Adaptive state-feedback stabilization for a large class of high-order stochastic nonlinear systems

Under the more general conditions on the power order and the nonlinear functions, this paper investigates the problem of adaptive state-feedback stabilization for a class of high-order stochastic nonlinear systems with time-varying control coefficients. Based on the backstepping design method and homogeneous domination technique, the closed-loop system can be proved to be globally stable in probability and the states can be regulated to the origin almost surely. The efficiency of the state-feedback controller is demonstrated by a simulation example.     

随机非完整链式系统的自适应状态反馈镇定

基于反步技术,对带有不确定非线性项和不确定非线性系数的随机非完整链式系统,设计了自适应状态反馈镇定器.给出了能够保证系统依概率几乎渐近稳定到平衡点的切换控制.最后用仿真验证了控制器的有效性.     

Adaptive state-feedback stabilization for a class of high-order nonlinear uncertain systems

For high-order nonlinear uncertain systems, there have been a lot of investigations under a strong assumption that the lower bounds of the unknown control coefficients should be exactly known. In this paper, this assumption is removed and a unified approach is developed to systematically construct a state-feedback adaptive stabilizing control law for a class of high-order nonlinear uncertain systems with unknown control coefficients. By using the method of the so-called adding a power integrator merging with adaptive technique, a recursive design procedure is provided to achieve a smooth adaptive state-feedback control law, which guarantees that the closed-loop system is globally uniformly stable while the original system states globally asymptotically converge to zero. Finally, a simulation example is given to illustrate the correctness of the theoretical results.     

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.     

Adaptive state-feedback stabilization for high-order stochastic non-linear systems with uncertain control coefficients

This paper investigates the adaptive state-feedback stabilization problem for a class of high-order stochastic non-linear systems with unknown lower and supper bounds for uncertain control coefficients. Under some weaker and reasonable assumptions, a smooth adaptive state-feedback controller is designed, which guarantees that the closed-loop system has an almost surely unique solution on [0,∞, the equilibrium of interest is globally stable in probability and the states can be regulated to the origin almost surely. A simulation example is given to show the systematic design and effectiveness of the controller.     

Adaptive global stabilization of nonholonomic systems with strong nonlinear drifts

A new input-to-state scaling scheme is first introduced to transform a class of nonholonomic systems in a chained form with strong nonlinear drifts and unknown constant parameters into a strict feedback form. The backstepping technique is then applied to design a global adaptive stabilization controller. A switching strategy based on the control input magnitude rather than the time is derived to get around the phenomenon of uncontrollability. Simulation examples validate the effectiveness of the proposed controller.     

Adaptive control of nonlinear systems with nonlinear parameterization

An adaptive feedback regulation scheme is proposed for a class of single input nonlinear systems, with nonlinear parameterizations. A proof of local regulation is given. The results are validated through a simulation study.     

Adaptive stabilization of multi-input nonlinear systems

Universal stabilizers are presented for two classes of nonlinear systems, linear in their multiple control inputs: (I) a class of pth order controlled differential inclusions on R″ with full state available for feedback, and (II) a class of nonlinearly perturbed linear systems with restricted state availability. The stabilizers are of a discontinuous feedback form (embedded in a set-valued map), and incorporate adaptive matrix-valued gain functions which exploit the existence of finite spectrum-unmixing sets associated with the systems under consideration. The analysis draws on an extension, to differential inclusions, of LaSalle's invariance principle for ordinary differential equations.     

