Pareto optimality for nonlinear infinite dimensional control systems

Abstract

In this note we establish the existence of Pareto optimal solutions for nonlinear, infinite dimensional control systems with state dependent control constraints and an integral criterion taking values in a separable, reflexive Banach lattice. An example is also presented in detail. Our result extends earlier ones obtained by Cesari and Suryanarayana.

Keywords

• Pareto efficient points
• Banach lattice
• mild solution
• evolution operator
• compactness
• Fatou's lemma
• orientor field
• nonlinear parabolic equation.