Stability Analysis of Variational Inequalities for Bang-Singular-Bang Controls

• Autorzy: Ursula Felgenhauer
• Języki publikacji: EN

Abstrakty

EN

The paper is related to parameter dependent optimal control problems for control-affine systems. The case of scalar reference control with bang-singular-bang structure is considered. The analysis starts from a variational inequality (VI) formulation of Pontryagin's Maximum Principle. In a first step, under appropriate higher-order sufficient optimality conditions, the existence of solutions for the linearized problem (LVI) is proven. In a second step, for a certain class of right-hand side perturbation, it is show that the controls from LVI have bang-singular-bang structure and, in L₁ topology, depend Lipschitz continuously on the data. Applying finally a common fixed-point approach to VI, the results are brought together to obtain existence and structural stability results for extremals of the original control problem under parameter perturbation. (original abstract)

Słowa kluczowe

EN

Control theory; Nonlinear programming; Approximation

PL

Teoria kontroli; Programowanie nieliniowe; Aproksymacja

• Czasopismo: Control and Cybernetics
• Rocznik: 2013
• Tom: 42
• Numer: nr 3
• Strony: 557--592

Twórcy

autor

Ursula Felgenhauer

• Brandenburgische Technische Universit¨at Cottbus

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