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Generalized solutions for singular optimal control problems

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This text presents a complete theory of existence/uniqueness and the structure of generalized solutions for singular linear-quadratic optimal control problems. Generalized optimal controls are distributions of order r and the corresponding generalized trajectories are distributions of order (r − 1). r is the “order of singularity” of the problem, an integer no greater than the dimension of the state space. Its value is obtained through a certain reduction procedure. In the final section, some perspectives and partial results concerning the extension of these results to nonlinear problems are briefly discussed.

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Authors and Affiliations

  1. ISEG/T.U. Lisbon and CEOC - U. Aveiro, Lisboa, Portugal

    M. Guerra

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Translated from Sovremennaya Matematika. Fundamental’nye Napravleniya (Contemporary Mathematics. Fundamental Directions), Vol. 27, Optimal Control, 2007.

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Guerra, M. Generalized solutions for singular optimal control problems. J Math Sci 156, 440–567 (2009). https://doi.org/10.1007/s10958-008-9274-1

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