Optimality Conditions for Control Problems Governed by Abstract Semilinear Differential Equations in Complex Banach Spaces
-
U. Ledzewicz
Abstract
We consider the problem to minimize an integral functional denned on the space of absolutely continuous functions and measurable controls with values in an infinite–dimensional complex Banach space. The states are governed by abstract first order semilinear differential equations and are subject to periodic or anti–periodic type boundary conditions. We derive necessary conditions for optimality and introduce the notion of a dual field of extremals to obtain sufficient conditions for optimality. Such a dual field of extremals is constructed and a dual optimal synthesis is proposed. The paper is an extension of an earlier paper written for real Banach spaces. This extension covers optimal control problems which are governed by equations like the Schrodinger equation and other equations arising in Quantum mechanics.
©Heldermann Verlag
Articles in the same Issue
- Optimal Synthesis for Nonoscillatory Controlled Objects
- Forced Oscillations of First Order Nonlinear Neutral Differential Equations
- Continuity of the Superposition of Set–Valued Functions
- On the Uniqueness of Lebesgue and Borel Measures
- Optimality Conditions for Control Problems Governed by Abstract Semilinear Differential Equations in Complex Banach Spaces
- On the Continuity of Random Operators
- Norms on Possibilities II: More CCC Ideals on 2ω
- Stationary Solutions for Heat Equation Perturbed by General Additive Noise
- Note on Decreasing Rearrangement of Fourier Series
Articles in the same Issue
- Optimal Synthesis for Nonoscillatory Controlled Objects
- Forced Oscillations of First Order Nonlinear Neutral Differential Equations
- Continuity of the Superposition of Set–Valued Functions
- On the Uniqueness of Lebesgue and Borel Measures
- Optimality Conditions for Control Problems Governed by Abstract Semilinear Differential Equations in Complex Banach Spaces
- On the Continuity of Random Operators
- Norms on Possibilities II: More CCC Ideals on 2ω
- Stationary Solutions for Heat Equation Perturbed by General Additive Noise
- Note on Decreasing Rearrangement of Fourier Series
