Global finite-time stabilization for switched stochastic nonlinear systems via output feedback

Global finite-time adaptive stabilization for nonlinear systems with multiple unknown control directions

This paper discusses the problem of global finite-time stabilization in probability for a class of stochastic high-order nonlinear systems whose drift and diffusion terms satisfy lower-triangular growth conditions. By adopting adding one power integrator technique and constructing twice continuous differential Lyapunov functions, a continuous state-feedback controller is recursively designed. Based on stochastic finite-time stability theorem, it is proved that the solution of the closed-loop system is finite-time stable in probability. Several simulation examples are given to illustrate the effectiveness of the proposed design procedure.

ABSTRACTThis paper considers the problem of global finite-time stabilisation by output feedback for a class of feedforward (upper triangular) nonlinear systems with input saturation. Based on the finite-time stability theorem, and by skillfully using the homogeneous domination approach and the nested saturation technique, a saturated output feedback controller is successfully constructed, which renders the origin of the closed-loop system globally finite-time stable. In simulation studies, a numerical example is illustrated to show the effectiveness of the control scheme. Moreover, the design strategy is successfully applied to solve the saturated finite-time control problem for vertical wheel on rotating table.

In this paper, the problem of global output feedback stabilization for a class of upper-triangular nonlinear systems with time-varying time-delay in the state is considered. The uncertain nonlinearities are assumed to be higher-order in the unmeasurable states. Based on the extended homogeneous domination approach, using a low gain observer in combination with controller, the delay-independent output feedback controller makes closed-loop system globally asymptotically stable under a homogeneous growth condition.

This paper addresses the problem of decentralized global stabilization by output feedback for a class of uncertain large-scale nonlinear systems. A new design method based on the homogeneous domination approach and finite-time stabilization technique is developed, which leads to global output feedback stabilization for large-scale uncertain nonlinear systems under a homogeneous growth condition. Firstly, a homogeneous observer and controller is constructed for the nominal system without the perturbing nonlinearities for each subsystem. Then, a scaling gain is introduced into the homogeneous observers and controllers to globally stabilize the uncertain nonlinear systems.

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This article focuses on global finite-time output feedback stabilization for uncertain nonlinear systems with unknown measurement sensitivity. The existence of the continuous measurement error resulting from limited accuracy of sensors invalidates the existing design strategies depending on the use of the precise output in the construction of an observer, which highlights the contribution of this article. Essentially, different from related works, we propose a new finite-time convergent observer by avoiding the use of the information on nonlinearities. By combining the homogeneous domination with the addition of a power integrator method, an output feedback controller composed of multiple nested sign functions is successfully developed. Finally, the effectiveness of the presented scheme is exhibited by a numerical example.

The problem of global finite-time stabilization for p-normal nonlinear systems subject to uncertain time-varying control coefficients and vanishing nonlinear uncertainties without homogeneous growth restriction is investigated in this paper. By virtue of the technique of homogeneous domination, a new dual-layer adaptive approach is presented to address the uncertainties and nonlinearities of the system. For one layer of the adaptive mechanism, a nonlinear adaptive parameter estimator is proposed to reconstruct the upper bounds of the unknown uncertainties. For the other, an explicit construction approach of a new adaptive dynamic gain mechanism is presented for the first time to cope with the uncertain time-varying control coefficients of the p-normal nonlinear systems. It is shown that the global boundedness of the systems under consideration is guaranteed by the presented approach, and in addition the time taken to converge to the equilibrium is rendered to be finite time.

This paper addresses the problem of global output feedback stabilization for a class of upper-triangular systems with delay in the input. By using a linear observer, a linear dynamic output feedback control law is explicitly constructed to globally stabilize the system. To dominate the nonlinear perturbing terms and handle the case with a larger input delay, a tunable scaling gain is introduced to the controller by using a coordinates change. With the help of appropriate Lyapunov-Krasoveskii functional and feedback domination approach, it is shown that upper-triangular nonlinear system with arbitrary large input delay can be globally stabilized by the proposed output feedback controller with appropriate gains.

Robust finite-time output feedback control of perturbed double integrator

This paper considers the problem of global stabilization by output feedback for a class of uncertain nonholonomic systems. By combining the output feedback domination design and nonsmooth change of coordinates together, we explicitly construct a simple output feedback controller, which can universally stabilize a whole family of uncertain nonholonomic systems. The effectiveness of the proposed approach is illustrated by solving the output feedback stabilization for wheeled mobile robots.

This paper investigates the problems of finite-time stability and finite-time stabilization for nonlinear quadratic systems with jumps. The jump time sequences here are assumed to satisfy some given constraints. Based on Lyapunov function and a particular presentation of the quadratic terms, sufficient conditions for finite-time stability and finite-time stabilization are developed to a set containing bilinear matrix inequalities (BLIMs) and linear matrix inequalities (LMIs). Numerical examples are given to illustrate the effectiveness of the proposed methodology.

Global stabilization of a class of partially known nonnegative systems

ABSTRACTThis paper is concerned with the problem of global finite-time control for switched nonlinear systems whose nonlinear terms satisfy homogenous growth conditions. At first, we design homogenous output feedback controllers for nominal switched nonlinear systems by adding a power integrator method. Then, we employ the homogeneous domination approach to scale homogeneous observers and controllers to render switched nonlinear systems with lower-triangular homogenous growth condition globally finite-time stable. Finally, the proposed control method can be extended to switched nonlinear systems satisfying with upper-triangular homogeneous growth condition. Two examples are provided to demonstrate the effectiveness of the proposed control scheme.

H finite-time control for switched nonlinear discrete-time systems with norm-bounded disturbance