一类LQ问题的最优控制和次优控制的综合方法

针对有某些限制的一类ＬＱ问题，给出了最优控制的一种闭合形式算式，讨论了相 应的最优控制系统的基本性质。同时讨论了限制较弱的一类较宽的ＬＱ问题．得到了次 优控制的闭合形式算式，分析了次优性能值的界限估计和相应的次优控制系统的鲁棒性。 所提出的新综合方法的特点是避免了对Ｒｉｃｃａｔｉ代数方程进行数值求解。文中还给出了 算例以说明其计算步骤。

A Synthesis Method for Determining the Optimal and Suboptimal Control Laws of a Class of LQ Regulator Problems

In this paper, a closed-form formula is given to determine the optimal control law and some essential properties of the resulting optimal control system are discussed for a class of the linear-quadratic(LQ) regulator problems in which some limitations are introduced. The discussion is extended to a wider class of LQ regulator problems in which less limitations are made. A closed-form formula of determining a suboptimal control law is obtained, an inequality is estabilished to estimate quantitatively the relation between the suboptimal and optimal costs, and the robustness of the resulting suboptimal control system is analyzed. A characteristic of the synthesis method given is that the necessity of solving numerically the Riccati matrix equation is avoided. An example is presented for illustration of the given approach.