Abstract:

Optimal control is an important branch of control theory, and its goal is to determine a control strategy that optimizes system performance indicators under the premise of satisfying dynamic systems and constraints. Optimal control has a wide range of applications in engineering, economics, finance, robotics, aerospace and other fields. The direct method is a common method to solve the optimal control problem. This method transforms the continuous optimal control problem into a finite-dimensional optimization problem by directly discretizing the control and state function. At present, the direct method mainly includes the direct collocation method and the control parameterization method. The direct collocation method uses a specific function form to approximate the state and control function at the same time; the control parameterization method uses a linear combination of basis functions to approximate the control function, thereby discretizing the control space. The purpose of the two methods is to transform the continuous optimal control problem into a finite-dimensional nonlinear programming problem, and then choose an appropriate optimization algorithm to solve it. Benefiting from its flexibility and ability to deal with constraints, the direct method has become the important method in recent years for practical applications requiring real-time control. Researchers and engineers continue to develop and improve direct methods to increase their efficiency and accuracy in solving complex optimal control problems. This article mainly introduces the relevant achievements and latest developments of the direct method for readers' reference, and discusses the research trends and potential research directions of the direct method.

Key words: optimal control, direct method, direct collocation method, control parameterization method