SPARSE PARAMETER IDENTIFICATION FOR STOCHASTIC SYSTEMS BASED ON Lγ REGULARIZATION

This paper is concerned with the reconstruction of the zero and nonzero elements of the sparse parameter vector of stochastic systems with general observation sequences. A sparse parameter identification algorithm based on the L-gamma penalty with 0 < gamma < 1 and the residual sum of squares is proposed. Without requiring independently and identically distributed (i.i.d.) and stationary conditions on the observation sequences, the proposed algorithm is proved that not only the contributing variable corresponding to the nonzero parameters can be selected out with probability converging to one but also the estimates of the nonzero parameters have the asymptotic normality property. In order to improve the performance of the L-gamma regularization method, a two-step algorithm based on the adaptively weighted L-gamma penalty with 0 < gamma <= 1 is designed whose set and parameter almost sure convergence are established with non-i.i.d. and nonstationary observation sequences. The proposed methods are applied to the structure selection of the nonlinear autoregressive models with exogenous variables and the sparse parameter identification of the linear feedback control systems. Finally, three numerical examples are given to verify the efficiency of the theoretical results.