Stabilization Of Stochastic Nonlinear Systems Research Articles

Event-triggered predictive control of nonlinear stochastic systems with output delay

In this paper, we focus on the stabilization of nonlinear stochastic systems with output delay. Based on the predictive scheme and event-triggering mechanism (ETM), a novel event-triggered predictive control is proposed to exponentially stabilize such stochastic systems. Moreover, this novel control law allows non-uniform sampled measurements and large delays involved in the output. Simultaneously, the control input error induced by ETM is considered and a positive lower bound on the inter-event times is obtained. Finally, an illustrative example is given to demonstrate the obtained results.

Output-Feedback stabilization for stochastic nonlinear systems with Markovian switching and time-varying powers.

This paper investigates the output-feedback stabilization for stochastic nonlinear systems with both Markovian switching and time-varying powers. Specifically, by developing a novel dynamic gain method and using the Itô formula of Markovian switching systems, a reduced-order observer with a dynamic gain and an output-feedback controller are designed. By using advanced stochastic analysis methods, we show that the closed-loop system has an almost surely unique solution and the states are regulated to the origin almost surely. A distinct feature of this paper is that even though there is no Markovian switching, our design is also new since it can deal with nonlinear growth rate, while the existing results can only deal with constant growth rate. Finally, the effectiveness of the design method is verified by a simulation example.

Adaptive Fast Finite-Time Fuzzy Control of Stochastic Nonlinear Systems

This article focuses on the adaptive fast finite-time tracking control for a class of stochastic nonlinear systems. To begin with, an adequate qualification is provided for the practically fast finite-time stability. Then, based upon this adequate qualification, a new adaptive fuzzy control scheme is presented. Due to the stochastic disturbance, criteria of the existing fast finite-time stability cannot be applied to the analysis of the stability of stochastic nonlinear systems. To solve this issue, based on Lemma 6, an original criterion of the fast finite-time stability is constructed first in Lemma 7 by using the theorem of the integral mean value. Meanwhile, it would have a huge impact on the analysis of the fast finite-time stability for stochastic nonlinear systems. Finally, a simulation example is carried out for evaluating the validity of the main result.

Fixed‐time stability of stochastic nonlinear systems and its application into stochastic multi‐agent systems

Fixed‐time stability of stochastic nonlinear systems and its application into stochastic multi‐agent systems

Adaptive Finite-Time Neural Control for a Class of Stochastic Nonlinear Systems With Known Hysteresis

This manuscript considers the finite time adaptive neural tracking control problem for a class of the nonstrict-feedback stochastic nonlinear systems with Bouc-Wen hysteresis input. During the design process, a Bouc-Wen model is first adopted to obtain the input hysteresis phenomenon. By fusion with the backstepping technique and the neural network approximation capability, the unknown nonlinearities are coped with, a constructive finite time adaptive neural network control strategy is proposed. Furthermore, the finite-time mean square stability of stochastic nonlinear systems is proved, and at last the effectiveness of the proposed control strategy is validated by the simulations.

Adaptive finite‐time stabilization of stochastic nonlinear systems with the powers of positive odd rational numbers

SummaryIn this paper, we give some new results on finite‐time stabilization for stochastic nonlinear systems whose powers of integrators are all positive odd rational numbers (ie, numerators and denominators of the powers are all positive odd integers) but not necessary only high order or low order. By adopting new conditions on drift and diffusion terms, Lyapunov function, and controller design method, a state feedback controller is designed to guarantee stochastic nonlinear systems finite‐time stable in probability. Moreover, when unknown parameters exist in systems, we give the adaptive finite‐time state feedback controller. Numerical examples demonstrate the effectiveness of the proposed results.

Finite-Time Fuzzy Control of Stochastic Nonlinear Systems.

This paper studies the finite-time stabilization of a class of stochastic nonlinear systems. Different from functions which are necessarily known in the conventional finite-time control of nonlinear systems, the nonlinear functions can be completely unknown in this paper. By applying fuzzy-logic systems to approximate the unknown nonlinearities, a novel adaptive finite-time control strategy is proposed. However, due to the existence of approximation errors, the existing finite-time stability criterion cannot be used to analyze the stability of stochastic nonlinear systems. To deal with this difficulty, a finite-time stability criterion, by utilizing the mean value theorem of integrals, is first established in Lemma 5, which plays a significant role in the finite-time stability analysis of stochastic nonlinear systems. Then, the finite-time mean square stability of a stochastic nonlinear system is proved by combining Lemma 3 with Jensen's inequality.

