Optimal control problems for some ordinary differential equations with behavior of blowup or quenching

Abstract

This paper is concerned with some optimal control problems for equations with blowup or quenching property. We first study the existence and Pontryagin's maximum principle for optimal controls which have the minimal energy among all the controls whose corresponding solutions blow up at the right-hand time end-point of a given functional. Then, the same problem for quenching case is discussed. Finally, we establish Pontryagin's maximum principle for optimal controls of extended problems after quenching.

Quaternary Boundary Optimal Control Problem Dominating by Quaternary Nonlinear Parabolic System

“…𝑦 𝑟 (𝑥, 0) = 𝑦 𝑟 0 (𝑥), on Ω (6) where 𝑓 ⃗ = (𝑓 1 , 𝑓 2 , 𝑓 3 , 𝑓 4 ) ∈ (𝐿 2 (𝑄)) 4 = 𝑳 𝟐 (𝑸), is a vector of function for each 𝑥 = (𝑥 1 , 𝑥 2 ) ∈ Ω, 𝑢 ⃗⃗ = (𝑢 1 , 𝑢 2 , 𝑢 3 , 𝑢 4 ) ∈ (𝐿 2 (Σ)) 4 = 𝑳 𝟐 (𝜮) is a QCCBCV and 𝑦 ⃗ ∈ (𝐻 2 (𝛺)) 4 = 𝑯 𝟐 (𝜴)is the QSVS corresponding to the QCCBCV𝑢 ⃗⃗,𝑎 𝑖𝑗 (𝑥, 𝑡)…”

“…Optimal control problems (OCPs) play an important role in many practical applications, such as in medicine [1], aircraft [2], economics [3], robotics [4], weather conditions [5] and many other scientific fields. There are two types of OCPs; the classical and the relax type, each one of these two types is dominated either by ODEqs [6] or by PDEqs [7]. The Continuous Classical boundary optimal control problem (CCBOCP) is dominated by a couple of nonlinear parabolic, elliptic or hyperbolic PDEqs that were studied in [8][9][10].…”

Quaternary Continuous Classical Boundary Optimal Control Problem Dominating by Parabolic System

“…Optimal control problems play an important role in many practical applications, such as in medicine [1], aircraft [2], economics [3], robotics [4], weather conditions [5] and many other scientific fields. They are two types of optimal control problems; the classical and the relax type, each one of these two types is dominated either by ODEqs [6] or PDEqs [7]. The Continuous Classical boundary optimal control problem (CCBOCP) dominated by a couple of parabolic, elliptic, or hyperbolic PDEqs was studied in [8][9][10].…”

The Classical Continuous Optimal Control for Quaternary Nonlinear Parabolic Boundary Value Problems

“…Optimal control problems (OCPs) play an important role in many practical applications, such as in weather conditions 2 , economics 3 , robotics 4 , aircraft 5 , medicine 6 , and many other scientific fields. They are two types of OCPs; the classical and the relax type, each one of these two types is dominated either by nonlinear ODEs 7 or by nonlinear PDEs (NLPDEs) 8 . The classical continuous optimal control problem ) CCOCP) dominated by nonlinear parabolic or elliptic or hyperbolic PDEs are studied in [9][10][11] respectively (resp.).…”