Optimal control problems with integral functional and phase constraints: reduction to optimal consistency parameter problems (Q2255648)

The author develops an iterative method to solve a class of optimal control problems with integral functional and phase constraints of the following form: \[ J=\int_0^T f_0(z(t),t)dt\to\min_{u(\cdot)\in Y_u} \] \[ \dot{z}(t) = f(z(t),t) + u(t)g(z(t)),\quad z(0)= z_0,\;z(t)\in Z(t) \;\;(t \in [0,T]), \] where \(Y_u=\{u(\cdot) :u(\cdot)\text{ is measurable}, u(t)\in U, t\in [0,T]\}\). The given method is based on the reduction of an optimal control problem to an optimal consistency parameter problem. An illustrative example is presented.