Kernel-enabled methods for subspace regression and efficient control
Kaustubh Patil, Abhijit J. Kulkarni · International Journal of Modelling Identification and Control · 2008
Due to many inherent desirable properties, kernel-based formalisms are quite popular and find many applications in diverse areas. They are routinely applied to solve important class of three machine learning problems viz. pattern classification, function approximation and density estimation. In the present work, three kernel variants of traditional algorithms viz. Principal Component Regression (PCR), Partial Least Squares (PLS) regression and Recursive Least Squares (RLS)regression are used and compared on two benchmark problems viz. Henon map and problem due to Narendra and Li. All the methods performed equally well. These methods are found to be robust in presence of noise also. Owing to its adaptive nature, Kernel Recursive Least Squares (KRLS) was used in controlling the above non-linear systems with set point stabilisation and trajectory tracking as two control objectives. KRLS performed well on all the systems for both the control objectives. In general, it was found that kernel-based formalisms deal effectively with the non-linearity in the data thereby making subspace regression and control accurate.