A Newton Method for Solving Non-Linear Optimal Control Problems with General Constraints

Abstract: Optimal control of general dynamic systems under realistic constraints on input signals and state variables is an important problem area in control theory. Many practical control problems can be formulated as optimization tasks, and this leads toa significant demand for efficient numerical solution algorithms.Several such algorithms have been developed, and they are typically derived from a dynamic programming view point. In this thesis a differentapproach is taken. The discretetime dynamic optimization problem is formulated as a static one, with the inputs as free variables. Newton's approach to solving such a problem with constraints, also known as Wilson's method, is then consistently pursued, anda algorithm is developed that isa true Newton algorithm for the problem, at the same time as the inherent structure is utilized for efficient calculations. An advantage with such an approach is that global and local convergence properties can be studied in a familiar framework.The algorithm is tested on several examples and comparisons to other algorithms are carried out. These show that the Newton algorithm performs well and is competitive with other methods. lt handles state variable constraints in a direct and efficient manner, and its practical convergence properties are robust.A general algorithm for !arge scale static problems is also developed in the thesis, and it is tested on a problem with load distribution in an electrical power network.