Decentralized adaptive output-feedback stabilization for large-scale stochastic nonlinear systems

In this paper, the problem of decentralized adaptive output-feedback stabilization is investigated for large-scale stochastic nonlinear systems with three types of uncertainties, including parametric uncertainties, nonlinear uncertain interactions and stochastic inverse dynamics. Under the assumption that the inverse dynamics of the subsystems are stochastic input-to-state stable, an adaptive output-feedback controller is constructively designed by the backstepping method. It is shown that under some general conditions, the closed-loop system trajectories are bounded in probability and the outputs can be regulated into a small neighborhood of the origin in probability. In addition, the equilibrium of interest is globally stable in probability and the outputs can be regulated to the origin almost surely when the drift and diffusion vector fields vanish at the origin. The contributions of the work are characterized by the following novel features: (1) even for centralized single-input single-output systems, this paper presents a first result in stochastic, nonlinear, adaptive, output-feedback asymptotic stabilization; (2) the methodology previously developed for deterministic large-scale systems is generalized to stochastic ones. At the same time, novel small-gain conditions for small signals are identified in the setting of stochastic systems design; (3) both drift and diffusion vector fields are allowed to be dependent not only on the measurable outputs but some unmeasurable states; (4) parameter update laws are used to counteract the parametric uncertainty existing in both drift and diffusion vector fields, which may appear nonlinearly; (5) the concept of stochastic input-to-state stability and the method of changing supply functions are adapted, for the first time, to deal with stochastic and nonlinear inverse dynamics in the context of decentralized control.     

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.     

Output-feedback stabilization for stochastic nonlinear systems whose linearizations are not stabilizable

This brief paper investigates the problem of output-feedback stabilization for a class of high-order stochastic nonlinear systems which are neither necessarily feedback linearizable nor affine in the control input. Based on the ideas of the homogeneous systems theory and the adding a power integrator technique, an output-feedback controller is constructed to ensure that the equilibrium at the origin of the closed-loop system is globally asymptotically stable (GAS) in probability. The efficiency of the output-feedback controller is demonstrated by a simulation example.     

On convergence of active disturbance rejection control for a class of uncertain stochastic nonlinear systems

In this paper, the practical mean-square convergence of active disturbance rejection control for a class of uncertain stochastic nonlinear systems modelled by the Itô-type stochastic differential equations with vast stochastic uncertainties is developed. We first design an extended state observer (ESO) to estimate both the unmeasured states and the stochastic total disturbance which includes unknown internal system dynamics, external stochastic disturbance without known statistical characteristics, unknown stochastic inverse dynamics, and uncertainty caused by the deviation of control parameter from its nominal value. The stochastic total disturbance is then cancelled (compensated) in the feedback loop. An ESO-based output-feedback control is finally designed analogously as for the system without uncertainties. The practical mean-square reference tracking and practical mean-square stability of the resulting closed-loop system are achieved. The numerical experiments are carried out to illustrate the effectiveness of the proposed approach.     

Decentralised output-feedback control for a class of large-scale stochastic high-order upper-triangular nonlinear systems

Under the weaker conditions on the drift and diffusion terms, this paper focuses on the global decentralised output-feedback control for a class of large-scale stochastic high-order upper-triangular nonlinear systems. By introducing an appropriate coordinate transformation, the original system is transformed into an equivalent one with tunable gain. After that, by reasonably combing the homogeneous domination approach with stochastic nonlinear systems stability criterion, and skillfully choosing the low gain scale, the decentralised output-feedback controller is constructed for each subsystem to ensure that the closed-loop system is globally asymptotically stable in probability. The simulation example is given to demonstrate the effectiveness of the proposed design scheme.     

Continuous output-feedback stabilization for a class of stochastic high-order nonlinear systems

This paper is concerned with the global stabilization via output-feedback for a class of high-order stochastic nonlinear systems with unmeasurable states dependent growth and uncertain control coefficients. Indeed, there have been abundant deterministic results which recently inspired the intense investigation for their stochastic analogous. However, because of the possibility of non-unique solutions to the systems, there lack basic concepts and theorems for the problem under investigation. First of all, two stochastic stability concepts are generalized to allow the stochastic systems with more than one solution, and a key theorem is given to provide the sufficient conditions for the stochastic stabilities in a weaker sense. Then, by introducing the suitable reduced order observer and appropriate control Lyapunov functions, and by using the method of adding a power integrator, a continuous (nonsmooth) output-feedback controller is successfully designed, which guarantees that the closed-loop system is globally asymptotically stable in probability.     

