A progressive domain expansion method for solving optimal control problem

Experience from years of operations seems to support this approach given the fact that a necessary and enough condition for the proper operation of the turbo-alternators is that the operating net head must satisfy the requirements for acceptable energy conversion by the turbine. [...]the optimal control problem solved in this work is the determination of the best control vector and resulting state trajectories which minimizes certain performance index, subject to system constraints. Many authors had proposed methods of solving an optimal control problem, these methods can be in the form of nonlinear programming, shooting method, forward backward sweep, steepest descent, conjugate gradient, dynamic programming, the variation of externals, quasi-linearization, gradient projection, collocation, etc [19, 20]. (2) where ? represents a scalar valued function. [...]3) presents the differential equation (model equation) that describes the operating head dynamics, ... [...]the problem addressed here adopts a performance index that includes penalties for deviation from a specified state and for deviations from some predefined value of the control variable. ..