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Analysis of nonlinear fractional control systems in Banach spaces. (English) Zbl 1223.93059
Summary: We consider the nonlinear control systems of fractional order and its optimal controls in Banach spaces. Using the fractional calculus, Hölder’s inequality, p-mean continuity, weakly singular inequality and Leray-Schauder’s fixed-point theorem with compact mapping, a sufficient condition is given for the existence and uniqueness of mild solutions for a broad class of fractional nonlinear infinite dimensional control systems. Utilizing the approximately lower semicontinuity of integral functionals and weakly compactness, we extend the existence result of optimal controls for nonlinear control systems to nonlinear fractional control systems under generally mild conditions. An example is given to illustrate the effectiveness of the results obtained.
MSC:
93C15Control systems governed by ODE
34G10Linear ODE in abstract spaces
34G20Nonlinear ODE in abstract spaces
34A08Fractional differential equations
49J15Optimal control problems with ODE (existence)
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