Discrete-time controller for stochastic nonlinear polynomial systems with Poisson noises

This paper presents a solution to the optimal control problem for discrete-time stochastic nonlinear polynomial systems confused with white Poisson noises subject to a quadratic criterion. The solution is obtained in the following way: a nonlinear optimal controller is first developed for polynomial systems, considering the state vector completely available for control design. Then, based on the solution of the state estimation problem for polynomial systems with white Poisson noises, the state estimate vector is used in the control law to obtain a closed-form solution. Performance of this controller is compared to that of the controller employing the extended Kalman filter and the linear-quadratic regulator and the controller designed for polynomial systems confused with white Gaussian noises.     

Discrete-time filtering for nonlinear polynomial systems over linear observations

This paper designs a discrete-time filter for nonlinear polynomial systems driven by additive white Gaussian noises over linear observations. The solution is obtained by computing the time-update and measurement-update equations for the state estimate and the error covariance matrix. A closed form of this filter is obtained by expressing the conditional expectations of polynomial terms as functions of the estimate and the error covariance. As a particular case, a third-degree polynomial is considered to obtain the finite-dimensional filtering equations. Numerical simulations are performed for a third-degree polynomial system and an induction motor model. Performance of the designed filter is compared with the extended Kalman one to verify its effectiveness.     

Discrete-time optimal control for stochastic nonlinear polynomial systems

This paper presents a solution to the discrete-time optimal control problem for stochastic nonlinear polynomial systems over linear observations and a quadratic criterion. The solution is obtained in two steps: the optimal control algorithm is developed for nonlinear polynomial systems by considering complete information when generating a control law. Then, the state estimate equations for discrete-time stochastic nonlinear polynomial system over linear observations are employed. The closed-form solution is finally obtained substituting the state estimates into the obtained control law. The designed optimal control algorithm can be applied to both distributed and lumped systems. To show effectiveness of the proposed controller, an illustrative example is presented for a second degree polynomial system. The obtained results are compared to the optimal control for the linearized system.     

Stochastically resilient extended Kalman filtering for discrete-time nonlinear systems with sensor failures

Missing sensor data is a common problem, which severely influences the overall performance of modern data-intensive control and computing applications. In order to address this important issue, a novel resilient extended Kalman filter is proposed for discrete-time nonlinear stochastic systems with sensor failures and random observer gain perturbations. The failure mechanisms of multiple sensors are assumed to be independent of each other with different failure rates. The locally unbiased robust minimum mean square filter is designed for state estimation under these conditions. The performance of the proposed estimation method is verified by means of numerical Monte Carlo simulation of two different nonlinear stochastic systems, involving a sinusoidal system and a Lorenz oscillator system.     

含结构参数摄动的线性离散系统的鲁棒约束方差状态估计

考虑状态矩阵中含不确定性的线性离散随机系统的鲁棒约束方差状态估计问题,即设计滤波增益,使摄动系统每个状态分量的估计误差方差的稳态值不大于各自预先给定值。给出了期望鲁棒滤波增益的存在条件及其解析表达式,并以数值算例说明了设计方法的直接性与有效性。     

Quantised polynomial filtering for nonlinear systems with missing measurements

This paper is concerned with the polynomial filtering problem for a class of nonlinear systems with quantisations and missing measurements. The nonlinear functions are approximated with polynomials of a chosen degree and the approximation errors are described as low-order polynomial terms with norm-bounded coefficients. The transmitted outputs are quantised by a logarithmic quantiser and are also subject to randomly missing measurements governed by a Bernoulli distributed sequence taking values on 0 or 1. Dedicated efforts are made to derive an upper bound of the filtering error covariance in the simultaneous presence of the polynomial approximation errors, the quantisations as well as the missing measurements at each time instant. Such an upper bound is then minimised through designing a suitable filter gain by solving a set of matrix equations. The filter design algorithm is recursive and therefore applicable for online computation. An illustrative example is exploited to show the effectiveness of the proposed algorithm.     

