THE SEQUENTIAL LINEAR-QUADRATIC PROGRAMMING ALGORITHM FOR SOLVING DYNAMIC OPTIMIZATION PROBLEMS - A REVIEW

The optimum principle for dynamic systems as formulated by Pontryagin in 1962 may be used for development of numerical algorithms to solve d ynamic optimization problems. This as opposed to the well known method s which discretize controls (and states) to transform the problem into a NLP framework. An obstacle for its use has been the extensive symbo lic manipulations needed to derive the optimality equations for a spec ific problem, and the difficulty of solving the resulting nonlinear tw o point boundary value problem. There are methods which make use of th e optimality conditions for dynamic systems (Pontryagin Minimum Princi ple) just as SQP methods use the Kuhn-Tucker conditions. As in SQP, a problem with linear constraints and quadratic objective function is so lved iteratively. Such a method is presented in this work. This is clo sely related to the dynamic optimization method based on a combination of a SQP solver and total discretization of the dynamic system. The d ynamic linear-quadratic model has a single analytical optimal control solution, acid is thus accurately and effectively solved. Thus, at eac h iteration, the optimal solution is found for the linear-quadratic ap proximate model. This gives a search direction which can be used in a iterative scheme to ensure good agreement between the linear-quadratic and the nonlinear model.