Equivalence between generating function method and Riccati transformation method for LQ terminal control
LQ终端控制的生成函数法与Riccati变换法的等价性

By defining the third-kind generating function(GF) for a linear Hamiltonian system, this paper relates the generating function approach to the Riccati transformation method for LQ terminal control problems; and proves the equivalence of optimal terminal control laws derived by these two different methods. Since the generating function approach is adaptive to different types of boundary constraints, it provides a substantial advantage over the classical Riccati transformation method. Firstly, considering the backward sweeping character of the Riccati transformation method, we formulate the third-kind generating function in accordance with the backward canonical transform of the linear Hamiltonian system. Next, solving a Hamiltonian two-point-boundary-value problem, we obtain the new optimal control law in term of the generating function. Finally, comparing all terms of each new control law with the conventional control law derived by the Riccati transformation method, we verify the equivalence of these two different solution strategies.