Numerical methods for solving problems of optimal generalized control (Q1324057)

Systems described by \(n\) ordinary differential equations of the form \(\dot x= f(x, t)+ b(x, t)\dot u\); \(0\leq t\leq T\) are considered. The scalar control variable \(u\) is assumed to be of bounded variation. A performance criterion is to be minimized. Methods for numerical integration of the system equations are proposed. The problem is then transcribed into a nonlinear programming problem. The maximum principle is used for deriving necessary optimality conditions. A method of sequential approximations based on these conditions is described. The method is applied to control systems described by matrix Riccati-type differential equations.