Abstract

A constructive solution of the optimal energy-efficient programmed control problem for distributed parameter systems with a given-precision uniform approximation of the space distribution of the controlled variable with respect to the desired state is proposed. The computational algorithm developed below involves a special-form preliminary parametrization procedure for control actions on finite-dimensional subsets of the terminal values of conjugate variables in the boundary-value problem of Pontryagin’s maximum principle, in combination with the subsequent reduction to a semi-infinite optimization problem, which is solved with respect to the requisite parameter vector using the alternance method suggested earlier. An example of optimal energy-efficient control of transient heat conduction, which is of independent interest, is given.

中文翻译：

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分布式参数系统的最佳节能程序控制

摘要

提出了一种结构合理的分布式参数系统最优节能编程控制问题的解决方案，该方法具有相对于所需状态的受控变量空间分布的给定精度均匀近似值。下面开发的计算算法涉及一种特殊形式的预参数化过程，用于控制庞特里亚金最大原理的边值问题中共轭变量终值的有限维子集上的控制动作，并结合其后的简化为半无穷大优化问题，它是使用先前建议的交替方法针对必要参数向量解决的。给出了一个独立感兴趣的瞬态热传导的最佳节能控制示例。