Generalized Lyapunov criteria on finite-time stability of stochastic nonlinear systems

This paper considers the problem of finite-time stability for stochastic nonlinear systems. A general Lyapunov theorem of stochastic finite-time stability is proposed, and an important corollary is obtained. Some comparisons with the existing results are also given. This theorem not only generalizes the classical stochastic finite-time theorem, but also somewhat shows that Brownian noise takes an active role in stochastic finite-time stability. In addition, more general conditions on stochastic finite-time stability via multiple Lyapunov functions are given to further relax the constraint of the differential operator LV. Moreover, with the help of this criterion, it shows that an unstable deterministic system can even be finite-time stabilized by Brownian noise. Some concrete examples are constructed to show the significant features of the proposed results, and simulations are presented to verify the theoretical analysis.

Adaptive finite-time control of stochastic nonlinear systems with actuator failures

This paper investigates a finite-time tracking control of stochastic nonlinear systems with actuator failures. As the nonlinearities and actuator failures are completely unknown, the existing control methods are unavailable. By applying an approximation property of fuzzy logic systems, an adaptive finite-time control strategy is presented. Since the existing finite time stability criterion can not deal with the finite time control under the effect of approximation error, Lemma 5 is first established. Under the proposed scheme, the actuator failures are compensated successfully, and the finite-time tracking performance and stability of stochastic nonlinear system are assured. Based on Lemma 5 and Jessen's inequality, the finite-time stability of stochastic nonlinear systems is proved.

Global output‐feedback stabilization for stochastic nonlinear systems: A double‐domination approach

SummaryThis paper is concerned with global stabilization via output feedback for a class of stochastic nonlinear systems with time‐varying continuous output function. Under linear growth conditions, a new double‐domination method is proposed for the first time to construct an output‐feedback stabilizing controller. Different from the related results, the design of the observer is performed without using the information on the output function and nonlinearities. This paper also provides a viewpoint at the feedback stabilization to eliminate the continuous measurement error originating from inaccurate detection of system state. A simulation example is presented to demonstrate the effectiveness of control strategy.

Stabilization of nonlinear stochastic systems without unforced dynamics via time--varying feedback

Stabilization of nonlinear stochastic systems without unforced dynamics via time--varying feedback

On Problem of Stability in Probability for "Partial" Equilibrium Positions of Nonlinear Stochastic Systems

The stability problems naturally arise in applications either from the requirement of proper performance of a system or in assessing system capability. In addition, a lot of actual (or desired) phenomena can be formulated in terms of these problems and be analyzed with these problems taken as the basis. The following multiaspect phenomena and problems can be indicated: adaptive stabilization; spacecraft stabilization (especially stabilization by rotors); drift of the gyroscope axis; Lotka-Volterra ecological principle, e.t.c. Also very effective is the approach to the problem of stability with respect to all variables based on preliminary analysis of stability. The article studies the problem of stability for nonlinear stochastic systems of differential equations Ito: stability with respect to a part of the variables in probability of partial zero equilibrium position. Initial perturbations of variables that do not define the given equilibrium position can be large (belonging to an arbitrary compact set) with respect to one part of the variables and arbitrary with respect to their other part. A conditions of stability of this type are obtained in the context of a stochastic analog of the Lyapunov functions method, which generalize a number of existing results. Example is given. The problem of unification of process of studying stability problems of stationary and non-stationary nonlinear stochastic systems of differential equations is also discussed.

A new integral sliding mode design method for nonlinear stochastic systems

Recently, several integral sliding mode control (ISMC) methodologies have been put forward to robust stabilization of nonlinear stochastic systems depicted by T–S fuzzy models. However, these results employ very restrictive assumptions on system matrices, which impose a great limitation to real applications. This paper aims to remove these assumptions and present a new ISMC method for fuzzy stochastic systems subjected to matched/mismatched uncertainties. To this end, a novel fuzzy integral sliding manifold function is adopted such that the matched uncertainties are completely rejected while the mismatched ones will not be enlarged during the sliding mode phase. Sufficient conditions are derived to ensure the stochastic stability of the closed-loop system under sliding motion. A fuzzy sliding mode controller is further presented to maintain the states of fuzzy stochastic system onto the predefined fuzzy manifold in the presence of uncertainties. The effectiveness and benefit of the developed new method are demonstrated by the inverted pendulum system.

