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A novel increment approach for optimal control problem of fractional-order (1, 2] nonlinear systems
Mathematical Methods in the Applied Sciences ( IF 2.1 ) Pub Date : 2021-07-28 , DOI: 10.1002/mma.7681 Rohit Patel 1 , Anurag Shukla 1 , Shimpi Jadon 1 , Ramalingam Udhayakumar 2
Mathematical Methods in the Applied Sciences ( IF 2.1 ) Pub Date : 2021-07-28 , DOI: 10.1002/mma.7681 Rohit Patel 1 , Anurag Shukla 1 , Shimpi Jadon 1 , Ramalingam Udhayakumar 2
Affiliation
This paper deals with fractional optimal control governed by semilinear equations using the increment approach. We have considered controlled object as
with the initial conditions:
where α ∈ (1, 2], s(τ) is state variable in , B(τ) ∈ Lp, ϱ(0, T), and . Let the m-dimensional control vector function be C(τ) and defined as . Assume the function η(τ, C(τ)) satisfies Caratheodory condition and defined on . We have obtained our results with the help of the adjoint equation and Pontryagin's maximum condition. For better understanding, we have included one example.
中文翻译:
分数阶 (1, 2] 非线性系统最优控制问题的一种新增量方法
本文使用增量方法处理由半线性方程控制的分数最优控制。我们将受控对象视为
初始条件:
其中α ∈ (1, 2], s ( τ ) 是状态变量, B ( τ ) ∈ L p , ϱ (0, T ) 和. 设m维控制向量函数为C ( τ ) 并定义为. 假设函数η ( τ , C ( τ )) 满足 Caratheodory 条件并定义在. 我们在伴随方程和 Pontryagin 最大条件的帮助下得到了我们的结果。为了更好地理解,我们举了一个例子。
更新日期:2021-07-28
中文翻译:
分数阶 (1, 2] 非线性系统最优控制问题的一种新增量方法
本文使用增量方法处理由半线性方程控制的分数最优控制。我们将受控对象视为