Finite-time state-feedback control for a class of stochastic high-order nonlinear systems

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

This paper presents a new Lyapunov theorem on almost surely finite-time stability for stochastic nonlinear systems with Markovian switching. Unlike the work in [3] that consider finite-time stability and stabilisation of conventional stochastic differential equation (SDE) systems, this paper aims to propose a weaker finite-time stability theory for a more general class of SDE systems with Markovian switching. A lemma is presented to discuss conditions that ensure the existence of a unique strong solution for such SDE systems with Markovian switching. Extended Comparison Principle and Bihari's inequality are derived, which relaxes some previous conditions and play an important role in the proof of the new Lyapunov theorem. Weaker conditions are proposed to ensure finite-time stability in probability one with supportive examples. Two simulation examples are given to illustrate the theoretical analysis.

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

This paper investigates the problem of the global stabilization via state feedback and adaptive technique for a class of high-order stochastic nonlinear systems with more uncertainties/unknowns. First of all, two stochastic stability concepts are slightly extended to allow the systems with more than one solution. To solve the stabilization problem, a lot of substantial technical obstacles should be overcome since the presence of severe uncertainties/unknowns and stochastic noise. By introducing the appropriate control Lyapunov function and suitable adaptive updated law for an unknown design parameter, and using the method of adding a power integrator, an adaptive continuous (nonsmooth) state feedback controller without overparameterization is successfully designed, which guarantees that the closed-loop states are bounded and the original system states eventually converge to zero, both with probability one.

Global stabilization of stochastic high-order feedforward nonlinear systems with time-varying delay

This paper investigates the problem of finite-time state feedback stabilization for nonholonomic mobile robot with stochastic disturbance in the forward velocity. First of all, an appropriate state/input transformation is introduced to convert the mentioned control model into stochastic nonholonomic system in chain form. Then, by using stochastic finite-time stability theorem and the method of adding a power integrator, a state feedback controller is obtained. Based on switching strategy to eliminate the phenomenon of uncontrollability, the proposed controller can guarantee that the closed-loop system is globally finite-time regulated at origin in probability. A simulation example is finally provided to demonstrate the validness of the proposed approach.

Traditional Lyapunov stability theory cannot directly apply to constrained stochastic nonlinear systems when using barrier Lyapunov functions due to their inherent lack of radial unboundedness. This article presents a novel approach to establishing finite-time stability for such systems by employing Lyapunov functions. The proposed stability analysis relies on a time-varying gain function that remains uniformly bounded. This approach ensures that the system achieves finite-time stability with an arbitrarily prescribed upper bound on the settling time, thereby effectively avoiding the unbounded controller gain problem. The resulting stability is further extended to the finite-time state-feedback control for strict-feedback stochastic nonlinear systems with output constraints. Simulation studies validate the effectiveness of the proposed control scheme.

This paper addresses the problem of state feedback control for a class of stochastic high-order feedforward nonlinear systems with multiple time-varying delays. A distinct property of the system to be investigated is that the control coefficients are not restricted to 1. By introducing the sign function and the adding one power integrator, a delay-independent state feedback controller is constructed. By Lyapunov-Krasovskii theorem and homogeneous domination approach, the global stochastic asymptotic stability of the closed-loop system under the above-mentioned controller is proved. Finally, a simulation example is given to illustrate the effectiveness of the results of this paper.

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

The homogeneous domination approach is introduced to solve the state feedback stabilization problem for stochastic high-order nonlinear systems with time-varying delay. Under the weaker conditions on the drift and diffusion terms, by using the homogeneous domination approach and solving several troublesome obstacles in the design and analysis procedure, a state feedback controller is constructed to render the closed-loop system globally asymptotically stable in probability.

On Stochastic Finite-Time Stabilization with Continuous State-Feedback Controllers

This paper considers the global asymptotic stabilization problem for a class of stochastic feedforward nonlinear time-delay systems. By extending the homogeneous domination approach to stochastic system, a state-feedback controller is designed such that the closed-loop system is globally asymptotically stable in probability.

The finite-time stabilization and robust control of stochastic nonlinear systems was discussed in this paper. First, by transforming the considered system to its equivalent Hamiltonian system, we showed that the stochastic dissipative Hamiltonian system was finite-time stable in probability if the Hamiltonian function and internal damping matrix possessed some structures. Then, we utilized the energy shaping and damping injection techniques to reformulate the internal structures and Hamiltonian function of the stochastic Hamiltonian system and constructed a finite-time stabilization controller. Finally, a robust finite-time controller was put forward for uncertain stochastic nonlinear systems by using the Hamiltonian function to construct a solution of Hamiltonian-Jacobi Inequality. Numerical simulations results demonstrated the effectiveness of the proposed stabilization and robust stabilization methods.

The finite-time stabilization for stochastic high-order nonlinear systems is considered in this paper using output feedback. The power orders in the system nonlinearities are relaxed to be rational number greater than one. A new constructive output-feedback, finite-time controller is designed based on a finite-time observer together with the homogeneous domination. The stochastic finite-time stability analysis is given rigorously for the closed-loop stochastic system.

Predefined-time stabilization of stochastic nonlinear systems with application to UAVs