Optimal filtering for networked systems with Markovian communication delays

This paper is concerned with optimal filter problems for networked systems with random transmission delays, while the delay process is modeled as a multi-state Markov chain. By defining a delay-free observation sequence, the optimal filter problems are transformed into ones of the Markov jumping parameter system. We first present an optimal Kalman filter, which is with time-varying, path-dependent filter gains, and the number of the paths grows exponentially in time delay. Thus an alternative optimal Markov jump linear filter is presented, in which the filter gains just depend on the present value of the Markov chain. Further, an optimal filter with constant-gains is developed, the existence condition for the stabilizing solutions to the filter is given, and it can be shown that the proposed Markov jump linear filter converges to the constant-gain filter under appropriate assumptions.     

Optimal errors-in-variables filtering

This paper deals with optimal (minimal variance) filtering in an errors-in-variables framework. Differently from many other contexts, errors-in-variables models treat all variables in a symmetric way (no partition of the variables into inputs and outputs is required) and assume additive noise on all the variables. The filtering technique described in this paper can be easily implemented in a recursive way and does not require the use of a Riccati equation at every update. The results of Monte Carlo simulations have shown the effectiveness and consistency of the approach.     

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.     

Real-time optimal filtering for stochastic systems with multiresolutional measurements

A real-time optimal filtering algorithm for stochastic systems with multiresolutional measurements is derived. The algorithm gives fused estimates based upon all available data at a particular time index. A multiresolutional distributed filtering scheme is employed. The wavelet transform is utilized as a bridge, effectively linking different resolution levels. A tree-like hierarchical data structure introduced in this paper facilitates the real-time multiresolutional filtering.     

一类具有数据包丢失的网络控制系统的最优控制

针对控制器和执行器均采用时钟驱动且最大丢包率和最大连续丢包长度被限定的短时延网络控制系统,提出一种数据包丢失的估值补偿方法.该方法可以根据历史状态向量和控制向量信息估算出当前的控制量.利用该方法和动态规划算法,导出了离散二次型性能指标下的网络控制系统的最优控制序列,进而给出最优控制律的实现算法.数值仿真算例验证了所得结果的有效性和正确性.     

A small gain theorem for linear stochastic systems

A well-known result in linear control theory is the so-called “small gain” theorem stating that if given two plants with transfer matrix functions T₁ and T₂ in H^∞ such that T₁ < γ and T₂ < 1/γ, when coupling T₂ to T₁ such that u₂ = y₁ and u₁ = y₂ one obtains an internally stable closed system. The aim of the present paper is to describe a corresponding result for stochastic systems with state-dependent white noise.     

Set-membership filtering for systems with sensor saturation

This paper addresses the set-membership filtering problem for a class of discrete time-varying systems with sensor saturation in the presence of unknown-but-bounded process and measurement noises. A sufficient condition for the existence of set-membership filter is derived. A convex optimisation method is proposed to determine a state estimation ellipsoid that is a set of states compatible with sensor saturation and unknown-but-bounded process and measurement noises. A recursive algorithm is developed for computing the ellipsoid that guarantees to contain the true state by solving a time-varying linear matrix inequality. Simulation results are provided to demonstrate the effectiveness of the proposed method.     

Optimal probability density function control for NARMAX stochastic systems

This paper presents a new control strategy for a class of non-Gaussian stochastic systems so that the output probability density function (PDF) of the system can be made to follow a desired PDF. The system considered is represented by an Nonlinear AutoRegressive and Moving Average with eXogenous (NARMAX) inputs with input channel time-delay and non-Gaussian noise. A multi-step-ahead nonlinear cumulative cost function is used to improve tracking performance. For this purpose, a relationship between the PDFs of all the inputs and the PDFs of multiple-step-ahead output is formulated by constructing an auxiliary multivariate mapping. By minimizing this performance function, a new explicit predictive controller design algorithm is established with less conservatism than some previous results. Furthermore, an improved approach is developed to guarantee the local stability of the closed-loop system by tuning the weighting parameters recursively. Simulations are given to demonstrate the effectiveness of the proposed control algorithm and desired results have been obtained.     

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.     

On controller & capacity allocation co-design for networked control systems

This paper presents a framework for examining joint optimal channel-capacity allocation and controller design for networked control systems using store-and-forward networks in a discrete-time linear time-invariant setting. The resultant framework provides a synthesis procedure for designing distributed linear control laws for capacity-constrained networks taking the allocation of the capacity within the network into account.