Lyapunov equation for infinite-dimensional discrete bilinear systems

Mean-square stability for discrete systems requires that uniform convergence is preserved between input and state correlation sequences. Such a convergence preserving property holds for an infinite-dimensional bilinear system if and only if the associate Lyapunov equation has a unique strictly positive solution.     

针对随机控制系统数值解的均方指数输入状态稳定性

分析了随机控制系统数值解的均方指数输入状态稳定性. 首先, 针对随机控制系统, 随机θ-方法满足有限时间强收敛条件. 然后, 我们证实, 在有限时间强收敛条件下, 随机控制系统是均方指数输入状态稳定的当且仅当随机θ-方法(充分小步长)是均方指数输入状态稳定的. 另外, 对一类满足单边Lipschitz条件的随机控制系统, 有两类隐式欧拉方法(对任意步长)能够继承原系统的均方指数输入状态稳定性. 最后, 一些数值实例证实了本文所获结论的正确性.     

随机型不确定中立时滞系统的鲁棒H∞控制

研究了一类具有不确定性的随机性中立时滞系统的鲁棒H∞状态反馈控制器的设计问题.假设时滞是已知的,且时滞同时出现在状态变量和控制变量中,利用线性矩阵不等式方法,给出了状态反馈控制器存在的时滞依赖的充分条件,保证了对于所有的参数不确定性,闭环系统是指数均方稳定的,且从干扰输入到被控输出的影响小于一个指定的性能指标.仿真算例验证了该方法的可行性.     

Approximate finite-dimensional filtering for polynomial states over polynomial observations

In this article, the mean-square filtering problem for polynomial system states over polynomial observations is studied proceeding from the general expression for the stochastic Ito differentials of the mean-square estimate and the error variance. In contrast to the previously obtained results, this article deals with the general case of nonlinear polynomial states and observations. As a result, the Ito differentials for the mean-square estimate and error variance corresponding to the stated filtering problem are first derived. The procedure for obtaining an approximate closed-form finite-dimensional system of the filtering equations for any polynomial state over observations with any polynomial drift is then established. In the example, the obtained closed-form filter is applied to solve the third-order sensor filtering problem for a quadratic state, assuming a conditionally Gaussian initial condition for the extended third-order state vector. The simulation results show that the designed filter yields a reliable and rapidly converging estimate.     

随机控制系统Euler-Maruyama方法的均方指数输入状态稳定性

分析了随机控制系统Euler-Maruyama (EM)方法的均方指数输入状态稳定性. 本文的目的是寻找随机控制系统和EM方法分享它们均方指数输入状态稳定性的条件. 在全局Lipschitz系数和均方连续随机输入的基础上, 二阶矩的界和合适形式的强收敛条件被得到了. 在该强收敛条件下, 我们证明了一个随机控制系统是均方指数输入状态稳定的, 当且仅当对充分小的步长, EM方法也是均方指数输入状态稳定的.     

Consensus problem of networked multi-agent systems with constant communication delay: stochastic switching topology case

This article proposes an observer-based control strategy for networked multi-agent systems with constant communication delay and stochastic switching topology. First, using the system transformation method, the mean-square consensus problem of multi-agent systems can be converted into the mean-square stability problem of an equivalent system, and some equivalent conditions concerning the mean-square consensus are presented. Then, an example is given to illustrate that the connection weights should be regarded as the parameters to be designed, since they have a great effect on the mean-square consensus of multi-agent systems. By choosing appropriate connection weights, the mean-square consensus problem can be converted into the mean-square stabilisation problem of N-1 delay systems with stochastic switching signal, whose related observer-based stabilisability criteria can be established in the form of linear matrix inequalities (LMIs). Furthermore, if the LMIs are feasible, the multi-agent systems achieve mean-square consensus if and only if the union of graphs in the switching topology set has a directed spanning tree. Finally, numerical simulations are given to illustrate our results.     

