Optimal Control of a Bilinear System with a Quadratic Cost Functional
Optimal Control of a Bilinear System with a Quadratic Cost Functional
复制标题
具有二次成本函数的双线性系统的最优控制
DOI：
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发表时间：
2018
期刊：
影响因子：
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通讯作者：
I. Kucuk
中科院分区：
文献类型：
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作者：
Seda Goktepe Korpeoglu;I. Kucuk
工程问题中的各种控制系统都用线性微分方程建模，其中使用线性控制。另一方面，线性模型不能表示以乘法方式应用控制的许多系统。这些乘法控制产生双线性系统（BLS）。状态和控制的产物都参与到BLS中，这意味着状态和控制分别是线性的，而不是共同线性的。研究了具有二次代价泛函的双线性系统的最优控制问题。考虑一个分布参数系统，采用双线性控制。通过降阶建模，将控制问题转化为模态控制问题。性能指标（成本函数）被定义为动态响应的度量和控制能量的惩罚项。利用庞特里亚金极大值原理求解了非线性两点边值问题的最优控制函数。利用最陡下降法求解该两点边值问题，确定了系统的最优控制和最优轨迹。在MATLAB平台上进行编程。数值结果显示了所引入的双线性控制对抛物型分布参数系统的有效性和适用性。
Various control systems in engineering problems are modelled with linear differential equations where a linear control is used. On the other hand, linear models are not capable of representing many systems where the control is applied in a multiplicative ways. These multiplicative controls yield bilinear systems (BLS). Products of state and control take part in BLS, which means that state and control are linear separately but not jointly. In this paper, optimal control of bilinear systems with a quadratic cost functional is studied. A distributed parameter system is considered and a bilinear control is applied to the system. The control problem is turned into a modal control problem by way of reduced order modelling. Performance index (cost functional) is defined as a measure of the dynamic response and a penalty term on control energy. Pontryagins maximum principle is used to obtain the optimal control function that leads to a nonlinear two-point boundary value problem. Optimal control and optimal trajectory of the system are determined by solving this two-point boundary value problem using steepest descent method. The programming is done in MATLAB platform. Numerical results are given in graphics for showing the effectiveness and applicability of the introduced bilinear control for a parabolic distributed parameter system.