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Discrete-time inverse linear quadratic optimal control over finite time-horizon under noisy output measurements
HanZhang,YibeiLi,XiaomingHu
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(1 Department of Automation, Shanghai Jiao Tong University, Shanghai 200240, China 2 Key Laboratory of System Control and Information Processing, Ministry of Education of China, Shanghai 200240, China 3 Shanghai Engineering Research Center of Intelligent Control and Management, Shanghai 200240, China;4 Department of Mathematics, KTH Royal Institute of Technology, 100 44 Stockholm, Sweden)
摘要:
In this paper, the problem of inverse quadratic optimal control over finite time-horizon for discrete-time linear systems is considered. Our goal is to recover the corresponding quadratic objective function using noisy observations. First, the identifiability of the model structure for the inverse optimal control problem is analyzed under relative degree assumption and we show the model structure is strictly globally identifiable. Next, we study the inverse optimal control problem whose initial state distribution and the observation noise distribution are unknown, yet the exact observations on the initial states are available. We formulate the problem as a risk minimization problem and approximate the problem using empirical average. It is further shown that the solution to the approximated problem is statistically consistent under the assumption of relative degrees. We then study the case where the exact observations on the initial states are not available, yet the observation noises are known to be white Gaussian distributed and the distribution of the initial state is also Gaussian (with unknown mean and covariance). EM-algorithm is used to estimate the parameters in the objective function. The effectiveness of our results are demonstrated by numerical examples.
关键词:  Inverse optimal control · Linear quadratic regulator · Statistical consistency · EM-algorithm
DOI:https://doi.org/10.1007/s11768-021-00066-8
基金项目:
Discrete-time inverse linear quadratic optimal control over finite time-horizon under noisy output measurements
Han Zhang,Yibei Li,Xiaoming Hu
(1 Department of Automation, Shanghai Jiao Tong University, Shanghai 200240, China 2 Key Laboratory of System Control and Information Processing, Ministry of Education of China, Shanghai 200240, China 3 Shanghai Engineering Research Center of Intelligent Control and Management, Shanghai 200240, China;4 Department of Mathematics, KTH Royal Institute of Technology, 100 44 Stockholm, Sweden)
Abstract:
In this paper, the problem of inverse quadratic optimal control over finite time-horizon for discrete-time linear systems is considered. Our goal is to recover the corresponding quadratic objective function using noisy observations. First, the identifiability of the model structure for the inverse optimal control problem is analyzed under relative degree assumption and we show the model structure is strictly globally identifiable. Next, we study the inverse optimal control problem whose initial state distribution and the observation noise distribution are unknown, yet the exact observations on the initial states are available. We formulate the problem as a risk minimization problem and approximate the problem using empirical average. It is further shown that the solution to the approximated problem is statistically consistent under the assumption of relative degrees. We then study the case where the exact observations on the initial states are not available, yet the observation noises are known to be white Gaussian distributed and the distribution of the initial state is also Gaussian (with unknown mean and covariance). EM-algorithm is used to estimate the parameters in the objective function. The effectiveness of our results are demonstrated by numerical examples.
Key words:  Inverse optimal control · Linear quadratic regulator · Statistical consistency · EM-algorithm