Predictive Tracking Under Persistent Disturbances and Data Errors Using $H_2$ FIR Approach
Yuriy S. Shmaliy, Yuan Xu, José A. Andrade-Lucio, Oscar Ibarra‐Manzano
Abstract
Industrial processes may incur a significant loss in information under unspecified impacts and data errors. Therefore, robust predictors are required to ensure the performance. In this article, we design an <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$H_2$</tex-math></inline-formula> optimal finite impulse response ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$H_2$</tex-math></inline-formula> -OFIR) predictor under persistent disturbances, measurement errors, and initial errors. The <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$H_2$</tex-math></inline-formula> -OFIR predictor is derived by minimizing the squared weighted Frobenius norms for each error. A suboptimal <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$H_2$</tex-math></inline-formula> finite impulse response (FIR) prediction algorithm is obtained using a linear matrix inequality. The <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$H_2$</tex-math></inline-formula> -OFIR predictive tracker is tested by simulations assuming Markov disturbances and data errors driven by the Gaussian, uniform, and industrial Cauchy heavy-tailed noise. It is shown experimentally that in predictive tracking of a moving robot using the ultrawideband technology, the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$H_2$</tex-math></inline-formula> -OFIR predictor operating with full error matrices is more robust than the Kalman and unbiased FIR predictors.