Research on an extended optimal guidance law with multiple constraints

An extended optimal guidance law with terminal miss distance and impact angle constrains is derived. The guidance law is obtained as the solution of a linear quadratic optimal control problem with the goal function weighted by a power of the time-to-go. Based on the analytical expression for the change of guidance command with time and the adjoint system analysis method, the command characteristics and dimensionless miss distance of guidance law are analyzed. The result shows that the acceleration command of guidance law can be converged into zero in the final time of guidance, which may create a good situation for terminal angle of attack control. A design principle for selection of guidance law gain is discussed. Finally, according to the requirements of engineering application, the methods on calculating the guidance initial condition and maximal required acceleration are given. The effectiveness and practicality of the guidance law are demonstrated through simulation.