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Linear Multistep Method with Application to Chaotic Processes
Published in Hemen Dutta, Mathematical Methods in Engineering and Applied Sciences, 2020
Kolade M. Owolabi, Adelegan L. Momoh
It is possible to write Eqs. (10.14), (10.15), and (10.16) as matrix difference equation of the form A0Y=A1Y¯+hΣm=01 BmFm
Linear Discrete-Time Optimal Control
Published in Raymond G. Jacquot, Modern Digital Control Systems, 2019
Consider the discrete-time dynamic system described by the vector-matrix difference equation () xk+1=Axk+Bukk=0,1,2,⋯
Recursive Adaptive Filtering
Published in David C. Swanson, ®, 2011
Embedding an ARMA filter into a lattice structure is very straightforward once one has established a matrix difference equation. Recall that the projection operator framework in Chapter 8 was completely general and derived in complex matrix form (the superscript H denotes transpose plus complex conjugate). All of the lattice and levinson recursions in Chapter 10 are also presented in complex matrix form. We start by writing the ARMA difference equations in matrix form. () [εnyεnx]=[ynxn]+∑i=1M[ai−bi−cidi][yn−ixn−i]
State estimation via prediction-based scheme for linear time-varying uncertain networks with communication transmission delays and stochastic coupling
Published in Systems Science & Control Engineering, 2021
Bing Xu, Jun Hu, Chaoqing Jia, Zhipeng Cao, Jinpeng Huang
Consider the state estimation error covariance matrices in (14) and set . Under the initial conditions , we assume that the matrix difference equation as follows: has the solution . After that, it can be summarized that Moreover, if is chose as where thus, the trace of the upper bound of state estimation error covariance matrix can be minimized at every sampling step and the optimal upper bound is expressed as
Robust recursive filtering for uncertain stochastic systems with amplify-and-forward relays
Published in International Journal of Systems Science, 2020
Hailong Tan, Bo Shen, Kaixiang Peng, Hongjian Liu
In this paper, we have addressed the filtering problem for a class of uncertain systems with the AF relays. The signal transmission between the sensor and the remote filter have been executed via a relay network where the transmission power of the relay and the sensor is random. Firstly, novel random transmission power models have been proposed for the sensors and the AF relays. Then, a robust filter has been constructed in which the average transmission power is contained. With the help of the matrix difference equation technique, an upper bound has been obtained on the filtering error covariance and the filter gain matrix has been designed by minimising the upper bound matrix. Furthermore, the boundness of the filtering error has been also examined. Finally, an illustrative example has been provided to show the effectiveness of the proposed filtering algorithm. One of our future research topics would be to apply the constructed transmission power model to control problems, such as the neuromuscular control problems for musculoskeletal systems (Chen & Qiao, 2020), the consensus control problems for multi-agent systems (Qian et al., 2019) and the sliding mode control problems for nonlinear systems (L. Liu et al., 2019).
Asymptotically Tracking Control of Structural Balance for Discrete-Time Links System Associated with External Stimulations and State Observer
Published in Cybernetics and Systems, 2023
Yi Peng, Peitao Gao, Yinhe Wang, Juanxia Zhao
(i) The discrete-time links system is described as a weight matrix its element is the weighted-values of links between nodes i and j. This paper just considers the undirected case, that is, (ii) Some phenomena can provide the background of the links system. For example, in the biological neural network, with the action of external stimulations, neurons doing gamma oscillations will cause the synaptic facilitation (links), which can be considered as a dynamic behavior of the links system. Similarly, in the biological ecosystems, the changes of species niche, such as overlapping and widening, will affect the competition strength (links) between species, which may be also considered as a dynamic behavior of the links system. (iii) Instead of utilizing continuous-time links model to research the problem of structural balance in Marvel et al. (2011), Wongkaew et al. (2015), and Gao, Wang, and Zhang (2018); Gao et al. (2018), this paper mainly focuses on the discrete-time situation. In fact, Eq. (1) is known as the discrete-time Riccati matrix difference equation or the Hermitian Stein equation. It is usually applied in Linear Quadratic optimal control (Ferrante et al., 2013a, 2013b). (iv) From the sociological perspective, the positive and negative links relationships represent amity and animosity relationships between social individuals, respectively (Antal, Krapivsky, and Redner 2005; Wongkaew et al. 2015). Moreover, the diagonal element in the matrix must be positive, and its social meaning is a kind of self-identity or internal incentive formed by other individuals (Marvel et al. 2011). (v)Equation (1) is mainly inspired by the literature (Hebb et al., 2013; Liu, Wang, and Gao 2020; Peng et al. 2022).