Consensus based overlapping decentralized estimation with missing observations and communication faults

In this paper a new algorithm for discrete-time overlapping decentralized state estimation of large scale systems is proposed in the form of a multi-agent network based on a combination of local estimators of Kalman filtering type and a dynamic consensus strategy, assuming intermittent observations and communication faults. Under general conditions concerning the agent resources and the network topology, conditions are derived for the convergence to zero of the estimation error mean and for the mean-square estimation error boundedness. A centralized strategy based on minimization of the steady-state mean-square estimation error is proposed for selection of the consensus gains; these gains can also be adjusted by local adaptation schemes. It is also demonstrated that there exists a connection between the network complexity and efficiency of denoising, i.e., of suppression of the measurement noise influence. Several numerical examples serve to illustrate characteristic properties of the proposed algorithm and to demonstrate its applicability to real problems.     

Stabilisation of stochastic coupled systems via feedback control based on discrete-time state observations

This paper is concerned with the stabilisation of stochastic coupled systems (SCSs) via feedback control based on discrete-time state observations. State feedback control based on discrete-time observations is designed in the drift parts of the SCSs. Based on graph theory and Lyapunov method, the upper bound of the duration between two consecutive state observations is obtained. And a systematic method is given to construct a global Lyapunov function for SCSs via feedback control based on discrete-time state observations. A Lyapunov-type theorem and a coefficient-type criterion are obtained to guarantee the stabilisation in the sense of mean-square asymptotical stability and mean-square exponential stability. Furthermore, we use the theoretical results to analyse the stabilisation of stochastic coupled oscillators. Finally, we give a numerical example to illustrate the effectiveness and feasibility of the developed theoretical results.     

欠驱动船舶航迹Backstepping自适应模糊控制

针对欠驱动船舶直线航迹跟踪问题,提出一种Backstepping自适应模糊控制方法．在模糊逼近误差存在未知上确界的假设条件下,基于Lyapunov~论证明了闭环系统在所有信号一致最终有界意义下具有均方意义稳定性．本文提出的控制器具有设计直观和结构简洁的特点,并且对参数摄动和外界干扰都具有良好的鲁棒性．在状态变量和控制输入共同约束下的仿真实验验证了该方法的有效性．     

State estimation for linear hybrid systems with periodic jumps and unknown inputs

In order to solve the state estimation problem for linear hybrid systems with periodic jumps and unknown inputs, some hybrid observers are proposed. The proposed observers admit a Luenberger‐like structure and the synthesis is given in terms of linear matrix inequalities (LMIs). Therefore, the proposed observer designs are completely constructive and provide some input‐to‐state stability properties with respect to unknown inputs. It is worth mentioning that the structure of the hybrid observers, as well as the structure of the LMIs, depends on some observability properties of the flow and jump dynamics, respectively. Then, in order to compensate the effect of the unknown inputs, a hybrid sliding‐mode observer is added to the Luenberger‐like observer structure, providing exponential convergence to zero of the state estimation error despite certain class of unknown inputs. The existence of the hybrid observers and the unknown input hybrid observer is guaranteed if and only if the hybrid system is observable and strongly observable, respectively. Some numerical examples illustrate the feasibility of the proposed estimation approach.     

A note on discrete-time positive realizations

A discrete-time positive linear system has the property that any nonnegative initial state and any nonnegative input produces a nonnegative trajectory in the state space and output for all time. Such systems are Rⁿ⁺-reachable if every state of the nonnegative orthant Rⁿ⁺ is reachable from origin with a nonnegative input function, in a finite-time interval. A simple necessary and sufficient condition for Rⁿ⁺-realizability, i.e. for the existence of a nonnegative realization that is also Rⁿ⁺-reachable, is stated. The realization procedure is straightforward.     

On the stability of the continuous-time Kalman filter subject to exponentially decaying perturbations

This paper details the stability analysis of the continuous-time Kalman filter dynamics for linear time-varying systems subject to exponentially decaying perturbations. It is assumed that estimates of the input, output, and matrices of the system are available, but subject to unknown perturbations which decay exponentially with time. It is shown that if the nominal system is uniformly completely observable and uniformly completely controllable, and if the state, input, and matrices of the system are bounded, then the Kalman filter built using the perturbed estimates is a suitable state observer for the nominal system, featuring exponentially convergent error dynamics.     

Noncooperative Model Predictive Game With Markov Jump Graph

In this paper,the distributed stochastic model predictive control(MPC) is proposed for the noncooperative game problem of the discrete-time multi-player systems(MPSs) with the undirected Markov jump graph.To reflect the reality,the state and input constraints have been considered along with the external disturbances.An iterative algorithm is designed such that model predictive noncooperative game could converge to the socalled ε-Nash equilibrium in a distributed manner.Sufficient conditions are ...     

