Robust adaptive backstepping tracking control of stochastic nonlinear systems with unknown input saturation: A command filter approach

Abstract

This paper studies the problem of adaptive observer-based radial basis function neural network tracking control for a class of strict-feedback stochastic nonlinear systems comprising an unknown input saturation, uncertainties, and unknown disturbances. To handle the issue of a non-smooth saturation input signal, a smooth function is chosen to approximate the saturation function and the state observer is used to estimate unmeasured states. By the so-called command filter method in the controller design procedure, the implementation complexity is reduced in the proposed backstepping method. Moreover, a radial basis function neural network is deployed to reconstruct the unknown nonlinear functions. In addition, the gains of all radial basis function neural networks are updated through one updating law leading to a minimal learning parameter which is independent of the number of neural nodes and the order of the system.Comparing with the existing results, the proposed approach can stabilize a constrained stochastic system more effectively and with less computational burden. Finally, a practical example shows the performance of the proposed controller design. K E Y W O R D Sadaptive neural network, command filter, input saturation, minimal learning parameter, observer, stochastic nonlinear systems 1 3296

Robust neural network‐based backstepping landing control of quadrotor on moving platform with stochastic noise

“…To alleviate this issue, it is assumed that the limitations of the control inputs are unknown, as . Inspiring from Reference 21, constrained control inputs can be represented as where By using the mean‐value theorem, 36 one can write where is a diagonal matrix, as follows: …”

“…Among the state‐of‐the‐art methods, backstepping control is distinguished as an effective and powerful approach for stochastic nonlinear systems 18,19 . Moreover, by utilizing the radial basis function (RBF) neural network (NN) with the conventional backstepping technique, adaptive NN backstepping methods have been presented to estimate uncertainties and disturbances appearing in the systems 20,21 . The design of an adaptive backstepping controller for a stochastic system has several difficulties.…”

“…The third difficulty is appearing non‐smooth saturation nonlinearities 24 . In Reference 21, the saturation nonlinearity is replaced with a smooth hyperbolic function and the so‐called mean‐value theorem was exploited. However, almost all of the stochastic backstepping techniques are applicable for fully actuated systems, which is not the case of quadrotor system dynamics.…”

Event‐triggered adaptive finite‐time prescribed performance tracking control for uncertain nonlinear systems

“…6 For stochastic nonlinear systems with input saturation, two adaptive fuzzy tracking control strategies were introduced. 7,8 Combining dynamic surface control and radial basis function (RBF) neural network, the problem about adaptive control for nonlinear systems with uncertainties was investigated. 9 Taking switched MIMO nonlinear systems with hysteresis as a research object, an adaptive output feedback tracking controller was constructed using fuzzy logic.…”

“…By replacing the inverse of deadzone nonlinearity with an output compensator, an adaptive robust control scheme was studied for nonlinear systems with unknown input deadzone 6 . For stochastic nonlinear systems with input saturation, two adaptive fuzzy tracking control strategies were introduced 7,8 . Combining dynamic surface control and radial basis function (RBF) neural network, the problem about adaptive control for nonlinear systems with uncertainties was investigated 9 .…”