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.     

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.     

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.     

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.     

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．     

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     

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.     

Distributed moving horizon state estimation for nonlinear systems with bounded uncertainties

In this work, we propose a distributed moving horizon state estimation (DMHE) design for a class of nonlinear systems with bounded output measurement noise and process disturbances. Specifically, we consider a class of nonlinear systems that are composed of several subsystems and the subsystems interact with each other via their subsystem states. First, a distributed estimation algorithm is designed which specifies the information exchange protocol between the subsystems and the implementation strategy of the DMHE. Subsequently, a local moving horizon estimation (MHE) scheme is designed for each subsystem. In the design of each subsystem MHE, an auxiliary nonlinear deterministic observer that can asymptotically track the corresponding nominal subsystem state when the subsystem interactions are absent is taken advantage of. For each subsystem, the nonlinear deterministic observer together with an error correction term is used to calculate a confidence region for the subsystem state every sampling time. Within the confidence region, the subsystem MHE is allowed to optimize its estimate. The proposed DMHE scheme is proved to give bounded estimation errors. It is also possible to tune the convergence rate of the state estimate given by the DMHE to the actual system state. The performance of the proposed DMHE is illustrated via the application to a reactor-separator process example.     

Event-triggered filtering and fault estimation for nonlinear systems with stochastic sensor saturations

This paper is concerned with the filtering problem for a class of nonlinear systems with stochastic sensor saturations and event-triggered measurement transmissions. An event-triggered transmission scheme is proposed with hope to ease the traffic burden and improve the energy efficiency. The measurements are subject to randomly occurring sensor saturations governed by Bernoulli-distributed sequences. Special effort is made to obtain an upper bound of the filtering error covariance in the presence of linearisation errors, stochastic sensor saturations as well as event-triggered transmissions. A filter is designed to minimise the obtained upper bound at each time step by solving two sets of Riccati-like matrix equations, and thus the recursive algorithm is suitable for online computation. Sufficient conditions are established under which the filtering error is exponentially bounded in mean square. The applicability of the presented method is demonstrated by dealing with the fault estimation problem. An illustrative example is exploited to show the effectiveness of the proposed algorithm.     

Discrete-time estimation in continuous-time communication systems

An alternative to continuous-time Kalman filtering is sampled digital processing. The purpose is to develop a good model for this situation and investigate the resulting performance. The error dependence on the sample rate is studied. It is found that a sample rate considerably higher than twice the half power-frequency is necessary to avoid loss of performance where zero-lag filtering is desired. Smoothing is discussed and in this context three results of major importance are found; (1) an optimal sample rate exists for each smoother (2) only a few steps of lag is necessary to approach the ideal unrealizable error (3) a considerable lower sample rate can be accepted for smoothing as compared with filtering. This finding is of interest as the corresponding ideal continuous-time smoother has been reported unstable. Finally a comparison is made with approximate models suggested in the relevant literature.     

Invariants and canonical forms for systems structural and parametric identification

The basic definitions regarding invariant functions and canonical forms for an equivalence relation on a generic set are first recalled.With reference to observable state space models and to the equivalence relation induced by a change of basis it is then shown how the image of a complete set of independent invariants for the considered equivalence relation can be used to parametrize a subset of canonical forms in the given set.Then the set of polynomial input-output models of the type P(z)y(t)=Q(z)u(t) and the equivalence relation induced by the premultiplication of P and Q by a unimodular matrix are considered and canonical forms parametrized by a complete set of independent invariants introduced.Since the two sets of canonical forms share common sets of complete independent invariants, very simple algebraical links between state space and input-output canonical forms can be deduced.The previous results are used to design efficient algorithms solving the problem of the canonical structural and parametric realization and identification of generic input-output sequences generated by a linear, discrete, time-invariant multivariable system.The results obtained in the identification of a real process are then reported.     

Parameter identification technique for multivariate stochastic systems

This paper considers the problem of obtaining accurate estimates of multivariate systems with reasonable computations. To avoid the structural identification problem which is associated with multivariate systems, we observe the system by a linear combination of the outputs. The two stage least square method is employed to estimate the model parameters. An optimum combination of the outputs is obtained such that the parameter estimates have the least asymptotic generalized variance. Computer simulations are provided to illustrate the usefulness of the proposed method.     

Unified Set Membership theory for identification, prediction and filtering of nonlinear systems

The problem of making inferences from data measured on nonlinear systems is investigated within a Set Membership (SM) framework and it is shown that identification, prediction and filtering can be treated as specific instances of the general presented theory. The SM framework presents an alternative view to the Parametric Statistical (PS) framework, more widely used for studying the above specific problems. In particular, in the SM framework, a bound only on the gradient of the model regression function is assumed, at difference from PS methods which assume the choice of a parametric functional form of the regression function. Moreover, the SM theory assumes only that the noise is bounded, in contrast with PS approaches, which rely on noise assumptions such as stationarity, uncorrelation, type of distribution, etc. The basic notions and results of the general inference making theory are presented. Moreover, some of the main results that can be obtained for the specific inferences of identification, prediction and filtering are reviewed. Concluding comments on the presented results are also reported, focused on the discussion of two basic questions: what may be gained in identification, prediction and filtering of nonlinear systems by using the presented SM framework instead of the widely diffused PS framework? why SM methods could provide stronger results than the PS methods, requiring weaker assumptions on system and on noise?     

Simple stability criteria for nonlinear time-varying discrete systems

We present two sufficient conditions for asymptotic stability of nonlinear time-varying discrete systems. Our main results generalize Mori's result for linear discrete time-invariant systems to nonlinear time-varying systems.     

Distributed agent-based control and estimation over unreliable networks for a class of nonlinear large-scale systems

A new technique for distributed estimation and control of large-scale systems is presented in this paper. The proposed method makes use of a set of agents that implement local H _∞ controllers and Luenberger-like observers, improved with consensus-based corrections that incorporate information received from other agents. The communication between agents is assumed to be unreliable, this is modelled by time-varying delays and packet dropouts. The proposed methodology is an application for a class of nonlinear system affected by external disturbances. Some simulations are presented to illustrate the performance of this technique compared to the centralised case.     

A continuous state feedback controller design for high-order nonlinear systems with polynomial growth nonlinearities

In this paper, we investigate the problem of global stabilization for a general class of high-order and non-smoothly stabilizable nonlinear systems with both lower-order and higher-order growth conditions. The designed continuous state feedback controller is recursively constructed to guarantee the global strong stabilization of the closed-loop system.     

Comments on: “Exact and approximate state estimation for nonlinear dynamic systems”

After deriving the realizable, nonlinear filtering algorithm for dynamic systems involving white and non-white processes, the above paper (Liang and Christensen, 1975) extended the algorithm to dynamic systems having noise-free observation. However, the resulted nonlinear noise-free filtering is not correct since the paper overlooked the Itô stochastic calculus to differentiate noise-free nonlinear measurements. Here we show the correct extension.     

Moving horizon estimation for switching nonlinear systems

This paper is concerned with moving horizon estimation for a class of constrained switching nonlinear systems, where the system mode is regarded as an unknown discrete state to be estimated together with the continuous state. In this work, we establish the observability framework of switching nonlinear systems by proposing a series of concepts about observability and analyzing the properties of such concepts. By fully applying the observability properties, we prove the stability of the proposed moving horizon estimators. Simulation results are reported to verify the derived results.