Linear approximations of nonlinear FIR systems for separable input processes

Nonlinear systems can be approximated by linear time-invariant (LTI) models in many ways. Here, LTI models that are optimal approximations in the mean-square error sense are analyzed. A necessary and sufficient condition on the input signal for the optimal LTI approximation of an arbitrary nonlinear finite impulse response (NFIR) system to be a linear finite impulse response (FIR) model is presented. This condition says that the input should be separable of a certain order, i.e., that certain conditional expectations should be linear. For the special case of Gaussian input signals, this condition is closely related to a generalized version of Bussgang's classic theorem about static nonlinearities. It is shown that this generalized theorem can be used for structure identification and for the identification of generalized Wiener-Hammerstein systems.     

Static decentralized control of a single-integrator network with Markovian sensing topology

Static stabilization of a decentralized discrete-time single-integrator network that is subject to Markovian variation in the communication/sensing topology is considered. In particular, we develop sufficient conditions on the Markovian topology for mean-square stabilization using a decentralized static controller that has no knowledge of the underlying Markov state. Our analysis exposes a deep connection between decentralized control of single-integrator networks with Markovian topology and those with fixed topology: static stabilization of the network with Markovian topology is possible whenever the steady-state time-average of the Markovian topology is amenable to static (fixed-topology-based) decentralized control.     

带马尔科夫跳的模态相关时变时滞随机系统的状态反馈控制器设计

针对带马尔科夫跳的模态相关时变时滞系统得到了一个改进的均方指数稳定结果并设计了状态反馈控制器. 首先, 通过构造一个改进的Lyapunov-Krasovskii泛函, 以线性矩阵不等式的形式给出一个均方指数稳定性条件; 这里, 衰减率可以是一个在区间内取值的有限常数, 同时, 时变时滞的导数上界不要求小于1; 基于得到的稳定性条件, 设计了状态反馈的控制器. 最后, 通过两个仿真算例验证了所得理论的结果的有效性, 并与已有结果相比较, 保守性较弱.     

Hermite Polynomials for Iterative Output Replanning for Flat Systems Affected by Additive Noise

The paper considers the output tracking problem for nonlinear systems whose performance output is also a flat output of the system itself. A desired output signal is sought on the actual performance output by using a feedforward inverse input that is periodically updated with discrete‐time feedback of the sampled state of the system. The proposed method is based on an iterative output replanning that uses the desired output trajectory and the sampled state to replan an output trajectory whose inverse input helps in reducing the tracking error. This iterative replanning exploits the Hermite interpolating polynomials to achieve an overall arbitrarily smooth input and a tracking error that can be made arbitrarily small if the state sampling period is sufficiently small and mild assumptions are considered. Some simulation results are presented for the cases of a unicycle and a one‐trailer system affected by additive noise.     

受外界干扰的离散多智能体系统的均方有界一致性

对有外界干扰的二阶离散多智能体系统,研究了在马尔可夫切换拓扑结构下的均方有界一致性问题.首先,设计了一个带有智能体位置和速度信息的控制协议.其次,在随机有界干扰的情况下,借助于矩阵分析方法以及Lyapunov函数,得到了闭环系统实现均方有界一致所需的代数条件,同时给出了各智能体状态误差的上界.最后,数值仿真验证了理论结果的有效性.     

Stochastic Iterative Learning Control With Faded Signals

Stochastic iterative learning control (ILC) is designed for solving the tracking problem of stochastic linear systems through fading channels. Consequently, the signals used in learning control algorithms are faded in the sense that a random variable is multiplied by the original signal. To achieve the tracking objective, a two-dimensional Kalman filtering method is used in this study to derive a learning gain matrix varying along both time and iteration axes. The learning gain matrix minimizes the trace of input error covariance. The asymptotic convergence of the generated input sequence to the desired input value is strictly proved in the mean-square sense. Both output and input fading are accounted for separately in turn, followed by a general formulation that both input and output fading coexists. Illustrative examples are provided to verify the effectiveness of the proposed schemes.