LQ终端控制的生成函数法与Riccati变换法的等价性-控制理论与应用.PDFVIP

26 8 Vol. 26 No. 8 2009 8 Control Theory Applications Aug. 2009 :2009 LQRiccati , , (, 116023) : 3, Riccati, . . Riccati, 3 , , . Riccati, . : LQ; LQ; ; Riccati; : TP273 : A Equivalence between generating function method and Riccati transformation method for LQ terminal control LI Zhen-hu, TAN Shu-jun, WU Zhi-gang (State Key Lab of Structural Analysis for Industrial Equipment, Dalian University of Technology, Dalian Liaoning 116023, China) Abstract: 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 equiv- alence 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 transfor- mation 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. Key words: LQ soft terminal control; LQ hard terminal control; generating function; Riccati transformation; Hamilto- nian system