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H∞ Filtering for Discrete-Time Systems with Time-Varying Delay
Huanshui Zhang,Wei Wang,Chunyan Han 제어·로봇·시스템학회 2010 International Journal of Control, Automation, and Vol.8 No.6
The problem of H∞ filtering for discrete-time systems with time-varying delay in measurement is investigated in this paper. First, under the assumption that the time-varying delay is of a known upper bound, the delayed measurement is re-described as the one with multiple state delays. Then the proposed H∞ filtering problem is transformed into one for systems with multiple measurement chan-nels that contain the same state information as the original measurement and each channel has a single constant delay. Finally, based on the reorganized innovation analysis approach in Krein space, a necessary and sufficient condition for the existence of an H∞ filter which guarantees a prescribed attenuation level is derived. The solution to the H∞ filtering is given in terms of the solutions to Riccati and matrix difference equations.
Huanshui Zhang,Xiao Lu,Weihai Zhang,Wei Wang 대한전기학회 2007 International Journal of Control, Automation, and Vol.5 No.4
The paper deals with the Kalman stochastic filtering problem for linear continuous-time systems with both instantaneous and time-delayed measurements. Different from the standard linear system, the system state is corrupted by multiplicative white noise, and the instantaneous measurement and the delayed measurement are also corrupted by multiplicative white noise. A new approach to the problem is presented by using projection formulation and re-organized innovation analysis. More importantly, the proposed approach in the paper can be applied to solve many complicated problems such as stochastic H∞ estimation, H∞ control stochastic system with preview and so on.
Fangfang Zhang,Jinfeng Gao,Huanshui Zhang,Cheng Tan,Wei Wang 제어·로봇·시스템학회 2017 International Journal of Control, Automation, and Vol.15 No.6
In this paper, the distributed control of the LQR problem for continuous-time multi-agent systems isconsidered. Based on the centralized optimal control, we prove that the solution of the algebraic Riccati equationis the maximal solution of the algebraic Riccati inequality. The algebraic relations of the solutions of the algebraicRiccati equations for different weighted matrices are shown and two distributed controllers are designed: the fullydistributed one and the interconnected distributed one. They can provide an upper bounds and a lower bounds ofthe centralized optimal cost function. The optimal closed-loop feedback control systems for the two distributedcontrollers are also asymptotically stable. Some examples are given to show the correctness of the proposed results.
Consensus Problems for Discrete-time Agents with Communication Delay
Zhenhua Wang,Huanshui Zhang,Xinmin Song,Huaxiang Zhang 제어·로봇·시스템학회 2017 International Journal of Control, Automation, and Vol.15 No.4
In this paper, consensus problems for first-order multi-agent systems with unstable pole are investigatedover undirected network, where the network is affected by communication delay. By jointly utilizing both thedelayed distributed state information and agent’s own historical input information in the protocol, sufficient conditionrelated to agent dynamic, network topology and communication delay is obtained for consensus, which isalso proven to be necessary in case of one step delay. Furthermore, the consensus problem is studied on conditionthat the delay is time-varying. Finally, numerical simulations are provided to demonstrate the effectiveness of theproposed theoretical results.
Filtering for Discrete-time Linear Noise Delay Systems
Peng Cui,Huanshui Zhang,Lihua Xie,Chenghui Zhang 제어·로봇·시스템학회 2009 International Journal of Control, Automation, and Vol.7 No.5
Optimal state estimation problem for discrete-time systems with delays in noise sequence is investigated. Predictor similar to the traditional Kalman ones is derived based on projection formula in Hilbert space. Filter and fixed-lag smoother are obtained at the same time. The estimators are presented by solving two coupled Riccati-type difference equations. One example shows the effectiveness of the proposed approach.
