State feedback control of a class of high‐order stochastic nonlinear systems

This paper poses and solves a new problem of state feedback stabilization for a class of high‐order stochastic nonlinear systems in which the power order restriction and growth condition are relaxed to a more general form. Based on the ideas of the homogeneous systems theory and the adding of a power integrator technique, a state feedback controller is constructed to ensure that the equilibrium at the origin of the closed‐loop system is globally asymptotically stable in probability and that the problem of inverse optimal stabilization in probability is solved. The efficiency of the state feedback controller is demonstrated by a simulation example. Copyright © 2011 John Wiley & Sons, Ltd.     

Adaptive NN output‐feedback decentralized stabilization for a class of large‐scale stochastic nonlinear strict‐feedback systems

In this paper, the decentralized adaptive neural network (NN) output‐feedback stabilization problem is investigated for a class of large‐scale stochastic nonlinear strict‐feedback systems, which interact through their outputs. The nonlinear interconnections are assumed to be bounded by some unknown nonlinear functions of the system outputs. In each subsystem, only a NN is employed to compensate for all unknown upper bounding functions, which depend on its own output. Therefore, the controller design for each subsystem only need its own information and is more simplified than the existing results. It is shown that, based on the backstepping method and the technique of nonlinear observer design, the whole closed‐loop system can be proved to be stable in probability by constructing an overall state‐quartic and parameter‐quadratic Lyapunov function. The simulation results demonstrate the effectiveness of the proposed control scheme. Copyright © 2010 John Wiley & Sons, Ltd.     

State feedback stabilization of stochastic nonlinear systems with SiISS inverse dynamics

This paper further considers a more general class of stochastic nonlinear systems with stochastic integral input‐to‐state stability (SiISS) inverse dynamics and drift and diffusion terms depending upon the other states besides stochastic inverse dynamics and the first state. By skillfully choosing the designed functions and the update laws of parameters, and using the important mathematical tools established in IEEE Trans. Automat. Contr. 2010; 55 (2):304–320, a unifying framework of state feedback controller is proposed to guarantee that all the signals of the closed‐loop system are bounded almost surely and the states can be regulated to zero almost surely. A simulation example demonstrates the effectiveness of the control scheme. Copyright © 2011 John Wiley & Sons, Ltd.     

Output‐feedback robust adaptive backstepping control for a class of multivariable nonlinear systems with guaranteed tracking performance

This paper is devoted to output‐feedback adaptive control for a class of multivariable nonlinear systems with both unknown parameters and unknown nonlinear functions. Under the Hurwitz condition for the high‐frequency gain matrix, a robust adaptive backstepping control scheme is proposed, which is able to guarantee the tracking performance and needs only one parameter to be updated online regardless of the system order and input–output dimension. To cope with the unknown nonlinear functions and improve the tracking performance, a kind of high‐gain K‐filters is introduced. It is proved that all signals of the closed‐loop system are globally uniformly bounded. Simulation results on coupled inverted double pendulums are presented to illustrate the effectiveness of the proposed scheme. Copyright © 2012 John Wiley & Sons, Ltd.     

State‐feedback stabilization for high‐order stochastic nonlinear systems with stochastic inverse dynamics

For a class of high‐order stochastic nonlinear systems with stochastic inverse dynamics which are neither necessarily feedback linearizable nor affine in the control input, this paper investigates the problem of state‐feedback stabilization for the first time. Under some weaker assumptions, a smooth state‐feedback controller is designed, which ensures that the closed‐loop system has an almost surely unique solution on [0, ∞), the equilibrium at the origin of the closed‐loop system is globally asymptotically stable in probability, and the states can be regulated to the origin almost surely. A simulation example demonstrates the control scheme. Copyright © 2007 John Wiley & Sons, Ltd.     

