Solution of Dynamic Optimization Problems by Successive Quadratic Programming and Orthogonal Collocation.

Optimal control and estimation problems are currently solved by embedding a differential equation solver into the optimization strategy. The optimization algorithm chooses the control profile, or parameter estimates, and requires the differential equation routine to solve the equations and evaluate the objective and constraint functionals at each step. Two popular methods for optimal control that follow this strategy are Control Vector Iteration CVI and Control Vector Parameterization CVP, CVI requires solution of the Euler-Lagrange equations and minimization of the Hamiltonian while CVP involves repeated differential equation solutions driven by direct search optimization. Both methods can be prohibitively expensive even for small problems because they tend to converge slowly and require solution of differential equations at each iteration. The author introduces a method that avoids this requirement by simultaneously converging to the optimum while solving the differential equations. To do this, he applies orthogonal collocation to the system of differential equations and convert them into algebraic ones. He then applies an optimization strategy that does not require satisfaction of equality constraints at each iteration. Here the method is applied to a small initial value optimal control problem, although he is by no means restricted to problems of this type. Author