A new LPV modeling approach using PCA-based parameter set mapping to design a PSS

Abstract

Graphical abstract

Manipulator Dynamic Nonlinearity Approximation Based on Polytopic LPV Modeling for Robot Tracking Control Problem

“…The basis of linearization scheduling (Rugh and Shamma 2000) that is formed by applying the Jacobian of the system equations around the operating points can be used to obtain the polytopic model of a nonlinear system. Polytopic LPV modeling is an effective way of overcoming the nonlinearity effects and parameter deviations of a nonlinear system (Abolhasani Jabali and Kazemi 2017a, b;Jabali and Kazemi 2017). In (Hoffmann and Werner 2014a), different LPV techniques for modeling and control purposes and different synthesis methods are reviewed.…”

“…PCAbased parameter set mapping has been used in Hashemi et al (2009); Kwiatkowski and Werner 2008) to reduce conservatism and complexity in controller design for the LPV model of the robot by finding a tighter region of the parameters. This strategy is useful in the case of parameters with large space and when the computational complexity may be occurred (Jabali and Kazemi 2017). In (Rizvi et al 2016) using kernel-based PCA, a model reduction method has been presented for the LPV model of robot manipulators.…”

A recursive LMI-based algorithm for efficient vertex reduction in LPV systems

“…(i) Principal component analysis (PCA), by detecting and neglecting the less significant directions in the parameter space without losing much information regarding the plant, thus allowing the attainment of a tighter parameter set (Jabali & Kazemi, 2017;Kwiatkowski & Werner, 2008;Rizvi, Mohammadpour, Tóth, & Meskin, 2016). Notably, some recent advances in this domain have led to the application of autoencoder neural networks, which achieve reduction of the varying parameters without being restricted to behave as linear maps (Rizvi et al, 2018).…”

LMI-based design of state-feedback controllers for pole clustering of LPV systems in a union of 𝒟R-regions

“…Moreover, R. showed the existence of a relationship between pole placement and the Lyapunov function. In fact, pole placement for gain-scheduled systems has progressed strongly in the last decades, with several results concerning the design of observers (Nejjari, Puig, de Oca, & Sadeghzadeh, 2009), state-feedback controllers (Bouazizi, Kochbati, & Ksouri, 2001;, H ∞ controllers Yu, Chen, & Woo, 2002), and application in many fields, such as aerospace vehicles (Ghersin & Pena, 2002), UAV (López-Estrada, Ponsart, Theilliol, Zhang, & Astorga-Zaragoza, 2016), missile (Shen, Yu, Luo, & Mei, 2017), power system (Jabali & Kazemi, 2017a), fuel cells (Rotondo, Fernandez-Canti, Tornil-Sin, Blesa, & Puig, 2016) and robotics (Jabali & Kazemi, 2017b).…”