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Article information
1999 , Volume 4, ¹ 2, p.3-25
Weber G.W.
Optimal control theory: on the global structure and connections with optimization. Part 1
We introduce and investigate different concepts on the global structure of nonlinear optimal control problems
such that nonlinear optimization problems of the form
become constitutive under a linear boundedness assumption on F. While in the particular structure the control variable u is still treated as a parameter, in the composite structure we take into account the full dependences, jointly on x and u in a more causal way. Therefore, implicit so-called Kuhn - Tucker functions become constitutive, too. The composite concept is based on the minimum principle and it can be guaranteed to be complete by means of regularity conditions on feasible sets (Mangasarian - Fromovitz), Kuhn - Tucker points (Kojima) and within the structure of piecewise differentiability (transversality). Namely, under such regularity conditions no kind of instability (vanishing, bifurcation) is necessary in order to state the structure. These two stability concepts also incorporate corresponding concepts of global (topological) stability. Under an overall compactness assumption, this structural stability can be characterized essentially by means of our regularity conditions. In this part 1 we present the particular structure and give foundations of the composite structure. The latter structure is completed in part 2 ([43]), where also the more stepwise decomposite structure is presented.
[full text] Classificator Msc2000:- *49K40 Sensitivity, stability, well-posedness
- 58E25 Applications to control theory
Keywords: Optimal control,finitely constrained or semi-infinite optimization,, strong stability, generic problem, local maximum, saddlepoint, Mangasaryan--Fromovitz constraint qualification, semi-infinite optimization problem, nonlinear optimal control problems, Mangasarian
Author(s):
Weber GerhardW.
Office: Institute of Applied Mathematics, METU
Address: 64289, Turkey, Ankara
E-mail: gweber@metu.edu.tr
Bibliography link:
Weber G.W. Optimal control theory: on the global structure and connections with optimization. Part 1 // Computational technologies. 1999. V. 4. ¹ 2. P. 3-25
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