Active disturbance rejection control to MIMO nonlinear systems with stochastic uncertainties: approximate decoupling and output-feedback stabilisation

ABSTRACT

In this paper, we apply the active disturbance rejection control, an emerging control technology, to output-feedback stabilisation for a class of uncertain multi-input multi-output nonlinear systems with vast stochastic uncertainties. Two types of extended state observers (ESO) are designed to estimate both unmeasured states and stochastic total disturbance which includes unknown system dynamics, unknown stochastic inverse dynamics, external stochastic disturbance without requiring the statistical characteristics, uncertain nonlinear interactions between subsystems, and uncertainties caused by the deviation of control parameters from their nominal values. The estimations decouple approximately the system after cancelling stochastic total disturbance in the feedback loop. As a result, we are able to design an ESO-based stabilising output-feedback and prove the practical mean square stability for the closed-loop system with constant gain ESO and the asymptotic mean square stability with time-varying gain ESO, respectively. Some numerical simulations are presented to demonstrate the effectiveness of the proposed output-feedback control scheme.     

Minimal-order observer and output-feedback stabilization control design of stochastic nonlinear systems

1IntroductionTheproblemofestimatingtheparametersofmultiplesinusoidsinnoisehasre-ceivedconsiderableattentioninthepastthirtyyears,andalotofalgorithmshavebeenestablishedtosolvetheproblem.Amongallofthealgorithms,themaximumlikelihood(ML)estimatorisaprominentone[1],andseveralalgorithms,suchasANP[2]andIMP[3,4]arerelatedtoML.ThedrawbackoftheMLestimatorisitshighcomputationalcomplexity,sothealternatingprojection(AP)algorithm[5]wasdevelopedtomakeitsrealtimerealizationpossible.Butthefundamentaldefic…     

具有奇整数比次方的随机高阶非线性系统的输出反馈镇定

研究了一类具有奇整数比次方的随机高阶非线性系统的输出反馈控制问题. 通过采用增加幂次积分方法, 引入一个新的标量变换和选取合适的李雅普诺夫函数, 所构造的输出反馈控制器使得闭环系统是依概率全局渐近稳定的, 输出几乎处处调节到原点. 进一步地, 我们解决了依概率逆最优镇定问题. 仿真例子证明了设计方法的有效性.     

H Optimal control for linear stochastic systems

The aim of the present paper is to provide an optimal solution to the H² state-feedback and output-feedback control problems for stochastic linear systems subjected both to Markov jumps and to multiplicative white noise. It is proved that in the state-feedback case the optimal solution is a static gain which is also optimal in the class of all higher-order controllers. In the output-feedback case the optimal H² controller has the same order as the given stochastic system. The realization of the optimal controllers depend on the stabilizing solutions of some appropriate systems of Riccati-type coupled equations. An effective iterative convergent algorithm to compute these stabilizing solutions is also presented. The paper gives some illustrative numerical example allowing to compare the results obtained by the proposed design approach with the ones presented in the recent control literature.     

随机非线性严格反馈系统的自适应神经网络输出反馈镇定

针对具有严格反馈形式的随机非线性系统, 首次引入神经网络控制技术, 设计了适当形式的随机控制 Lyapunov函数, 并运用反推(Backstepping)技术和非线性观测器设计技术, 构造出一类自适应神经网络输出反馈控制器. 在一定条件下, 证明了闭环系统平衡点依概率稳定. 仿真算例验证了所给控制方案的有效性.     

一类上三角随机非线性系统的输出反馈控制

针对一类上三角随机非线性系统的输出反馈控制问题,首先利用反推技术,为其对应的标称系统设计稳定的输出反馈控制器;然后利用低增益齐次占优技术,为整个系统设计输出反馈控制器.所设计的控制器能保证闭环系统的平衡点为依概率全局渐近稳定的,并将低增益齐次占优技术推广到了随机系统,首次解决了一类上三角随机系统的镇定问题.最后通过数值仿真验证了所提出控制方案的有效性.     

