Adaptive backstepping control for a class of nonlinear systems using neural network approximations

Abstract

SUMMARYIn this paper, an adaptive neural network (NN) backstepping technique is developed for tracking control of a class of nonlinear systems. NNs are used to compensate for the unknown nonlinear functions in the system. A systematic backstepping approach is established to synthesize the adaptive NN control scheme that ensures the boundedness of all the signals in the closed-loop system, and yields a small tracking error. The issue of transient performance is also addressed under an analytical framework. The effectiveness of the proposed scheme is demonstrated by computer simulations.

Robust approximation‐based adaptive control of multiple state delayed nonlinear systems with unmodeled dynamics

“…The main idea of this methodology is to employ a universal approximator() to model the unknown uncertainties in system dynamics, and a stable controller is constructed by fusing adaptive technique with backstepping. () Many significant results on output‐feedback control, quantized control, output tracking,() and sampled‐data control have been reported.…”

Adaptive control of hydrodynamic loads in splash zone

“…Since neural networks are used to approximate unknown nonlinear functions, the controllers can overcome some limitations of conventional adaptive controllers. Neural networks has also been embedded in the overall control strategy for modelling and compensation purposes in [7], [8], [9] and [10]. Some in-depth developments in neural networks for modelling and control purposes have been made in [11], [12] and [13].…”

Improved nonlinear trajectory tracking using RBFNN for a robotic helicopter

“…Especially for robotic helicopters operating in a narrow environment or in the formation flight, the controller should have a fast and accurate tracking ability of determining the minimum proximity to objects in surrounding environment. With respect to this issue, the backstepping technique can be a good strategy because it stabilizes all states simultaneously without the timescale separation assumption [19,20]. The backstepping design method is a recursive procedure for systematically selecting the control Lyapunov function (CLF) and using the fast states as the control inputs of the slow states intermediately [21][22][23][24].…”

“…Therefore, the performance of the approximate controllers must be analyzed to ensure that the unmodeled dynamics do not destroy the stability of the closed-loop system [10][11][12][13][14][15][16][17]. On the other hand, a neural-network (NN) function is usually implemented to approximately compensate for the inversion error or the unknown dynamics on line due to its universal approximation capability [19,27]. The NN-based direct adaptive control has recently emerged as an enabling technology for practical flight control systems that allow on-line adaptation to uncertainties [11,12].…”

“…Among many NN methodologies, radial basis function neural network (RBFNN) has been successfully used as a linearly parameterized function approximation to solve many problems. The updating law of RBFNN weighting parameters can also be based on Lyapunov technique to guarantee the stability of the closed-loop systems [19,21].…”