On the H∞ Deconvolution Fixed-lag Smoothing
Xiao Lu,Huanshui Zhang,Jie Yan 제어·로봇·시스템학회 2010 International Journal of Control, Automation, and Vol.8 No.4
The paper deals with the H∞ deconvolution fixed-lag smoothing problem for a linear time-invariant discrete-time system with both known and unknown input series. The H∞ fixed-lag smoother is derived by proposing a new approach termed as re-organized innovation analysis in Krein space. Under the new approach, it is clearly shown that the central deconvolution smoother in an H∞ setting is the same as the one in an H2 setting associated with one self-constructed stochastic state-space model. This insight allows us to calculate the complicated H∞ deconvolution smoother in an intuitive and simple way. The deconvolution smoother is calculated by performing Riccati equation with the same order as the original system.
Optimal Estimation for Continuous-Time Markovian Jump Linear Systems with Delayed Measurements
Chunyan Han,Huanshui Zhang 제어·로봇·시스템학회 2009 International Journal of Control, Automation, and Vol.7 No.6
This paper is to investigate the linear minimum mean square error estimation for continuous-time Markovian jump linear systems with delayed measurements. The key technique applied for treating the measurement delay is the reorganization innovation analysis, by which the state estimation with delayed measurements is transformed into a standard linear mean square filter of an associated delay-free system. The optimal filter is derived based on the innovation analysis method together with geometric arguments in Hilbert space. An analytical solution to the filter is obtained in terms of two Riccati differential equations, and hence is very simple in computation. Computer simulations are carried out to evaluate the performance of the proposed algorithms. The problem of tracking a maneuvering target is addressed.
Optimal Control with Terminal State Constraints for Multichannel Input Linear Systems
Qichao Sun,Juanjuan Xu,Huanshui Zhang 제어·로봇·시스템학회 2022 International Journal of Control, Automation, and Vol.20 No.10
This paper is concerned with the linear quadratic (LQ) control problem with multiple input channels and terminal state constraints. The problem can be solved by augmenting all the inputs into one. However, the calculation will be much more involved especially for the case with large scale of inputs. To overcome this complexity, we adopt a leader-follower game theory approach. The optimal controller is obtained in the feedback of the state in terms of Riccati equations. A numerical example is provided to demonstrate the effectiveness of the derived result.
An LMI Approach to Robust Congestion Control of ATM Networks
Jun Lin,Lihua Xie,Huanshui Zhang 대한전기학회 2006 International Journal of Control, Automation, and Vol.4 No.1
In this paper, ATM network congestion control with explicit rate feedback is considered. In ATM networks, delays commonly appear in data transmission and have to be considered in congestion control design. In this paper, a bounded single round delay on the return path is considered. Our objective is to design an explicit rate feedback control that achieves a robust optimal H₂ performance regardless of the bounded time-varying delays. An optimization approach in terms of linear matrix inequalities (LMIs) is given. Saturation in source rate and queue buffer is also taken into consideration in the proposed design. Simulations for the cases of single source and multiple sources are presented to demonstrate the effectiveness of the design.
Solution to Mixed H2/H∞ Control for Discrete-time Systems with (x,u,v)-dependent Noise
Xiaoqian Li,Wei Wang,Juanjuan Xu,Huanshui Zhang 제어·로봇·시스템학회 2019 International Journal of Control, Automation, and Vol.17 No.2
In this paper, the stochastic H2=H∞ control problem for linear discrete-time systems with (x;u;v)-dependent noise is studied. By applying the leader-follower stochastic game approach, the disturbance is treatedas the follower and the control input is treated as the leader, respectively. Necessary and sufficient conditions forthe mixed control problem are presented which guarantee the existence and uniqueness of the optimal solution. Byapplying the stochastic maximum principle, the follower first solves a stochastic linear quadratic optimal controlproblem which is given in the form of H∞-norm with the aid of stochastic Riccati equations. Then the leader solves astochastic linear quadratic problem with the aid of forward and backward equations. The main technique is to introducetwo new co-states to capture the future information, the encountered difficulty is to establish a homogeneousrelationship between the new co-states.