An introduction to infinite-dimensional linear systems theory
An introduction to infinite-dimensional linear systems theory
Robust adaptive control
Stable Adaptive Neural Network Control
Stable Adaptive Neural Network Control
Adaptive Approximation Based Control: Unifying Neural, Fuzzy and Traditional Adaptive Approximation Approaches (Adaptive and Learning Systems for Signal Processing, Communications and Control Series)
IEEE Transactions on Fuzzy Systems
Design of Robust Adaptive Controllers for Nonlinear Systems with Dynamic Uncertainties
Automatica (Journal of IFAC)
Stable adaptive neuro-control design via Lyapunov function derivative estimation
Automatica (Journal of IFAC)
Adaptive output feedback control methodology applicable to non-minimum phase nonlinear systems
Automatica (Journal of IFAC)
Brief Analysis and control of parabolic PDE systems with input constraints
Automatica (Journal of IFAC)
Adaptive neural control of uncertain MIMO nonlinear systems
IEEE Transactions on Neural Networks
Semiglobal ISpS Disturbance Attenuation With Output Tracking via Direct Adaptive Design
IEEE Transactions on Neural Networks
IEEE Transactions on Neural Networks
Neuro-adaptive force/position control with prescribed performance and guaranteed contact maintenance
IEEE Transactions on Neural Networks
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In this paper, an adaptive neural network (NN) control with a guaranteed L∞-gain performance is proposed for a class of parabolic partial differential equation (PDE) systems with unknown nonlinearities and persistent bounded disturbances. Initially, Galerkin method is applied to the PDE system to derive a low-order ordinary differential equation (ODE) system that accurately describes the dynamics of the dominant (slow) modes of the PDE system. Subsequently, based on the low-order slow model and the Lyapunov technique, an adaptive modal feedback controller is developed such that the closed-loop slow system is semiglobally input-to-state practically stable (ISpS) with an L∞-gain performance. In the proposed control scheme, a radial basis function (RBF) NN is employed to approximate the unknown term in the derivative of the Lyapunov function due to the unknown system nonlinearities. The outcome of the adaptive L∞-gain control problem is formulated as a linear matrix inequality (LMI) problem. Moreover, by using the existing LMI optimization technique, a suboptimal controller is obtained in the sense of minimizing an upper bound of the L∞-gain, while control constraints are respected. Furthermore, it is shown that the proposed controller can ensure the semiglobal input-to-state practical stability and L∞-gain performance of the closed-loop PDE system. Finally, by applying the developed design method to the temperature profile control of a catalytic rod, the achieved simulation results show the effectiveness of the proposed controller.