Online Estimation of Missing Data Using Sparse Optimization Techniques With Applications to Classical Control

Abstract

This paper proposes and describes a method based on sparse optimization techniques for online estimation of missing data. The basic idea of the proposed method is to represent the noise-free signal of interest sparsely in a composite dictionary. The proposed algorithm offers three prime advantages: 1) handles nonlinear processes that are locally linearizable; 2) requires lower computational power than the existing algorithms; and 3) adapts to the changing process conditions by optimally selecting the most relevant feature for that window of time. Results show that the proposed algorithm outperforms the existing neural network-based method. An application of the proposed algorithm to classical (PID) control using measurements with missing data is presented. In this context, an added benefit of the proposed method is that it serves as a feature selection operator for the process, which can be useful in other applications. Numerical (simulation) studies are carried out to study the influence of user-defined parameter in the algorithm and two stochastic factors, namely, the random sampling scheme and noise , on the stability and performance of the closed-loop system. Results show that the closed-loop system with the proposed algorithm is stable and yields a satisfactory performance.