Linear quadratic regulation for discrete‐time systems with multiplicative noise and multiple input delays

Summary We study in this paper the linear quadratic optimal control (linear quadratic regulation, LQR for short) for discrete‐time complex‐valued linear systems, which have several potential applications in control theory. Firstly, an iterative algorithm was proposed to solve the discrete‐time bimatrix Riccati equation associated with the LQR problem. It is shown that the proposed algorithm converges to the unique positive definite solution (bimatrix) to the bimatrix Riccati equation with appropriate initial conditions. With the help of this iterative algorithm, the LQR problem for the antilinear system, which is a special case of complex‐valued linear system, was carefully examined and three different Riccati equations–based approaches were provided, namely, bimatrix Riccati equation, anti‐Riccati equation, and normal Riccati equation. The established approach is then used to solve the LQR problem for a discrete‐time time‐delay system with one‐step state delay, and a numerical example was used to illustrate the effectiveness of the proposed methods.

“…Let the bimatrix Riccati equation (9) have a positive definite solution {P 1 , P 2 }. The bimatrix {R 1 , R 2 } defined in (14) associated with the antilinear system (3) is given by…”

Section: The Anti-riccati Equation-based Approachmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

On linear quadratic optimal control of discrete‐time complex‐valued linear systems

Zhou

2019

“…Remark Note that the cost function can be rewritten as

\begin{matrix} right J (x_{k}, k) & left = \sum_{i = 0}^{N} x_{k + i}^{'} Q x_{k + i} + \sum_{i = 0}^{N - d} u_{k + i}^{'} R u_{k + i} & right \\ right & left + \sum_{i = N - d + 1}^{N} u_{k + i}^{'} (R + F_{2}) u_{k + i} \\ right & left + x_{k + N + 1}^{'} F_{1} x_{k + N + 1} . \end{matrix}

It is obvious that Equation has different control weighting matrices of R and R + F 2 at different time of ( k , k +1,⋯, k + N − d ) and ( k + N − d +1,⋯, k + N ), respectively. Thus, R s is written as the piecewise function (Equation ) according to Li et al…”

Section: Receding Horizon Control For Discrete‐time Systems With Multmentioning

confidence: 99%

“…The explicit solution was obtained based on duality principle. Only recently, in Li et al, a complete solution to the linear quadratic regulation problem for discrete‐time case with multiple input delay was obtained, where an explicit solution was derived based on Pontragin's maximum principle. It should be noted that the stabilization problem has not been solved in Li et al …”

Section: Introductionmentioning

confidence: 99%

Receding horizon control for discrete‐time multiple input delay systems

Gao

Liu

Zhang

2017

Summary This paper is concerned with stabilization problem for discrete‐time systems with multiple input delay. By defining a new cost function, the stabilization condition is derived based on monotonically nonincreasing of the optimal cost. It is shown that if the 2 weighting matrices in the cost function satisfy the given linear matrix inequality, receding horizon controller can stabilize the input delay systems. Moreover, the explicit stabilization controller with the new cost function is obtained by solving a finite horizon optimal control problem. A numerical example illustrates the effectiveness of the proposed method.

“…Control and state estimation over networks have attracted great attention because of the increasing development in communication networks . Because the random time delay and packet dropout are unavoidable in communication transmission through unreliable networks, the data obtained by the receiver may not be up‐to‐date.…”

Section: Introductionmentioning

confidence: 99%

Linear optimal filter for system subject to random delay and packet dropout

Liang

Zhang

2016

Summary This note is concerned with the linear estimation problems for discrete‐time systems where the measurements are subject to random time delay and packet dropout. Different from most of previous works, the time‐stamping is assumed to be unavailable in this paper. In this case, the estimation problems for such systems are very difficult because the information of the received measurements is not exactly known in most cases. To overcome the difficulty caused by the random delay and unavailability of time‐stamping, a new observation is introduced by the summation of all the measurements received in the same time. Then, the random time delay measurement system is converted into a constant‐delay measurement system with multiplicative noises where the noise is binary distributed random variables with known distributions. Finally, the linear optimal estimator is derived by using the transformation of auto‐regressive moving average model to state‐space model and the standard Kalman filtering. The convergence and stability of the filter are also analyzed. A simulation example is given to show the effectiveness of the proposed estimator. Copyright © 2016 John Wiley & Sons, Ltd.