Identifiability and Solvability in Inverse Linear Quadratic Optimal Control Problems  

作　　者：LI Yibei WAHLBERG Bo HU Xiaoming 

机构地区：[1]Optimization and Systems Theory,Department of Mathematics,KTH Royal Institute of Technology,SE-10044,Stockholm,Sweden [2]Division of Decision and Control,School of Electrical Engineering and Computer Science,KTH Royal Institute of Technology,SE-10044,Stockholm,Sweden

出　　处：《Journal of Systems Science & Complexity》2021年第5期1840-1857,共18页系统科学与复杂性学报（英文版）

摘　　要：In this paper, the inverse linear quadratic(LQ) problem over finite time-horizon is studied.Given the output observations of a dynamic process, the goal is to recover the corresponding LQ cost function. Firstly, by considering the inverse problem as an identification problem, its model structure is shown to be strictly globally identifiable under the assumption of system invertibility. Next, in the noiseless case a necessary and sufficient condition is proposed for the solvability of a positive semidefinite weighting matrix and its unique solution is obtained with two proposed algorithms under the condition of persistent excitation. Furthermore, a residual optimization problem is also formulated to solve a best-fit approximate cost function from sub-optimal observations. Finally, numerical simulations are used to demonstrate the effectiveness of the proposed methods.

关 键 词：Inverse optimal control linear quadratic regulators model identifiability 

分 类 号：O224[理学—运筹学与控制论]