The paper proposes a method to integrate numerically an interconnected system, based on an idea of orthogonal approximation of functions. Here, block pulse functions (BPFs) are chosen as the orthogonal set. The main advantage of using this technique is its ability to transform the original optimal control problem to a mathematical programming problem relatively easier to solve. The primary focus of this paper is to exploit and rigorously develop the BPFs parametrization technique for the synthesis of a decentralized observer-based optimal control for large-scale interconnected systems. In addition, we develop a mathematical model of a double-parallel inverted pendulum coupled by a spring, taking into account all possible changes of the connecting position of the elastic spring. In so doing, we conducted advanced simulations applying the new optimal control method to the studied interconnected system. Our results demonstrate the validity and the effectiveness of the developed decentralized observer-based optimal control approach.

中文翻译：

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使用块脉冲功能对互连系统进行分散的基于观测器的优化控制

本文基于函数正交逼近的思想，提出了一种对互连系统进行数值积分的方法。这里，块脉冲函数 (BPF) 被选为正交集。使用这种技术的主要优点是它能够将原始最优控制问题转换为相对容易解决的数学规划问题。本文的主要重点是开发和严格开发 BPFs 参数化技术，用于合成大规模互连系统的分散式基于观察者的最优控制。此外，我们开发了一个由弹簧耦合的双平行倒立摆的数学模型，考虑了弹性弹簧连接位置的所有可能变化。这样做时，我们将新的最优控制方法应用于研究的互连系统进行了高级模拟。我们的结果证明了所开发的基于分散观察者的最优控制方法的有效性和有效性。