Robust discrete‐time nonlinear sliding mode state estimation of uncertain nonlinear systems

In this paper, we propose a discrete‐time nonlinear sliding mode observer for state and unknown input estimations of a class of single‐input/single‐output nonlinear uncertain systems. The uncertainties are characterized by a state‐dependent vector and a scalar disturbance/unknown input. The discrete‐time model is derived through Taylor series expansion together with nonlinear state transformation. A design methodology that combines the discrete‐time sliding mode (DSM) and a nonlinear observer design is adopted, and a strategy is developed to guarantee the convergence of the estimation error to a bound within the specified boundary layer. A relation between sliding mode gain and boundary layer is established for the existence of DSM, and the estimation is made robust to external disturbances and uncertainties. The unknown input or disturbance can also be estimated through the sliding mode. The conditions for the asymptotical stability of the estimation error are analysed. Application to a bioreactor is given and the simulation results demonstrate the effectiveness of the proposed scheme. Copyright © 2006 John Wiley & Sons, Ltd.     

Mean-square filter design for stochastic polynomial systems with Gaussian and Poisson noises

This paper addresses the mean-square finite-dimensional filtering problem for polynomial system states with both, Gaussian and Poisson, white noises over linear observations. A constructive procedure is established to design the mean-square filtering equations for system states described by polynomial equations of an arbitrary finite degree. An explicit closed form of the designed filter is obtained in case of a third-order polynomial system. The theoretical result is complemented with an illustrative example verifying performance of the designed filter.     

Fixed‐time state estimation for a class of switched nonlinear time‐varying systems

This paper deals with the state estimation problem of a class of nonlinear time‐varying systems with switched dynamics. Based on the concept of fixed‐time stability, an observer is designed to reconstruct the continuous state of switched nonlinear time‐varying systems with state jumps, satisfying the minimal dwell‐time condition. Using the past input and output values of the studied system, some sufficient conditions are provided to estimate the state before the next switching. Some numerical results illustrate the effectiveness of the proposed scheme.     

Optimal guaranteed cost filtering for uncertain discrete-time linear systems

This paper presents a result on the design of a steady-state robust state estimator for a class of uncertain discrete-time linear systems with normal bounded uncertainty. This result extends the steady state Kalman filter to the case in which the underlying system is uncertain. A procedure is given for the construction of a state estimator which minimizes a bound on the state error covariance. It is shown that this leads to a state estimator which is optimal with respect to a notion of quadratic guaranteed cost state estimation.     

离散变结构系统的衰减变速控制

提出离散变结构控制系统基于衰减控制的变速趋近律。这种新型控制策略保留了比例 等速 变速控制策略的优点 ;而且其构造也相当简单。并论证了离散系统的指数趋近律实质上也是一种基于衰减控制的等速趋近律     

一类不确定非线性离散时滞系统的鲁棒H∞滤波设计

考虑一类同时带有非线性动态和参数不确定性的离散时滞系统的鲁棒H-infinity滤波设计问题. 假设参数不确定性具有线性分式形式, 而非线性动态满足Lipschitz条件, 给出滤波器使误差系统鲁棒渐近稳定且达到指定的干扰抑制水平. 对参数已知情形, 先建立广义有界实引理, 然后给出H-infinity滤波器的存在条件, 证明了H-infinity滤波器的存在性可归结为线性矩阵不等式的可解性, 基于线性矩阵不等式给出了H-infinity滤波器的综合方法和步骤. 对参数不确定性情形, 通过引进标度参数, 将不确定非线性离散时滞系统的鲁棒H-infinity滤波问题转化为确定系统的H-infinity滤波设计. 最后给出仿真例子验证所得结果的有效性.     

一类不确定非线性离散时滞系统的鲁棒H∞滤波设计

考虑一类同时带有非线性动态和参数不确定性的离散时滞系统的鲁棒H∞滤波设计问题．假设参数不确定性具有线性分式形式,而非线性动态满足Lipschitz条件,给出滤波器使误差系统鲁棒渐近稳定且达到指定的干扰抑制水平．对参数已知情形,先建立广义有界实引理,然后给出H∞滤波器的存在条件,证明了H∞滤波器的存在性可归结为线性矩阵不等式的可解性,基于线性矩阵不等式给出了H∞滤波器的综合方法和步骤．对参数不确定性情形,通过引进标度参数,将不确定非线性离散时滞系统的鲁棒H∞滤波问题转化为确定系统的H∞滤波设计．最后给出仿真例子验证所得结果的有效性．     

Robust Kalman filtering for uncertain discrete‐time linear systems

This paper presents a steady‐state robust state estimator for a class of uncertain discrete‐time linear systems with norm‐bounded uncertainty. It is shown that if the system satisfies some particular structural conditions and if the uncertainty has a specific structure, the gain of the robust estimator (which assures a guaranteed cost) can be calculated using a formula only involving the original system matrices. Among the conditions the system has to satisfy, the strongest one relies on a minimum phase argument. It is also shown that under the assumptions considered, the robust estimator is in fact the Kalman filter for the nominal system. Copyright © 2003 John Wiley & Sons, Ltd.     

