Flight path optimization is designed for minimizing aircraft noise, fuel consumption and air pollution around airports. This paper gives theoretical considerations and algorithms solving the Hamilton-Jacobi-Bellman equation (HJB) of aircraft trajectory optimization. Comparisons with direct and indirect methods are carried out. The OCP problem is transformed into new equalities-constrained as a viscosity problem. This constitutes an original dynamical system extension where subsystems are linked to the original dynamics via algebraic coupling equations. A feedback control method using dynamic programming has been developed. Comparisons show its fast computing times. It provides the best optimized flight paths which could be more suitable for CDA approach applicability. A two-segment approach is provided by HJB method which also favors fuel consumption saving. This improved CDA approach could benefit both airlines and communities. Because of the processing speed and efficiency of the HJB method, it can be better interfaced with the in-flight management system respecting airspace system regulation constraints. Hamilton-Jacobi-Bellman equation, Dynamic programming, Aircraft, Flight path optimization, environment
