Well-posedness and Porosity in Nonconvex Optimal control

2013 ◽  
pp. 63-85
Author(s):  
Alexander J. Zaslavski
Keyword(s):  
Optimal Control ◽  
Well Posedness

Generic well-posedness of nonconvex optimal control problems

2004 ◽  
Vol 59 (7) ◽  
pp. 1091-1124 ◽  
Author(s):  
Alexander J. Zaslavski
Keyword(s):  
Optimal Control ◽  
Optimal Control Problems ◽  
Control Problems ◽  
Well Posedness

scholarly journals Second-order analysis of an optimal control problem in a phase field tumor growth model with singular potentials and chemotaxis

2021 ◽  
Author(s):  
Pierluigi Colli ◽  
Andrea Signori ◽  
Jürgen Sprekels
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Tumor Growth ◽  
Control Problem ◽  
Growth Model ◽  
Second Order ◽  
Well Posedness ◽  
Singular Potentials ◽  
Order Analysis ◽  
Tumor Growth Model

This paper concerns a distributed optimal control problem for a tumor growth model of Cahn–Hilliard type including chemotaxis with possibly singular potentials, where the control and state variables are nonlinearly coupled. First, we discuss the weak well-posedness of the system under very general assumptions for the potentials, which may be singular and nonsmooth. Then, we establish the strong well-posedness of the system in a reduced setting, which however admits the logarithmic potential: this analysis will lay the foundation for the study of the corresponding optimal control problem. Concerning the optimization problem, we address the existence of minimizers and establish both first-order necessary and second-order sufficient conditions for optimality. The mathematically challenging second-order analysis is completely performed here, after showing that the solution mapping is twice continuously differentiable between suitable Banach spaces via the implicit function theorem. Then, we completely identify the second-order Fr ́echet derivative of the control-to-state operator and carry out a thorough and detailed investigation about the related properties.

Discrete-Time Uncertain LQ Optimal Control with Indefinite Control Weight Costs

2016 ◽  
Vol 20 (4) ◽  
pp. 633-639 ◽  
Author(s):  
Yuefen Chen ◽  
◽  
Liubao Deng ◽  
Keyword(s):  
Optimal Control ◽  
Discrete Time ◽  
Recurrence Equation ◽  
State Feedback Control ◽  
Necessary Condition ◽  
Well Posedness ◽  
Linear Quadratic ◽  
Lq Optimal Control ◽  
Optimal State Feedback ◽  
Lq Problem

This paper deals with a discrete-time uncertain linear quadratic (LQ) optimal control, where the control weight costs are indefinite . Based on Bellman’s principle of optimality, the recurrence equation of the uncertain LQ optimal control is proposed. Then, by using the recurrence equation, a necessary condition of the optimal state feedback control for the LQ problem is obtained. Moreover, a sufficient condition of well-posedness for the LQ problem is presented. Furthermore, an algorithm to compute the optimal control and optimal value is provided. Finally, a numerical example to illustrate that the LQ problem is still well-posedness with indefinite control weight costs.

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