State estimation for a class of discrete nonlinear systems with randomly occurring uncertainties and distributed sensor delays

In this paper, the state estimation problem is investigated for a class of discrete nonlinear systems with randomly occurring uncertainties and distributed sensor delays. The norm-bounded uncertainties enter into the system in a randomly way, and such randomly occurring uncertainties (ROUs) obey certain Bernoulli distributed white noise sequence with known conditional probability. By constructing a new Lyapunov–Krasovskii functional, sufficient conditions are proposed to guarantee the convergence of the estimation error for all discrete time-varying delays, ROUs and distributed sensor delays. Subsequently, the explicit form of the estimator parameter is derived by solving two linear matrix inequalities (LMIs) which can be easily tested by using standard numerical software. Finally, a simulation example is given to illustrate the feasibility and effectiveness of the proposed estimation scheme.     

Discrete-time adaptive control for deterministic time-varying systems

There is currently considerable interest in the application of recently developed self-tuning control algorithms to real control problems. However, there exist few algorithms which will work for other than slow time-varying systems. A new algorithm which is able to successfully control unknown systems with quite rapidly varying parameters is presented. Several simulation results are also presented. A convergence proof in the linearly time-varying parameter case is given.     

基于凸空间收缩滤波的噪声不确定时滞系统状态估计

针对受未知但有界噪声干扰的噪声不确定时滞系统, 提出了一种基于凸空间收缩滤波的系统状态估计方法. 首先, 利用凸空间定义包裹系统真实状态的可行集, 求解下一时刻的凸空间体形状矩阵; 随后从凸空间收缩角度, 利用当前时刻噪声和扰动构造带空间, 得到满足状态预测和量测更新条件的凸空间结构; 进而, 依据时滞系统约束条件构造线性规划不等式方程组, 利用线性规划求解该凸空间, 得到包裹状态可行集的最紧致凸空间体; 最后, 通过数值仿真与电池化成工艺变换器案例仿真, 验证了本文所提方法解决不确定时滞系统状态估计问题的有效性和准确性.     

Dissipative interval observer design for discrete‐time nonlinear systems

This paper studies the problem of designing interval observers for a family of discrete‐time nonlinear systems subject to parametric uncertainties and external disturbances. The design approach states that the interval observers are constituted by a couple of preserving order observers, one providing an upper estimation of the state while the other provides a lower one. The design aim is to apply the cooperative and dissipative properties to the discrete‐time estimation error dynamics in order to guarantee that the upper and lower estimations are always above and below the true state trajectory for all times, while both estimations asymptotically converge towards a neighborhood of the true state values. The approach represents an extension to the original method proposed by the authors, which focuses on the continuous‐time nonlinear systems. In some situations, the design conditions can be formulated as bilinear matrix inequalities (BMIs) and/or linear matrix inequalities (LMIs). Two simulation examples are provided to show the effectiveness of the design approach.     

基于Kalman滤波的带相关噪声系统统一的Wiener状态估值器

基于Kalman滤波和白噪声估值器, 对带非零均值相关噪声系统提出了渐近稳定的统一的和通用的Wiener状态估值器. 它们可统一处理滤波、平滑和预报问题, 且避免了计算最优初始状态估值. 它们揭示了Kalman滤波器和Wiener滤波器之间的关系.一个仿真例子说明其有效性.     

Experimental application of nonlinear minimum variance estimation for fault detection systems

The purpose of this paper is to present an experimental design and application of a novel model-based fault detection technique by using a nonlinear minimum variance (NMV) estimator. The NMV estimation technique is used to generate a residual signal which is then used to detect faults in the system. The main advantage of the approach is the simplicity of the nonlinear estimator theory and the straightforward structure of the resulting solution. The proposed method is implemented and validated experimentally on DC servo system. Experimental results demonstrate that the technique can produce acceptable performance in terms of fault detection and false alarm.