| 引用本文: | 张维海.广义代数Riccati方程和最优调节器的研究[J].控制理论与应用,2003,20(4):637~640.[点击复制] |
| ZHANG Wei-hai.Study on generalized algebraic Riccati equations and optimal regulators[J].Control Theory and Technology,2003,20(4):637~640.[点击复制] |
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| 广义代数Riccati方程和最优调节器的研究 |
| Study on generalized algebraic Riccati equations and optimal regulators |
| 摘要点击 2378 全文点击 1326 投稿时间：2001-11-23 修订日期：2002-05-23 |
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| DOI编号 |
| 2003,20(4):637-640 |
| 中文关键词 广义代数Riccati方程 精确能观性 能稳性 调节器问题 |
| 英文关键词 generalized algebraic Riccati equation exact observability stabilization regulator problems |
| 基金项目 山东省自然科学基金(Q99G01). |
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| 中文摘要 |
| 利用能稳性和精确能观性, 对广义代数Riccati方程和相关的随机最优调节器问题进行了深入的研究. 对广义代数Riccati方程得到了下列结果: 如果随机系统既是能稳定的又是精确能观的, 则广义代数Riccati方程有一个最大解, 同时也是一个反馈镇定解. 在精确能观性的假设下, 广义代数Riccati方程的所有非负定解(如果存在的话)必是正的反馈镇定解. 作为应用, 最优调节器问题, 广义代数Riccati方程的最大解, 反馈镇定解三者之间的关系获得了澄清. 所有这些结果在随机控制和随机稳定性理论中是有 |
| 英文摘要 |
| By means of stabilization and exact observability, the generalized algebraic Riccati equation (GARE) and related stochastic optimal regulator problem were studied extensively. For GARE, it was shown that, if the stochastic system was both stabilizable and exactly observable, GARE had a maximal solution, which was also a feedback stabilizing solution. If only exact observability was imposed, all the nonnegative definite solutions of GARE, if existed, must be positive definite feedback stabilizing solutions. As applications, the relation among the optimal regulator problem, the maximal solution and feedback stabilizing solution of GARE had been clarified. All there obtained consequences are valuable in the study of stochastic control and stability theory. |
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