Physical Meanings of Optimal Control in Guidance Applications

Abstract

This talk aims to introduce new insights into optimal control in guidance applications. The optimal control has been widely applied to the guidance applications due to its benefits. First, the design process is systematically well-posed. Second, it can readily provide a guidance solution that can satisfy terminal constraints for guidance operations. Also, it can consider specific performance criteria when designing guidance laws. Last but not least, it can a state feedback form of guidance laws as well. Although the optimal guidance laws have been extensively utilized, little effort has been made to understand the working principle of the optimal guidance laws so far. Based on this perspective, in this talk, we dedicate to investigate the physical meaning of the optimal guidance laws, which is unrevealed so far. To this end, an alternative form of the optimal guidance laws is first derived. In this form, the physical meaning of the optimal guidance laws is clearly shown. From the alternative form of the optimal guidance laws, we reveal that guidance laws based on the optimal control theory can be newly interpreted as combination of a state predictor for estimating a final state to be constrained and a specific form of governing equation for reducing a tracking error optimally. In practice, this information is essential to ensure confidence in the performance and reliability of guidance laws based on the optimal control theory when implementing the optimal guidance laws in a real system. Also, the results obtained can provide a link between existing guidance laws based on nonlinear control and guidance laws based on optimal control. Therefore, the advantages of both techniques can be fully exploited by utilizing the results obtained. To be more specific, existing nonlinear guidance laws can be directly converted to their optimal forms, and the physical meaning of them can then be easily explained. In this talk, finally, illustration examples are provided to show how to utilize the results obtained to guidance applications.