Estimation of Sampling Period for Stochastic Nonlinear Sampled-Data Systems With Emulated Controllers

This note focuses on determining the value of the maximum allowable sampling period (MASP) that guarantees the stability of stochastic nonlinear sampled-data systems with emulated controllers. Two methods are proposed to compute MASP, one based on sufficient Lyapunov-like conditions on stabilization of stochastic nonlinear systems in mean square and the other from applying Barbalat's Lemma. Comparison studies are made and illustrated for the two methods by a numerical example.

Path-Wise Bounds and iISS of Nonlinear Systems Exposed to Global Stochastic Noise

This paper peruses path-wise bounds, integral input-to-state stability and integral noise-to-state stability for stochastic nonlinear systems and proposes their Lyapunov-type characterizations. The characterizations are utilized to develop small-gain criteria to verify stability of interconnected systems. In contrast to preceding results, the developments allow stochastic noise to be active globally in the state space. The obtained criteria are made parallel to deterministic ones by resolving fundamental issues arising from stochastic noises.

Finite‐time stabilization of stochastic nonlinear systems with SiISS inverse dynamics

SummaryThis paper investigates the finite‐time control problem for a class of stochastic nonlinear systems with stochastic integral input‐to‐state stablility (SiISS) inverse dynamics. Motivated by finite‐time stochastic input‐to‐state stability and the concept of SiISS using Lyapunov functions, a novel finite‐time SiISS using Lyapunov functions is introduced firstly. Then, by adopting this novel finite‐time SiISS small‐gain arguments, using the backstepping technique and stochastic finite‐time stability theory, a systematic design and analysis algorithm is proposed. Given the control laws that guarantee global stability in probability or asymptotic stability in probability, our design algorithm presents a state‐feedback controller that can ensure the solution of the closed‐loop system to be finite‐time stable in probability. Finally, a simulation example is given to demonstrate the effectiveness of the proposed control scheme. Copyright © 2017 John Wiley & Sons, Ltd.

A Tool for the Global Stabilization of Stochastic Nonlinear Systems

This technical note investigates the robust global stabilization problem for nonlinear systems subject to dynamic and stochastic disturbance, from the perspective of stochastic input-to-state stability. A new stochastic gain assignment method is developed. This method can be combined with the nonlinear small-gain theorem to design partial-state feedback controllers for stochastic nonlinear systems. A numerical example is given to illustrate the effectiveness of the proposed method.

Stabilization of nonlinear stochastic systems without unforced dynamics via time-varying feedback

In this paper we give sufficient conditions under which a nonlinear stochastic differential system without unforced dynamics is globally asymptotically stabilizable in probability via time-varying smooth feedback laws. The technique developed to design explicitly the time-varying stabilizers is based on the stochastic Lyapunov technique combined with the strategy used to construct bounded smooth stabilizing feedback laws for passive nonlinear stochastic differential systems. The interest of this work is that the class of stochastic systems considered in this paper contains a lot of systems which cannot be stabilized via time-invariant feedback laws.

Robust reliable control of uncertain nonlinear stochastic systems subject to actuator fault

This paper addresses the issue of robust reliable stabilization for a class of uncertain nonlinear stochastic systems with both discrete and distributed time-varying delays and possible occurrence of actuator faults. By constructing a new Lyapunov functional and using linear matrix inequality technique, a new set of sufficient conditions is established for the stochastic stability of the uncertain nonlinear stochastic systems. Then, sufficient conditions are obtained for the solvability of the robust stabilization problem via robust reliable controller. More precisely, the derived control law guarantees the robust stabilization of nonlinear stochastic systems in the presence of known actuator failure matrix and uncertainties. Further, the results are extended to study the stabilization of stochastic systems with unknown actuator failure matrix. Moreover, the obtained criteria are formulated in terms of LMIs and also the reliable controller can be designed in terms of the solutions to certain linear matrix inequalities. Finally, numerical examples with simulation result are presented to demonstrate the validity and less conservatism of the obtained results.

Adaptive Stabilization of Stochastic Nonlinear Systems Disturbed by Unknown Time Delay and Covariance Noise

This paper considers a more general stochastic nonlinear time-delay system driven by unknown covariance noise and investigates its adaptive state-feedback control problem. As a remarkable feature, the growth assumptions imposed on delay-dependent nonlinear terms are removed. Then, with the help of Lyapunov-Krasovskii functionals and adaptive backstepping technique, an adaptive state-feedback controller is constructed by overcoming the negative effects brought by unknown time delay and covariance noise. Based on the designed controller, the closed-loop system can be guaranteed to be globally asymptotically stable (GAS) in probability. Finally, a simulation example demonstrates the effectiveness of the proposed scheme.