Neural-network control of nonaffine nonlinear system with zero dynamics by state and output feedback

By Shuzhi Sam Ge, Jin Zhang. IEEE Trans. Neural Networks, 2003

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Neural Network Control of a Robotic Manipulator With Input Deadzone and Output Constraint (2016, background): “Lemma 2 [66]: Suppose the system output and its ﬁrst derivatives are bounded, so that | y ( k ) | Y k with a positive constant Y k .”
A low-complexity global approximation-free control scheme with prescribed performance for unknown pure feedback systems (2014, background): “Works incorporating the Mean Value Theorem (Chien et al., 2011; Ge & Wang, 2002; Ge & Zhang, 2003; Labiod & Guerra, 2007; Ren et al., 2009; Wang, Chien et al., 2011, 2010; Wang, Ge et al., 2010; Wang et al., 2006; Wang, Liu et al., 2011; Zhang & Ge, 2008; Zhang et al., 2010, 2012), the Taylor…”
Robust Adaptive Neural Network Control for a Class of Uncertain MIMO Nonlinear Systems With Input Nonlinearities (2010, background): “Various control techniques have been proposed for both theoretical interests and practical applications including robust adaptive control [1]–[3], sliding mode control [4], [5], backstepping control [6]–[9], and intelligent control [10]–[12].”
Control of fully actuated ocean surface vessels using a class of feedforward approximators (2006, background): “Lemma 3: [18] Consider the following linear system:”
Direct Adaptive Neural Control for a Class of Uncertain Nonaffine Nonlinear Systems Based on Disturbance Observer (2013, background): “Lemma 2 [81], [82]: Consider the following linear system:”