The condition of Clebsch for mixed constrained optimal control problems
Abstract
The second order necessary condition of Legendre in the calculus of variations, which playes a crucial role in the theory, has been generalized in several directions.In particular, for certain classes of optimal control problems, it corresponds to the condition of Clebsch, which can be derived as a consequence of the maximum principle.However, as we show in this paper, the usual normality assumptions imposed for problems involving mixed equality and inequality constraints can be weakened, leaving the condition of Clebsch unchanged.A simple example, which lies beyond the scope found in the literature, illustrates the usefulness of our main result.
Fields of Study & Subjects
Optimization and Variational Analysis
Aerospace Engineering and Control Systems
Soil
Finite Element Methods
Publication details
- Journal / source
- Communications in Optimization Theory
- Publisher
- Mathematical Research Press
- Volume
- 2026
- Issue
- 1
- Publication date
- 1 January 2026