Linearized maximum principle for neutral-type, variable-structure optimal problems with delays in controls. (English. Russian original) Zbl 1180.35541
J. Math. Sci., New York 148, No. 3, 382-398 (2008); translation from Sovrem. Mat. Prilozh. 42, 84-99 (2006).
Summary: The authors state and study an optimal problem for variable-structure systems described by neutral-type quasilinear differential equations with discontinuous initial condition and incommensurable delays. The variation of the system structure means that in the process of motion, at a certain instant of time not known in advance, the object considered can pass from one law of motion to another, and, moreover, the initial condition for each of the subsequent states of the system depends on the state of the next to the last. The discontinuity of the initial condition means that at the initial instant of time, the value of the initial function and that of the trajectory do not coincide in general. The necessary optimality conditions are proved in the form of the linearized integral maximum principle for controls and initial functions and in the form of inequalities and equalities for the initial and final instants of structure change.
MSC:
| 35R10 | Partial functional-differential equations |
| 49J20 | Existence theories for optimal control problems involving partial differential equations |
| 49K20 | Optimality conditions for problems involving partial differential equations |
| 35B50 | Maximum principles in context of PDEs |
Keywords:
neutral-type quasilinear differential equations; discontinuous initial condition; incommensurable delaysReferences:
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