Sequential quadratic programming methods for optimal control problems with state constraints
Some sequential quadratic programming methods for general optimal control problems with nonlinear dynamics, with fixed end time, with Bolza-type performance index, and with general boundary conditions on the initial and final states are proposed. It is assumed that all functions (including the controls) are of \(C^ 2\). After the repetition of the first and second order necessary and second order sufficient conditions of optimality, the quadratic approximation of the performance index and the linear approximation of the state equation and boundary condition in a neighbourhood of the optimal solution is constructed. This way (combined with the penalty function method) a linear-quadratic optimal control problem is obtained, which is next treated as a quadratic programming problem in a Banach space. Using the optimality conditions, a linear multipoint boundary value problem is constructed, the solution of which gives us the correction for the control and for the trajectory. Next, the discrete (i.e., finite-dimensional) sequential quadratic programming method is proposed after the discretization of the time, state equation, and performance index. The augmented Lagrangian with a penalty term is constructed and the corresponding iterative procedure is presented. There aren't any examples and comparison with other methods.
sequential quadratic programming methods
scientific article; zbMATH DE number 549488
scientific article