Abstract
We prove a maximum principle for an abstract semilinear nonsmooth optimal control problem under a fairly weak set of assumptions that typically do not imply the existence of solution of the equation. The result is further applied to obtain maximum principles in a problem with a distributed time delay and in a problem for a system of semilinear elliptic equations with domain and boundary controls.
The second author’s research was supported by the US-Israel Binational Science Foundation grant 90-00455.
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Ginsburg, B., Ioffe, A. (1996). The Maximum Principle in Optimal Control of Systems Governed by Semilinear Equations. In: Mordukhovich, B.S., Sussmann, H.J. (eds) Nonsmooth Analysis and Geometric Methods in Deterministic Optimal Control. The IMA Volumes in Mathematics and its Applications, vol 78. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-8489-2_4
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