of control directions, this paper investigates the robust asymptotic regulating problem for a class of high-order non-linear cascade systems with both dynamic and static uncertainties. Under some weaker assumptions, a partial-state feedback controller is proposed which ensures that all the signals of closed-loop system are globally uniformly bounded and all states can be regulated to the origin. The design procedure is illustrated through an example.

Finite-time output feedback stabilisation of chained-form systems with inputs saturation

ABSTRACT This paper investigates the problem of finite-time stabilisation by output feedback for a class of non-holonomic systems in chained form with input saturation. Rigorous design procedure for saturated output feedback control is presented by using the homogeneous domination approach and the nested saturation technique. Together with a novel switching control strategy, the designed controller renders that the states of closed-loop system are regulated to zero in a finite time. A simulation example is provided to illustrate the effectiveness of the proposed approach.

Global robust output regulation control for cascaded nonlinear systems using the internal model principle

This article considers the global robust output regulation problem via output feedback for a class of cascaded nonlinear systems with input-to-state stable inverse dynamics. The system uncertainties depend not only on the measured output but also all the unmeasurable states. By introducing an internal model, the output regulation problem is converted into a stabilisation problem for an appropriately augmented system. The designed dynamic controller could achieve the global asymptotic tracking control for a class of time-varying reference signals for the system output while keeping all other closed-loop signals bounded. It is of interest to note that the developed control approach can be applied to the speed tracking control of the fan speed control system. The simulation results demonstrate its effectiveness.

Adaptive stabilization of uncertain nonholonomic systems by output feedback

In this paper, an adaptive output feedback control strategy is presented for a class of nonholomic systems in chained form with drift nonlinearity uncertainties. The control law is developed using the systematic strategy combines the input-state-scaling technique with the so-called backstepping techniques. In particular, a dynamic output feedback controller for general case of uncertain chained system is developed with a filter of observer gain. A novel switching control strategy is employed to get around the smooth stabilization issue (difficulty) associated with nonholonomic systems when the initial state of system is known. The objective is to design robust nonlinear adaptive output feedback laws such that the closed-loop systems are globally exponentially stable. The simulation example demonstrates the efficiency and robust features of the proposed method.