Direct numerical method for solving optimal control problemsстатья
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Дата последнего поиска статьи во внешних источниках: 18 июля 2013 г.
Аннотация: To control a system means to specify a possibly discontinuous or generalized function u(t) on a time interval such that the evolution of the system is governed, for example, by differential equations of the form
dx dt=f(t,x,u),x(0)=x 0 ,(1)
where t is an independent variable, x is the state vector of dimension n, and f and u are vector functions. The optimal control (OC) problem is characterized by the presence of simple constraints of the type |u|≤1 or mixed nonlinear pointwise constraints g(x,u)≤0. As a rule, the dimension of u is lower than that of x. More complicated settings include additional terminal constraints x(T)≥x T , etc.
In this paper, the OC problem is treated as the inverse problem of recovering the control u(t) from input data, including approximate ones. Moreover, we develop an algorithm for minimizing the functional with the use of a Tikhonov stabilizer. The numerical method proposed for its solution is referred to as direct.