يك روش مستقيم براي حل مسائل كنترل بهينه ي غيرخطي تأخيري چندگانه با محدوديت هاي تركيبي روي متغيرهاي حالت و كنترل

چكيده انگليسي :

A direct approach for the solution of nonlinear optimal control problems with multiple delays subject to mixed state control constraints Zahra Zamani Moorkani zamani zahra@math iut ac ir 2021 Master of Science Thesis in Farsi Departement of Mathematical Sciences Isfahan University of Technology Isfahan 84156 8311 IranSupervisor Dr Hamid Reza Marzban hmarzban@cc iut ac ir2000 MSC 34K35 93C23 97N50 65K05 Keywords Nonlinear optimal control Multiple delays Block pulse functions Lagrange interpolation polynomials Operational matrix of derivative Abstract Time delays appear in many physical processes and engineering systems including transmission lines biologicalmodels communication and information technologies Time delays have a significant influence on the stability andcontrollability of the system under study In many realistic phenomena time delay is a major source of instability As a result analysis parameter identification and optimal control of delay differential equations are of theoreticaland practical importance Due to their significance and their wide applicability in various fields of science and engi neering a large body of literature has been devoted to the numerical treatment of the mentioned systems It should bepointed out that the solution associated with a time delay system is a piecewise smooth function As a consequence smooth basis functions such as Lagrange interpolating polynomials and Legendre polynomials cannot produce anadmissible approximation to different types of delay differential equations This fact justifies the use of a flexibleframework to efficiently model the dynamical behavior of the time delay system under consideration To numericallysolve a time delay system most of the computational methods available in the literature encounter some challenges The main difficulty arises in seeking a closed form solution to this class of systems It is important to note that in thecase of smooth function it is preferable to employ a global approximation and obtain the suitable polynomial degree In the case of a piecewise smooth function it is superior to design a multi domain decomposition scheme based on thethe locations of the switching points that arise in the control input In this thesis we are concerned with the numericalexamination of nonlinear optimal control problems involving multiple delays in both state trajectory and control inputin which the state and control variables are subject to mixed state control constraints The presence of both delays andinequality constraints make the method of solution much more complicated Computational techniques for solvingdifferent types of optimal control problems can be classified into two categories direct and indirect approaches Thefoundation of the indirect methods is based upon the necessary optimality conditions In this thesis we use a directmethod based on a hybrid of block pulse functions and Lagrange interpolating polynomials Combining block pulsefunctions and Lagrange interpolating polynomials allows one to simultaneously make use of the properties of the twomentioned bases The inequality constraints are replaced with equality constraints by employing the penalty functiontechnique introduced in The operational matrices of delay derivative and product corresponding to the hybrid func tions are then utilized to convert the control problem under investigation into a mathematical programming one Theresulting optimization problem is then solved by the well known Lagrange multipliers method The correct choice ofN the order of block pulse functions considerably improves the efficiency and accuracy of the suggested numericalscheme The computational results are compared with either exact or existing numerical solutions in the literature The simulation results demonstrate the superiority of the generalized interpolation method over the conventional one Numerous numerical examples with different inequalities constraints on the state trajectory and control input arecar

زماني موركاني، زهرا

يك روش مستقيم براي حل مسائل كنترل بهينه ي غيرخطي تأخيري چندگانه با محدوديت هاي تركيبي روي متغيرهاي حالت و كنترل

كنترل بهينه ي غير خطي , تأخير هاي چند گانه , توابع بلاك پالس , چند جمله اي هاي درونياب لاگرانژ , ماتريس عملياتي مشتق