DIRECT COLLOCATION METHOD FOR SOLVING OPTIMAL CONTROL PROBLEMS

Objective: The purpose of this work was to present in details the development and use of the direct collocation method to solve optimal control problems. Methods: This was made in three parts: the first addresses how to formulate the optimal control problem, the second presents the direct collocation method addressing its construction, operation and comparison with other methods, and, finally, the third part introduces and example of an optimal control problem applied to a mechanical system (mass-spring-damper) and solved by the direct collocation method, making the algorithm used available to the reader. Results: The results obtained with the application of the optimal control to the mechanical system were the optimal states (position and velocity) and the optimal force needed to move the mass between three predefined points. Conclusion: With the work was possible to understand in detail the development and application of the direct collocation method to solve optimal control problem as well as to infer that it is a powerful and efficient tool when compared with other numerical methods.