New results in global stabilization for stochastic nonlinear systems

This paper presents new results on the robust global stabilization and the gain assignment problems for stochastic nonlinear systems. Three stochastic nonlinear control design schemes are developed. Furthermore, a new stochastic gain assignment method is developed for a class of uncertain interconnected stochastic nonlinear systems. This method can be combined with the nonlinear small-gain theorem to design partial-state feedback controllers for stochastic nonlinear systems. Two numerical examples are given to illustrate the effectiveness of the proposed methodology.     

On passivity-based output feedback global stabilization of euler-lagrange systems

It is well known that in systems described by Euler-Lagrange equations the stability of the equilibria is determined by the potential energy function. Further, these equilibria are asymptotically stable if suitable damping is present in the system. These properties motivated the development of a passivity-based controller design methodology which aims at modifying the potential energy of the closed loop and the addition of the required dissipation. To achieve the latter objective measurement of the generalized velocities is typically required. Our main contribution in this paper is the proof that damping injection without velocity measurement is possible via the inclusion of a dynamic extension provided the system satisfies a dissipation propggation condition. This allows us to determine a class of Euler-Lagrange systems that can be globally asymptotically stabilized with dynamic output feedback. We illustrate this result with the problem of set-point control of elastic joints robots. Our research contributes, if modestly, to the development of a theory for stabilization of nonlinear systems with physical structures which effectively exploits its energy dissipation properties.     

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.     

Global asymptotic stabilisation in probability of nonlinear stochastic systems via passivity

The purpose of this paper is to develop a systematic method for global asymptotic stabilisation in probability of nonlinear control stochastic systems with stable in probability unforced dynamics. The method is based on the theory of passivity for nonaffine stochastic differential systems combined with the technique of Lyapunov asymptotic stability in probability for stochastic differential equations. In particular, we prove that a nonlinear stochastic differential system whose unforced dynamics are Lyapunov stable in probability is globally asymptotically stabilisable in probability provided some rank conditions involving the affine part of the system coefficients are satisfied. In this framework, we show that a stabilising smooth state feedback law can be designed explicitly. A dynamic output feedback compensator for a class of nonaffine stochastic systems is constructed as an application of our analysis.     

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.     

一类高阶次随机非线性系统的状态反馈镇定

针对一类高阶次随机非线性系统,研究其状态反馈镇定问题.基于最近发展起来的增加幂次积分器技术,通过适当地选取Lyapunov函数和设计参数,给出了一个光滑的状态反馈反推控制器的设计过程,所设计的控制器保证了闭环系统在原点处的平衡点是概率意义下全局渐近稳定的.     

On stabilization for a class of nonlinear stochastic time-delay systems： a matrix inequality approach

This paper treats the feedback stabilization of nonlinear stochastic time-delay systems with state and control-dependent noise. Some locally （globally） robustly stabilizable conditions are given in terms of matrix inequalities that are independent of the delay size. When it is applied to linear stochastic time-delay systems, sufficient conditions for the state-feedback stabilization are presented via linear matrix inequalities. Several previous results are extended to more general systems with both state and control-dependent noise, and easy computation algorithms are also given.     

On stabilization for a class of nonlinear stochastic time-delay systems:a matrix inequality approach

This paper treats the feedback stabilization of nonlinear stochastic time-delay systems with state and control-dependent noise. Some locally (globally) robustly stabilizable conditions are given in terms of matrix inequalities that are independent of the delay size. When it is applied to linear stochastic time-delay systems, sufficient conditions for the state-feedback stabilization are presented via linear matrix inequalities. Several previous results are extended to more general systems with both state and control-dependent noise, and easy computation algorithms are also eiven.     

State feedback stabilization for high-order stochastic nonlinear systems with zero dynamics

In this paper, for a class of high-order stochastic nonlinear systems with zero dynamics which are neither necessarily feedback linearizable nor affine in the control input, the problem of state feedback stabilization is investigated 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 all the states can be regulated to the origin almost surely. A simulation example demonstrates the control scheme.     

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.     

Dynamic output feedback linearization and global stabilization

We present a class of single-input single-output nonlinear systems which are globally transformable by a dynamic output feedback control and a time-varying state space transformation into a linear, observable and minimum phase system. We then show how those systems can be globally stabilized by a dynamic output feedback nonlinear control and how global output tracking can be achieved as well.     

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.     

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。     

Further results on state feedback stabilization of stochastic high-order nonlinear systems

In this paper,a combined homogeneous domination and sign function design approach is presented to state feedback control for a class of stochastic high-order nonlinear systems with time-varying delay.The use of the combined approach relaxes the restriction on nonlinear functions and makes the closed-loop system globally asymptotically stable in probability.     

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.     

Sampled‐data output feedback stabilization for a class of switched stochastic nonlinear systems

This paper investigates a global sampled‐data output feedback stabilization problem for a class of switched stochastic nonlinear systems whose output and system mode are available only at the sampling instants. An observer is designed to estimate the unmeasurable state and thus a sampled‐data controller is constructed with the sampled estimated state. As a distinctive feature, a merging virtual switching signal is introduced to describe the asynchronous switching generated by detecting the system mode via a sampler. By choosing an appropriate piecewise Lyapunov function, it is proved that the proposed sampled‐data controller with allowable sampling period can stabilize the considered switched stochastic nonlinear systems under an average dwell‐time condition. Finally, two simulation results are presented to illustrate the effectiveness of the proposed method.     

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     

On the simultaneous stabilization of stochastic nonlinear systems

In this paper, the problem of simultaneous stabilization in probability by state feedback is investigated for a class of stochastic nonlinear systems whose drift and diffusion terms are dependent on the control and for which classical methods are not applicable. Under the assumption that a collection of stochastic control Lyapunov functions (SCLFs) is known and based on the generalized stochastic Lyapunov theorem, we derive sufficient conditions for the simultaneous stabilization in probability by a continuous state feedback controller that we explicitly compute. We also derive a necessary condition when the system coefficients satisfy some regularity conditions. This work generalizes previous results on the simultaneous stabilization of stochastic nonlinear systems. The obtained results are illustrated by a numerical example.     

Stability and stabilization of nonlinear discrete‐time stochastic systems

This paper mainly studies the locally/globally asymptotic stability and stabilization in probability for nonlinear discrete‐time stochastic systems. Firstly, for more general stochastic difference systems, two very useful results on locally and globally asymptotic stability in probability are obtained, which can be viewed as the discrete versions of continuous‐time Itô systems. Then, for a class of quasi‐linear discrete‐time stochastic control systems, both state‐ and output‐feedback asymptotic stabilization are studied, for which, sufficient conditions are presented in terms of linear matrix inequalities. Two simulation examples are given to illustrate the effectiveness of our main results.