Direct numerical method for solving optimal control problems

An algorithm for minimizing functional is presented with the use of a Tikhonov stabilizer. the OC problem is treated as the inverse problem of recovering the control u(t)from input data. Advantages of the direct numerical method is that it applies to a wide class of linear and nonlinear systems and to problems with state and mixed constraints. It does not require additional information on the functional class of controls, it applies to OC problems with approximate or uncertain input data, including problems with moving ends, and it can be applied to pulse control problems. OC problems can be solved numerically by using difference approximations of integral equations, the inequalities arising from the state constraints, objective functional, and the boundary conditions.