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(x,u,v)-依赖噪声的离散时间平均场随机H2/H∞控制
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Abstract:
本文研究了一类(x,u,v)(状态，输入，扰动)-依赖噪声的离散时间平均场随机系统的有限时域混合H2/H∞控制问题。首先，给出了已有的平均场随机有界实引理(SBRL)；其次，呈现了离散时间平均场随机线性二次(LQ)最优控制问题可解的充分条件。最后，基于SBRL和LQ最优控制的结果，通过耦合矩阵差分方程的可解性得到了离散时间平均场随机H2/H∞控制存在的充分必要条件，延伸了之前的结果。
This paper is concerned with the finite horizon mixed H2/H∞ control problem for a class of dis-crete-time mean-field stochastic systems with (x,u,v) -dependent noise. Firstly, the existing mean-field stochastic bounded real lemma (SBRL) is given. Then, we presented a sufficient condi-tion for the solvability of discrete-time mean-field stochastic linear quadratic (LQ) optimal control problem for the considered system. Finally, based on the results of SBRL and LQ optimal control, a necessary and sufficient condition is obtained for the existence of discrete-time mean-field stochas-tic H2/H∞ control via the coupled matrix difference equations, which extends the previous results.
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