Adaptive backstepping controller design using stochastic small-gain theorem

A more general class of stochastic nonlinear systems with unmodeled dynamics and uncertain nonlinear functions are considered in this paper. With the concept of input-to-state practical stability (ISpS) and nonlinear small-gain theorem being extended to stochastic case, by combining stochastic small-gain theorem with backstepping design technique, an adaptive output-feedback controller is proposed. It is shown that the closed-loop system is practically stable in probability. A simulation example demonstrates the control scheme.     

随机Marino-Tomei系统的输出反馈鲁棒自适应跟踪

研究了一类Marino-Tomei非线性模型在不确定噪声干扰下的输出反馈鲁棒自适应跟 踪问题.通过滤波变换,采用随机控制Lyapunov设计方法,对于受方差未知的Wiener噪声干 扰的Marino-Tomei非线性系统,给出了参数自适应律和控制律,使得闭环系统成为噪声--状 态稳定的,并且跟踪误差的4次均方值在时间平均意义下收敛到一个足够小的区域内.     

Stochastic adaptive backstepping controller design by introducing dynamic signal and changing supply function

A more general class of stochastic non-linear systems with unmodelled dynamics and uncertain non-linear functions are considered in this paper. With the concept of ISpS being extended to stochastic case, by combining changing supply function technique with backstepping design technique, an adaptive output-feedback controller is proposed. It is shown that all the solutions of the closed-loop system are uniformly bounded in probability, and the output can be regulated to an arbitrarily small neighbourhood of the origin in probability. A simulation example demonstrates the control scheme.     

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．     

Global adaptive control for a class of uncertain stochastic nonlinear systems with unknown output gain

This paper addresses the global adaptive control problem for a class of uncertain stochastic nonlinear systems in the output-feedback form. Due to the unknown output gain, we construct a full-order homogeneous observer instead of using the system output. Then, by adding a power integrator technique, an output-feedback controller is designed, as well as an adaptive law to deal with the unknown nonlinear growth rates. Based on the generalized stochastic Lyapunov stability theorem, it can be proved that all the signals of the closed-loop system are bounded in probability, and the system states converge to the origin almost surely.     

Distributed output-feedback controllers design for Markovian jump systems interconnected over an undirected graph with time-varying delay

This paper considers the problems of stochastic stability analysis and distributed output-feedback controllers design for Markovian jump systems interconnected over an undirected graph with state time-varying delay. Specifically, a sufficient condition for the well-posedness, stochastic stability and contractiveness of the resultant closed-loop system is first developed in the form of non-linear matrix inequalities. Then, to avoid the difficulty of solving non-linear matrix inequalities, the sufficient condition is relaxed to an equivalent one in terms of coupling linear matrix inequalities (LMIs), which provides an effective way to confirm the existence of a distributed output-feedback controller inheriting the structure of the given plant. Furthermore, a constructive algorithm is given for the design of such a distributed output-feedback controller to achieve the well-posedness, stochastic stability as well as the contractiveness of the corresponding closed-loop system. Finally, numerical simulations are given to illustrate the validity of the proposed method.     

含参数不确定性的马尔可夫跳变过程鲁棒正实控制

讨论一类具有随机跳变参数的线性系统正实控制问题,其跳变参数的跃迁由有限状 态的马尔可夫过程描述.基于随机李亚普诺夫函数的方法,并结合线性矩阵不等式,分别提出依 赖于模态的状态反馈和输出反馈控制,以保证相应闭环系统的严格正实性.进一步针对系统含 参数不确定性的情形,引入鲁棒正实性分析,得到鲁棒正实控制器存在的充分条件和设计方法.     

Static and output-feedback of discrete-time LTI systems with state multiplicative noise

A parameter dependent approach for designing static output-feedback controller for linear time-invariant systems with state-multiplicative noise is introduced which achieves a minimum bound on either the stochastic H₂ or the H_∞ performance levels. A solution is obtained also for the case where, in addition to the stochastic parameters, the system matrices reside in a given polytope. In this case, a parameter dependent Lyapunov function is described which enables the derivation of the required constant feedback gain via a solution of a set of linear matrix inequalities that correspond to the vertices of the uncertainty polytope.The stochastic parameters appear in both the dynamics and the input matrices of the state space model of the system. The problems are solved using the expected value of the standard performance indices over the stochastic parameters. The theory developed is demonstrated by a simple example.