A new design approach for solving linear quadratic nash games of multiparameter singularly perturbed systems
A new design approach for solving linear quadratic nash games of multiparameter singularly perturbed systems
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DOI：
10.1109/tcsi.2005.846668
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发表时间：
2005-07
期刊：
影响因子：
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通讯作者：
H. Mukaidani
中科院分区：
文献类型：
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作者：
H. Mukaidani
本文讨论了无限时域非标准多参数奇异摄动系统（MSPS）的线性二次Nash对策问题，而不需要已有结果所需的非奇异性假设。通过求解广义交叉耦合多参数代数Riccati方程组（GCMARE）得到了新的策略。首先，新建立了GCMARE的渐近展开式。本文的主要结果是，所提出的算法是基于牛顿法求解GCMARE保证二次收敛。仿真结果表明，与已有的算法相比，该算法在收敛速度上有明显的提高。它还表明，所得到的控制器实现O（/spl par//spl mu//spl par//sup 2n/）的最优成本近似。
In this paper, the linear quadratic Nash games for infinite horizon nonstandard multiparameter singularly perturbed systems (MSPS) without the nonsingularity assumption that is needed for the existing result are discussed. The new strategies are obtained by solving the generalized cross-coupled multiparameter algebraic Riccati equations (GCMARE). Firstly, the asymptotic expansions for the GCMARE are newly established. The main result in this paper is that the proposed algorithm which is based on the Newton's method for solving the GCMARE guarantees the quadratic convergence. In fact, the simulation results show that the proposed algorithm succeed in improving the convergence rate dramatically compared with the previous results. It is also shown that the resulting controller achieves O(/spl par//spl mu//spl par//sup 2n/) approximation of the optimal cost.