Why Optimal Control Software?

1. Analytical solution can be hard. 2. If the controls and states are discretized, then an optimal control problem is converted to a nonlinear programming problem. However... Discretization and conversion is professional. Selection and use of nonlinear programming package is an art. For large scale problems, direct discretization may not be feasible. 2 Classi¯cation of methods for solving optimal control prob-lems A technique is often classi¯ed as either a direct method or an indirect method. An indirect method attempts to solve the optimal control necessary conditions. Thus,for an indirect method, it is nec-essary to explicitly derive the costate equations, the control equations, and all of the transversality conditions. A direct method treats an OCP as an mathematical program-ming problem after discretization. Direct method does not require explicit derivation and construction of the necessary conditions. 3 What is RIOTS? RIOTS is a group of programs and utilities, written mostly in C, Fortran, and M-¯le scripts and designed as a toolbox for Matlab, that provides an interactive environment for solving a very broad class of optimal control problems. 4 Main contributions and features of RIOTS: The ¯rst implementation of consistent approximation using discretization methods based on Runge-Kutta integration Solves a very large class of ¯nite-time optimal control prob-lems { trajectory and endpoint constraints { control bounds { variable initial conditions and free ¯nal time problems { problems with integral and/or endpoint cost function