12505

11442

كارشناسي ارشد

رياضي كاربردي

اصفهان: دانشگاه صنعتي اصفهان، دانشكده علوم رياضي

1396

يازده،[93]ص.:مصور، جدول، نمودار

ص. ع. به فارسي و انگليسي

حميدرضا مرزبان

واژه نامه

محسن مجيري، رضا مختاري

1396/04/12

كتابنامه

علوم رياضي

رياضي

ID11442

A numerical solution for fractional optimalcontrol problems via Bernoulli polynomials Seyyed Abbas Nasrollahzadeh a nasrollahzadeh@math iut ac ir 2017 Department of Mathematical Sciences Isfahan University of Technology Isfahan 84156 83111 Iran Supervisor Dr Hamid Reza Marzban hmarzban@cc iut ac ir 2010 MSC Keywords Fractional order optimal control Caputo fractional derivative Riemann Liouville fractionalintegration Bernoulli polynomial basis operational matrix numerical solution AbstractMany real world physical systems display fractional order dynamics that is their behavior is governed by frac tional differential equations FDEs FDEs are generalizations of ordinary differential equations to an arbitrary non integer order In mechanics fractional calculus plays an important role for example it has been suc cessfully employd to model damping forces with memory effects to described state feedback controllers Inparticular 1 2 order derivative or 3 2 order derivative describe the frequency dependent damping materials sat isfactorily Other examples are nonlinear oscillation of earthquakes fluid dynamic traffic model continuumand statistical mechanics colored noise solid mechanics economics bioengineering anomalous transport anddynamics of interfaces between soft nanoparticles and rough substrates When the FDEs are used in conjunc tion with the performance index and a set of initial conditions they lead to fractional optimal control problems FOCPs Optimal control problems have found applications in many different fields including engineering science and economics As the demand for more accurate and high precision systems increases the demandto develop formulation and numerical scheme of Fractional Optimal Control Problems also increases Optimalcontrol problem requires the minimization of a functional over an admissible set of control functions subject todynamic constraints on the state and control variables A FOCP is an optimal control problem in which eitherthe performance index or the differential equations governing the dynamics of the system or both contain at leastone fractional order derivative term FOCPs can be defined with different definitions of fractional derivatives The most important types of fractional derivatives are Riemann Liouville and Caputo fractional derivatives In the Hamiltonian systems of equations there exist both right and left fractional differential operators whose

حميدرضا مرزبان

محسن مجيري، رضا مختاري