This article studies input design of kernel-based regularization methods for linear dynamical systems, which has been formulated as a nonconvex optimization problem with the criterion being a scalar measure of the posterior covariance of the Bayesian estimate, subject to a spherical constraint on the input. The nonconvex nature of such input design problems poses significant challenges in deriving optimality conditions and efficient numerical algorithms. In this work, we first derive a sufficient condition for guaranteeing that a stationary point of the regularized input design problem is a global minimum. Next, we propose a spherical constraint preserving (SCP) algorithm to efficiently reach a stationary point of the design problem. Numerical simulation results show that the SCP algorithm finds the global minimum of the original design problem for all simulated cases and its average computational time is only approximately one tenth of that of the algorithms for previous methods.  

　　Publication:  

　　IEEE Transactions on Automatic Control ( Volume: 68, Issue: 9, September 2023)  

　　http://dx.doi.org/10.1109/TAC.2022.3228200  

　　Author:  

　　Biqiang Mu  

　　Key Laboratory of Systems and Control, Institute of Systems Science, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, China  

　　Email: bqmu@amss.ac.cn  

　　He Kong  

　　Shenzhen Key Laboratory of Biomimetic Robotics and Intelligent Systems, Department of Mechanical and Energy Engineering, Southern University of Science and Technology (SUSTech), Shenzhen, China  

　　Guangdong Provincial Key Laboratory of Human-Augmentation and Rehabilitation Robotics in Universities, SUSTech, Shenzhen, China  

　　Tianshi Chen  

　　School of Data Science and Shenzhen Research Institute of Big Data, The Chinese University of Hong Kong, Shenzhen, China  

　　Bo Jiang  

　　School of Mathematical Sciences, Nanjing Normal University, Nanjing, China  

　　Lei Wang  

　　College of Control Science and Engineering, Zhejiang University, Hangzhou, China  

　　Junfeng Wu  

　　School of Data Science and Shenzhen Research Institute of Big Data, The Chinese University of Hong Kong, Shenzhen, China