Sparse parameter identification of stochastic dynamical systems

摘要:

Sparsity of a parameter vector in stochastic dynamic systems and precise reconstruction of its zero and nonzero elements appear in many areas including systems and control [1,2,3,4], signal processing [5,?6], statistics [7,?8], and machine learning [9,?10] since it provides a way to discover a parsimonious model that leads to more reliable and robust prediction. Classical system identification theory has been a well-developed field [11,?12]. It usually characterizes the identification error between the estimates and the unknown parameters using different criteria such as randomness of noises, frequency domain sample data, and uncertainty bound of system, so that consistency, convergence rate, and asymptotical normality of estimates can be established as the number of data points goes to infinity. However, these theory and methods are ill suited for sparse identification if the dimension of the unknown parameter vector is high....

Abstract:

Sparsity of a parameter vector in stochastic dynamic systems and precise reconstruction of its zero and nonzero elements appear in many areas including systems and control [1,2,3,4], signal processing [5,?6], statistics [7,?8], and machine learning [9,?10] since it provides a way to discover a parsimonious model that leads to more reliable and robust prediction. Classical system identification theory has been a well-developed field [11,?12]. It usually characterizes the identification error between the estimates and the unknown parameters using different criteria such as randomness of noises, frequency domain sample data, and uncertainty bound of system, so that consistency, convergence rate, and asymptotical normality of estimates can be established as the number of data points goes to infinity. However, these theory and methods are ill suited for sparse identification if the dimension of the unknown parameter vector is high....