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本文应用李雅普诺夫第二方法与贝尔曼的动态规则法,讨论了最优控制器的分析设计问题,并提出了一种对理论分析与实际计算都比较方便的序列逼近法.在第一节中,给出了最优控制器分析设计问题的一般提法与作为必要条件的贝尔曼方程.在第二节中,给出了对进一步研究所需的有关李雅普诺夫第二方法的基本结果,以便使以后的论证更为简捷.在第三节中,给出了在一般提法下分析设计问题的一般性结果,其中包括唯一性定理、贝尔曼方程的充分性、序列逼近法及其基本性质.在第四节中,研究了常系数线性系统,解决了最优控制的存在唯一性问题,文中列举了数例,以说明序列逼近法具有较快的收斂速度,并论证了这种方法的收斂速度系按指数进行的.在第五节中,研究了拟常系数线性系统,并分别对缓变系数线性系统与定常拟线性系统进行了讨论,给出了例题以说明理论结果.最后在第六节中,讨论了某些进一步推广的问题.本文所引入的方法,均直接针对综合问题而给出,因而在理论研究与实际运用上,是方便可行的.
In this paper, Lyapunov’s second method and Beelman’s dynamic rule method are applied to discuss the design and analysis of the optimal controller, and a sequence approximation method which is more convenient for both theoretical analysis and practical calculation is proposed.In the first section , We give the general formulation of the optimal controller design problem and the Bellman’s equation as a necessary condition.In the second section, we present the basic results of the second Lyapunov method for further research , In order to make the subsequent argument more concise.In the third section, given the general formulation of the analysis of design problems under the general results, including the uniqueness of the theorem, the adequacy of the Berman equation, the sequence approximation method and its In the fourth section, we study the linear system of constant coefficients and solve the problem of the existence and uniqueness of the optimal control. Several examples are given to show that the sequence approximation method has a faster convergence rate. The convergence speed of the method is exponentially.In Section 5, the quasi-constant coefficient linear systems are studied, and the linear systems with slowly varying coefficients and quasi-linear systems with constant coefficients are discussed respectively. The theoretical results. Finally, section VI, discusses some further promote the issue. The method introduced herein are given directly to the overall problem, so in theory and practical application, is easily feasible.