Output feedback stabilization of stochastic feedforward nonlinear systems with input and state delay

This paper considers the problem of output feedback stabilization for a class of stochastic feedforward nonlinear systems with input and state delay. Under a set of coordinate transformations, we first design a linear output feedback controller for a nominal system. Then, with the aid of feedback domination technique and an appropriate Lyapunov–Krasovskii functional, it is proved that the proposed linear output feedback controller can drive the closed‐loop system globally asymptotically stable in probability. Copyright © 2015 John Wiley & Sons, Ltd.     

State‐feedback stabilization for a class of stochastic time‐delay nonlinear systems

This paper investigates the problem of state‐feedback stabilization for a class of lower‐triangular stochastic time‐delay nonlinear systems without controllable linearization. By extending the adding‐a‐power‐integrator technique to the stochastic time‐delay systems, a state‐feedback controller is explicitly constructed such that the origin of closed‐loop system is globally asymptotically stable in probability. The main design difficulty is to deal with the uncontrollable linearization and the nonsmooth system perturbation, which, under some appropriate assumptions, can be solved by using the adding‐a‐power‐integrator technique. Two simulation examples are given to illustrate the effectiveness of the control algorithm proposed in this paper.Copyright © 2011 John Wiley & Sons, Ltd.     

Global output‐feedback stabilization for a class of stochastic nonlinear systems via sampled‐data control

In this paper, the global sampled‐data output‐feedback stabilization problem is considered for a class of stochastic nonlinear systems. First, based on output‐feedback domination technique and emulation approach, a systematic design procedure for sampled‐data output‐feedback controller is proposed for a class of stochastic lower‐triangular nonlinear systems. It is proved that the proposed sampled‐data output‐feedback controller will stabilize the given stochastic nonlinear system in the sense of mean square exponential stability. Because of the domination nature of the proposed control approach, it is shown that the proposed control approach can also be used to handle the global sampled‐data output‐feedback stabilization problems for a more general class of stochastic non‐triangular nonlinear systems. Finally, simulation examples are given to demonstrate the effectiveness of the proposed method. Copyright © 2017 John Wiley & Sons, Ltd.     

State‐feedback stabilization for stochastic high‐order nonlinear systems with SISS inverse dynamics

This paper investigates the problem of state‐feedback control for a class of stochastic high‐order nonlinear systems with stochastic inverse dynamics. Under the assumption that the inverse dynamics of the subsystem are stochastic input‐to‐state stable (SISS), by extending through adding a power integrator technique, choosing an appropriate Lyapunov function and using the idea of changing supply function, a smooth state‐feedback controller is explicitly constructed to render the system globally asymptotically stable in probability and the states can be regulated to the origin. A simulation example is provided to show the effectiveness of the proposed scheme. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

非线性随机时滞系统输出反馈镇定

研究了非线性随机时滞系统的镇定问题，运用Backstepping递推设计方法，得到了使得非线性随机时滞系统镇定的输出反馈控制器的设计算法。     

非线性随机时滞系统输出反馈镇定

研究了非线性随机时滞系统的镇定问题. 运用Backstepping递推设计方法, 得到了使得非线性随机时滞系统镇定的输出反馈控制器的设计算法.     

Output feedback for stochastic nonlinear systems with unmeasurable inverse dynamics

This paper considers a concrete stochastic nonlinear system with stochastic unmeasurable inverse dynamics. Motivated by the concept of integral input-to-state stability （iISS） in deterministic systems and stochastic input-to-state stability （SISS） in stochastic systems, a concept of stochastic integral input-to-state stability （SiISS） using Lyapunov functions is first introduced. A constructive strategy is proposed to design a dynamic output feedback control law, which drives the state to the origin almost surely while keeping all other closed-loop signals almost surely bounded. At last, a simulation is given to verify the effectiveness of the control law.     