一类高阶次随机非线性系统的输出反馈镇定

针对一类高阶次随机非线性系统,研究其输出反馈镇定问题．通过选择有效的观测器和李雅普诺夫函数,所设计的光滑输出反馈控制器保证了闭环系统的平衡点是依概率全局渐近稳定的,输出几乎处处调节到零．数值仿真验证了控制方案的有效性．     

Adaptive estimation of discrete-time systems with nonlinear parameterization

This paper concerns adaptive estimation of dynamic systems which are nonlinearly parameterized. A majority of adaptive algorithms employ a gradient approach to determine the direction of adjustment, which ensures stable estimation when parameters occur linearly. These algorithms, however, do not suffice for estimation in systems with nonlinear parameterization. We introduce in this paper a new algorithm for such systems and show that it leads to globally stable estimation by employing a different regression vector and selecting a suitable step size. Both concave/convex parameterizations as well as general nonlinear parameterizations are considered. Stable estimation in the presence of both nonlinear parameters and linear parameters which may appear multiplicatively is established. For the case of concave/convex parameterizations, parameter convergence is shown to result under certain conditions of persistent excitation.     

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

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.     

Output-feedback stabilization for stochastic high-order nonlinear systems with time-varying delay

This paper investigates output-feedback control for a class of stochastic high-order nonlinear systems with time-varying delay for the first time. By introducing the adding a power integrator technique in the stochastic systems and a rescaling transformation, and choosing an appropriate Lyapunov-Krasoviskii functional, an output-feedback controller is constructed to render the closed-loop system globally asymptotically stable in probability and the output can be regulated to the origin almost surely. A simulation example is provided to show the effectiveness of the designed controller.     

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 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.     

Adaptive stabilization of time-delay feedforward nonlinear systems

In this paper, we consider the adaptive stabilization problem for feedforward nonlinear systems with time delays. An adaptive stabilizer is proposed. Our stabilizer takes a nested saturation feedback, and a set of switching logics is designed to tune online the saturation levels in a piecewise constant or switching manner. It has been shown that under our proposed control, all closed-loop states are bounded and asymptotic regulation is achieved.     

不确定高次随机非线性系统的自适应控制

针对一类含有噪声干扰和非线性参数的高次随机非线性系统,研究了依概率全局自适应稳定问题.在噪声的协方差未知的情况下,利用自适应增加幂积分方法和参数分离技术,提出了一种反馈占优设计方法并构造了一个光滑自适应控制器.该控制器能保证闭环系统依概率全局稳定,并且系统的状态几乎必然收敛到零.仿真例子验证了控制方案的有效性.     

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

This paper aims to relax the results in Xie and Tian (2009) from the following two aspects: completely removing the power order restriction and largely relaxing the growth conditions of nonlinear functions. By using the backstepping design method and homogeneous domination technique, this paper investigates the problem of adaptive state-feedback stabilization for a class of stochastic high-order nonlinear systems with nonlinear parameterization. The closed-loop system can be proved to be globally stable in probability and the states can be regulated to the origin almost surely. The efficiency of the adaptive state-feedback controller is demonstrated by a simulation example.     

Adaptive control of a class of nonlinear systems with convex/concave parameterization

This paper deals with adaptive control of a class of second-order nonlinear systems with a triangular structure and convex/concave parameterization. In Annaswamy et al. (Automatica 33(11) (1998) 1975–1995) it was shown that nonlinearly parameterized systems that satisfy certain matching conditions can be adaptively controlled in a stable manner. In this paper, we relax these matching conditions and include additional dynamics between the nonlinearities and the control input. Global boundedness and convergence to within a desired precision is established. No overparameterization of the adaptive controller is required.     

Continuous simultaneous stabilization of single‐input nonlinear stochastic systems

This paper investigates the simultaneous stabilization of a collection of continuous single‐input non‐linear stochastic systems, with coefficients that are not necessarily locally Lipschitz. A sufficient condition for the existence of a continuous simultaneously stabilizing feedback control is proposed — it is based on the generalized stochastic Lyapunov theorem and on the technique of stochastic control Lyapunov functions. This condition is also necessary, provided that the system's coefficients satisfy some regularity conditions. Moreover, the proposed feedback can be chosen to be bounded under the assumption that appropriate control Lyapunov functions are known. All the proposed simultaneously stabilizing state feedback controllers are explicitly constructed. Finally, two simulation examples are provided to demonstrate the effectiveness of the proposed approach.