Adaptive neural control of uncertain MIMO nonlinear systems

By Shuzhi Sam Ge, Cong Wang. IEEE Transactions on Neural Networks, 2004

872 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Computer Networks and Communications, Control and Systems Engineering

View Paper: https://www.semanticscholar.org/paper/c134604361c2b3587dab0f92be0f429925357514

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Citations in the corpus

Distributed adaptive control for synchronization of unknown nonlinear networked systems (2010, background): “Ge and Wang (2004) and Lewis et al. (1999). Note that the set defined by (49) depends on the initial errors and the graph structural properties. Therefore, proper accommodation of large initial errors requires a larger number of neurons in the NN. The proof also reveals that, for a given number of n”
Adaptive Fuzzy Control of a Class of Nonlinear Systems by Fuzzy Approximation Approach (2012, background): “Alternatively, in recent years, intensive research has been carried out on approximation-based adaptive neural network control or adaptive fuzzy control of nonlinear systems with lower triangle form via the backstepping technique, for instance, see [5], [7], [11], [20], [29], [33], [34], [41], and [”
Adaptive Neural Network Control of a Robotic Manipulator With Time-Varying Output Constraints (2017, background): “Lemma 1 [67]: For a continuous Lyapunov function V(w, t), if it satisfies 1(‖w‖) ≤ V(w, t) ≤ 2(‖w‖) and its derivative V̇(w, t) = dV(w, t)/dt satisfies V̇(w, t) ≤ −κV(w, t) + C, where κ and C are positive constants, then the solution w(t) is bounded.”
Adaptive Neural Output Feedback Tracking Control for a Class of Uncertain Discrete-Time Nonlinear Systems (2011, methodology): “, u j (k) ] ; n j denotes the order of the j th subsystem; m jl represents the order difference between the j th and the lth subsystem, as introduced in [11], [20], and [34].”
Adaptive Neural Fault-Tolerant Control of a 3-DOF Model Helicopter System (2016, background): “Lemma 1 [65]: As a class of linearly parameterized neural networks, RBFNNs are adopted to approximate the continuous function f (Z) : Rq → R, and can be expressed as follows: f (Z) = ŴTφ(Z)+ ε (12)”
Direct adaptive fuzzy control of nonlinear strict-feedback systems (2009, positive): “(33) So far, it follows immediately from (33) and Lemma 1.1 in Ge and Wang (2004) that V (t) is bounded and V (t) ≤ ( V (0)− b0 a0 ) e−a0t + b0 a0 , t ≥ 0, (34) which implies that for t ≥ 0, e = [e1, . . . , en, θ̃ ]T belongs to the compact set Ω = { e|V (e(t)) ≤ V (0)+ b0 a0 } .”
Robust Adaptive Neural Network Control for a Class of Uncertain MIMO Nonlinear Systems With Input Nonlinearities (2010, methodology): “By exploiting the special properties of the affine terms, adaptive neural control for two classes of uncertain MIMO nonlinear systems was proposed [24].”
Direct Adaptive Neural Control for a Class of Uncertain Nonaffine Nonlinear Systems Based on Disturbance Observer (2013, background): “Lemma 1 [75]: For bounded initial conditions, if there exists a C(1) continuous and positive definite Lyapunov function V (x) satisfying π1(‖x‖) ≤ V (x) ≤ π2(‖x‖) such that V̇ (x) ≤ −c1V (x) + c2, where π1, π2 : R → R are class K functions and c1, c2 are positive constants, then the solution x(t) is”
Adaptive tracking control of uncertain MIMO nonlinear systems with input constraints (2011, neutral): “…technique for the uncertain MIMO nonlinear systems, and various robust adaptive control strategies have been proposed (Chang, 2000, 2001; Chang & Yen, 2005; Ge, 1998; Ge & Wang, 2004; Ge & Tee, 2007; Ge, Li, Zhang, & Lee, 2004; Ge, Zhang, & Lee, 2004; Lee & Lee, 2004; Zhang, Ge, & Lee, 2005).”
Neural Network Control of a Robotic Manipulator With Input Deadzone and Output Constraint (2016, background): “Lemma 1 [65]: A Lyapunov function candidate V(x) is bounded if the initial condition V(0) is bounded, V(x) is positive definite and continuous and if V̇(x) ≤ −ρV(x)+ C (3)”
Adaptive Fuzzy Control via Observer Design for Uncertain Nonlinear Systems With Unmodeled Dynamics (2013, methodology): “Moreover, by using backstepping design and the approximation property of the FLSs or the NNs, several adaptive control algorithms were developed in [25]–[27] to achieve the tracking performance for nonlinear interconnected systems in the nested form with completely unknown functions.”