Continuous finite‐time state feedback stabilizers for some nonlinear stochastic systems

This paper is concerned with the problem of finite‐time stabilization for some nonlinear stochastic systems. Based on the stochastic Lyapunov theorem on finite‐time stability that has been established by the authors in the paper, it is proven that Euler‐type stochastic nonlinear systems can be finite‐time stabilized via a family of continuous feedback controllers. Using the technique of adding a power integrator, a continuous, global state feedback controller is constructed to stabilize in finite time a large class of two‐dimensional lower‐triangular stochastic nonlinear systems. Also, for a class of three‐dimensional lower‐triangular stochastic nonlinear systems, a recursive design scheme of finite‐time stabilization is given by developing the technique of adding a power integrator and constructing a continuous feedback controller. Finally, a simulation example is given to illustrate the theoretical results. Copyright © 2014 John Wiley & Sons, Ltd.     

Dynamic self‐triggered output‐feedback control for nonlinear stochastic systems with time delays

In this paper, the dynamic self‐triggered output‐feedback control problem is investigated for a class of nonlinear stochastic systems with time delays. To reduce the network resource consumption, the dynamic event‐triggered mechanism is implemented in the sensor‐to‐controller channel. Criteria are first established for the closed‐loop system to be stochastically input‐to‐state stable under the event‐triggered mechanism. Furthermore, sufficient conditions are given under which the closed‐loop system with dynamic event‐triggered mechanism is almost surely stable, and the output‐feedback controller as well as the dynamic event‐triggered mechanism are co‐designed. Moreover, a dynamic self‐triggered mechanism is proposed such that the nonlinear stochastic system with the designed output‐feedback controller is stochastically input‐to‐state stable and the Zeno phenomenon is excluded. Finally, a numerical example is provided to illustrate the effectiveness of proposed dynamic self‐triggered output‐feedback control scheme.     

Finite‐time stabilization of stochastic low‐order nonlinear systems with FT‐SISS inverse dynamics

This paper studies finite‐time stabilization problem for stochastic low‐order nonlinear systems with stochastic inverse dynamics. By characterizing unmeasured stochastic inverse dynamics with finite‐time stochastic input‐to‐state stability, combining the Lyapunov function and adding a power integrator technique, and using the stochastic finite‐time stability theory, a state feedback controller is designed to guarantee global finite‐time stability in probability of stochastic low‐order nonlinear systems with finite‐time stochastic input‐to‐state stability inverse dynamics.     

Output feedback control for a class of stochastic high‐order nonlinear systems with time‐varying delays

This paper discusses the problem of output feedback stabilization for a more general class of stochastic high‐order nonlinear systems with time‐varying delays. On the basis of a subtle homogeneous observer and controller construction, and the homogeneous domination approach, the closed‐loop system is globally asymptotically stable in probability, by choosing an appropriate Lyapunov–Krasovskii functional. An example is given to illustrate the effectiveness of the proposed design procedure. Copyright © 2013 John Wiley & Sons, Ltd.     

Input‐to‐state stability of nonlinear stochastic time‐varying systems with impulsive effects

This paper considers the input‐to‐state stability, integral‐ISS, and stochastic‐ISS for impulsive nonlinear stochastic systems. The Lyapunov function considered in this paper is indefinite, that is, the rate coefficient of the Lyapunov function is time‐varying, which can be positive or negative along time evolution. Lyapunov‐based sufficient conditions are established for ensuring ISS of impulsive nonlinear stochastic systems. Three examples involving one from networked control systems are provided to illustrate the effectiveness of theoretical results obtained. Copyright © 2016 John Wiley & Sons, Ltd.     

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

This 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.     

Adaptive state feedback control for switched stochastic high‐order nonlinear systems under arbitrary switchings

This paper studies the adaptive state feedback control for a class of switched time‐varying stochastic high‐order nonlinear systems under arbitrary switchings. Based on the common Lyapunov function and using the inductive method, virtual controllers are designed step by step and the form of the input signal of the system is constructed at the last. The unknown parameters are addressed by the tuning function method. In particular, both the designed state feedback controller and the adaptive law are independent of switching signals. Based on the designed controller, the boundness of the state variables can be guaranteed in probability. Furthermore, without considering the Wiener process or with the known parameter in the assumption, adaptive finite‐time stabilization and finite‐time stabilization in probability can be obtained, respectively. Finally, numerical simulation results are presented to illustrate the effectiveness of the proposed method.