حل مسائل كنترل بهينه ي بنگ-بنگ با استفاده از روش شبه طيفي لژاندر اصلاح شده

چكيده انگليسي :

Abstract Bang Bang type controls arise in some well known application areas such as industrial robots aerospace engineering cranes applied physics game theory and biological systems Because of difficulty in obtaining switching times and optimal solution the simulation and numerical approximation of bang bang optimal control problems have received considerable attention Over the last two decades pseudospectral methods have been successfully used to solve a wide variety of optimal control problems arising in diverse areas of engineering and science These methods can effectively solve optimal control problems whose solutions are smooth Although pseudospectral methods enjoy some nice properties they also suffer from many drawbacks For instance they do not provide a satisfactory approximation for non smooth problems such as bang bang optimal control problems Due to the fact that obtaining the analytical solution for bang bang optimal control problems is difficult therefore it is important to provide a numerical solution for solving such problems In this thesis a modified Legendre pseudospectral method is used to obtain accurate and efficient solution of bang bang optimal control problems In this method control and state variables are considered as piecewise constant and piecewise continuous functions respectively and the switching points are also taken as decision variables This method has two major differences with the traditional pseudospectral methods First instead of approximating the states and controls by a polynomial in the whole computational domain as suggested in the classical pseudospectral methods we look for a piecewise continuous approximation polynomial for each state and a piecewise constant function for each control function For this purpose the computational domain is partitioned into subdomains where the size of each subdomain is considered as an unknown parameter and this enables us to compute the switching times Second in contrast with the traditional pseudospectral methods the integral form of the optimal control problem is discretized This equivalent form is found by integrating the differential dynamics and adding in the initial conditions The advantage of using the integral form lies in the fact that this form releases us of imposing the patching conditions for continuity enforcement of states in the boundary of subdomains Thus the problem converts to a non linear mathematical programming whose solution is much more easier than the original one The main advantages of this approach are 1 It obtains good results even by using a small number of collocation points and the rate of convergence is high 2 The switching times can be captured accurately 3 If the number of switching points is not selected correctly it is possible to correct this mistake with simulation and numerical results Various types of bang bang optimal control problems are included to show the efficiency and the accuracy of the proposed discretization scheme PDF created with pdfFactory trial version www pdffactory com

ميرزائي، سمانه

حل مسائل كنترل بهينه ي بنگ-بنگ با استفاده از روش شبه طيفي لژاندر اصلاح شده