Abstract

We state an optimal control problem for a class of dynamical systems whose nonlinear objects can be represented as objects with linear structure and state-dependent parameters. The linearity of the structure of the transformed nonlinear system and the quadratic performance functional allow one to move from the need to search for solutions of the Hamilton–Jacobi equation to an equation of the Riccati type with state-dependent parameters when synthesizing the optimal control, i.e., the controller parameters. The main problem of implementing the optimal control is related to the problem of being capable of finding solutions of such an equation online, at the object operation rate. An algorithmic method for the parametric optimization of the controller is proposed. The method is based on using the necessary optimality conditions for the control system in question. Our algorithms can be used both to optimize the time-varying objects themselves given an appropriate choice of the parameters for this purpose and to optimize the entire control system using an appropriate parametric adjustment of the controllers. The efficiency of the algorithms is demonstrated by the example of drug treatment of patients with HIV.

中文翻译：

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使用扩展线性化方法的模型表示的非线性系统的参数优化

摘要

我们针对一类动力学系统提出了一个最优控制问题，该动力学系统的非线性对象可以表示为具有线性结构和状态相关参数的对象。在合成最优控制时，变换后的非线性系统的结构线性和二次性能函数使人们可以从寻找汉密尔顿-雅各比方程的解的需求转移到具有状态相关参数的Riccati类型的方程，即控制器参数。实施最优控制的主要问题与能够以目标操作率在线找到这样的方程式的解的问题有关。提出了一种控制器参数优化的算法方法。该方法基于对所讨论的控制系统使用必要的最优条件。我们的算法既可以用于优化时变对象本身，也可以为此目的选择适当的参数，也可以使用控制器的适当参数调整来优化整个控制系统。以艾滋病毒患者的药物治疗为例，证明了算法的有效性。