Optimal Control Applications and Methods · 2008 · 24 citations · 7 references
Natural SciencesIndustrial EngineeringOptimizationProcess ControlProcess Systems EngineeringControl TheoryConvex OptimizationMulti-objective OptimizationNonlinear ProgrammingOptimal ControlOptimization TheoryMaximum PrinciplesNonlinear Optimal ControlOptimal Control Of Nonlinear SystemsPontryagin Maximum PrinciplePontryagin's Maximum PrinciplePontryagin's Minimum Principle
Abstract We introduce the class of MP‐pseudoinvex multiobjective optimal control problems. We show that the concept of MP‐pseudoinvexity is a sufficient condition of optimality and, further, that problems such that every control process satisfying Pontryagin's maximum principle is an optimal process are necessarily MP‐pseudoinvex problems. Moreover, a sub‐class of the MP‐pseudoinvex problems, which we call MP‐invex multiobjective optimal control problems, is defined. We prove that the set of optimal solutions of MP‐invex multiobjective problems coincides with the set of optimal solutions of a related scalar problem. Copyright © 2008 John Wiley & Sons, Ltd.
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