论文标题
马尔可夫开关和泊松扰动的随机结构的随机动力系统的稳定
Stabilization of stochastic dynamical systems of a random structure with Markov switches and Poisson perturbations
论文作者
论文摘要
动态系统的最佳控制优化了特定的目标函数。在这里，我们考虑为具有随机结构，泊松扰动和随机跳跃的随机动力系统的最佳控制构建，这使得该系统的概率稳定。使用第二种Lyapunov方法获得了概率稳定性的足够条件，其中相应函数的构建起着重要作用。在这里，我们提供了解决一般情况下最佳稳定问题的解决方案。对于具有二次质量函数的线性系统，我们根据Riccati方程的解决方案提供了一种合成最佳控制的方法。最后，在自主情况下，构建了一个微分方程系统，以获得用于建造最佳控制的未知矩阵。小参数的方法是合理的，用于对最佳控制的算法搜索。这种方法为具有随机结构，马尔可夫开关和泊松扰动的随机动力学系统的最佳稳定问题带来了新的解决方案。
An optimal control for a dynamical system optimizes a certain objective function. Here we consider the construction of an optimal control for a stochastic dynamical system with a random structure, Poisson perturbations and random jumps, which makes the system stable in probability. Sufficient conditions of the stability in probability are obtained, using the second Lyapunov method, in which the construction of the corresponding functions plays an important role. Here we provide a solution to the problem of optimal stabilization in a general case. For a linear system with a quadratic quality function, we give a method of synthesis of optimal control based on the solution of Riccati equations. Finally, in an autonomous case, a system of differential equations was constructed to obtain unknown matrices that are used for the building of an optimal control. The method of a small parameter is justified for the algorithmic search of an optimal control. This approach brings a novel solution to the problem of optimal stabilization for a stochastic dynamical system with a random structure, Markov switches and Poisson perturbations.
