广义代数Riccati方程和最优调节器的研究

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

Study on generalized algebraic Riccati equations and optimal regulators

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.