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Distributed Suboptimal Controller Synthesis for Multi-agent Systems
Fangfang Zhang,Wei Wang,Huan-Shui Zhang 제어·로봇·시스템학회 2015 International Journal of Control, Automation, and Vol.13 No.3
In this paper, the distributed suboptimal LQR control problem for discrete-time multi-agent systems is considered. The distributed controllers that each subsystem can sense and/or exchange information with only a subset of its neighbors are designed, which are based on the topological structure of the system. Using the “averaged” optimization approach, the suboptimal feedback gain matrices are presented and the distributed suboptimal controllers are obtained. Under mild conditions, the asymptotical convergence of the modified Riccati equation is proved. Accordingly, the infinite-time distributed suboptimal controllers are presented. Examples are given to show the efficiency of the proposed results.
H<SUB>∞</SUB> Multi-Step Prediction for Linear Discrete-Time Systems
Hao-qian Wang,Huan-shui Zhang,Hong Hu 대한전기학회 2008 International Journal of Control, Automation, and Vol.6 No.1
A new approach to H∞ multi-step prediction is developed by applying the innovation analysis theory. Although the predictor is derived by resorting to state augmentation, nevertheless, it is completely different from the previous works with state augmentation. The augmented state here is considered just as a theoretical mathematic tool for deriving the estimator. A distributed algorithm for the Riccati equation of the augmented system is presented. By using the reorganized innovation analysis, calculation of the estimator does not require any augmentation. A numerical example demonstrates the effect in reducing computing burden.
Optimal Filtering for Linear Discrete-Time Systems with Single Delayed Measurement
Hong-Guo Zhao,Huan-Shui Zhang,Cheng-Hui Zhang,Xin-Min Song 대한전기학회 2008 International Journal of Control, Automation, and Vol.6 No.3
This paper aims to present a polynomial approach to the steady-state optimal filtering for delayed systems. The design of the steady-state filter involves solving one polynomial equation and one spectral factorization. The key problem in this paper is the derivation of spectral factorization for systems with delayed measurement, which is more difficult than the standard systems without delays. To get the spectral factorization, we apply the reorganized innovation approach. The calculation of spectral factorization comes down to two Riccati equations with the same dimension as the original systems.
Spectral Factorization for Multiple Input Delayed Discrete-Time Systems with Applications to Control
Hong-Guo Zhao,Huan-Shui Zhang,Peng Cui,Xiao Lu 제어·로봇·시스템학회 2010 International Journal of Control, Automation, and Vol.8 No.3
This paper deals with the linear quadratic regulation problems for the linear discrete-time systems with input delays. The design of the optimal control law is transformed into solving one Diophantine equation and one spectral factorization with delays. A new and simple approach for the spectral factorization is proposed based on reorganized innovation analysis. The calculation of spectral factor comes down to solving Riccati equations with the same dimension as the original systems.
Game Theory Approach to Optimal Control Problem with Multi-Channel Control
Wei Wang,Juanjuan Xu,Huan-Shui Zhang 제어·로봇·시스템학회 2015 International Journal of Control, Automation, and Vol.13 No.1
In this paper, we mainly study the optimal control problem with multi-channel control. The main contribution is to treat the optimal control problem as a leader-follower problem with multihierarchy decision makers in game theory. According to the sequence of the decision makers, the optimal controller is derived by the maximum principle. It is worth mentioning that the optimal solution is in the feedback form related to two symmetric Riccati equations with same dimension as the original state. Furthermore, the obtained solution is sufficient and necessary.
Na-Na Jin,Shuai Liu,Huan-Shui Zhang 제어·로봇·시스템학회 2021 International Journal of Control, Automation, and Vol.19 No.3
In this paper, we investigate the linear optimal estimation problems of discrete-time and continuous-time systems with multiple state delays in measurements. For discrete-time systems, we obtain the linear optimal estimation of state by direct calculation of optimal gain in terms of the solution to a retarded Riccati-like difference equation instead of a group of Riccati difference equations. For continuous-time systems, we also obtain the analytical expression of linear optimal estimation without resorting to Riccati partial differential equations. All the Riccati equations are of the same dimension as the system to be estimated and the computational cost is much saved. Infinite horizon case is also studied by stability analysis. Kalman filter can be recovered from our result when delays disappear. A numerical example is provided to demonstrate the results.