Global output feedback control for nonlinear cascade systems with unknown output functions and unknown control directions

Abstract

Summary This paper investigates the output feedback control for the uncertain nonlinear system with the integral input‐to‐state stable (iISS) cascade subsystem, which allow not only the unknown control direction but also the unknown output function. The unknown output function only needs to have a generalized derivative (which may not be derivable), and the upper and lower bounds of the generalized derivative need not to be known. To deal with the challenge raised by the unknown output function and the unknown control direction, we choose a special Nussbaum function with a faster growth rate to ensure the integrability for the derivative of the selected Lyapunov function. Then, a dynamic output feedback controller is designed to drive the system states to the origin while keeping the boundedness for all other closed‐loop signals. Moreover, via some appropriate transformations, the proposed control scheme is extended to deal with more general uncertain nonlinear cascade systems with quantized input signals. Finally, two simulation examples are given to show the effectiveness of the control scheme.

Global stabilization control for multiple input multiple output nonlinear systems with unknown function vector

“…Then, the controller is designed by backstepping method, so that the closed‐loop system can get the global stabilization control. For example, Reference 34 solves the global output feedback problem of nonlinear systems with unknown functions, it assumes that the unknown function $$$ {g}_i\left(\eta (t),y(t)\right) $$$ in the system is $$$ \mid {g}_i\left(\eta (t),y(t)\right)\mid \le {\mu}_{i1}{g}_{i1}\left(|\eta |\right)+{\mu}_{i2}{g}_{i2}\left(|y|\right) $$$, where $$$ {g}_{i1}\left(|\eta |\right) $$$ and $$$ {g}_{i2}\left(|y|\right) $$$ are known smooth functions. From the above description, it can be seen that although these assumptions are used to solve the global stabilization control problem of nonlinear systems, they also increase the conservatism of the control algorithm.…”

Decentralized adaptive tracking control for nonlinear large‐scale systems with unknown control directions

“…As indicated in the work of Chen et al, 29 the control direction representing the motion direction of some practical systems may be unknown (e.g., combustion control systems 30 and course control of marine vessels 31 ). To overcome the challenge caused by unknown control directions, an effective compensation scheme is to use the Nussbaum function technique, 32 which has been successfully applied to deal with the stabilization problems of the single nonlinear system 33,34 and the output consensus problem for nonlinear MASs 35 without considering nonlinear function uncertainty and actuator fault. However, since the introduction of Nussbaum function will affect the integrability of the derivative of the Lynapunov function, there exist only a few research works for nonlinear interconnected LSSs with unknown control directions 36,37 .…”

Adaptive tracking control for uncertain nonlinear systems subject to unknown control coefficients, state constraints, and input saturation

“…By using the Nussbaum gain technology, article [14] investigated the adaptive tracking control problem for a class of strict-feedback nonlinear systems with unknown control direction. A Nussbaum gain function-based quantized feedback control was proposed for nonlinear feedforward systems with both unknown control coefficients and unknown output functions in article [15]. In [16], Sun et al proposed a novel Nussbaum-type function, based on which an adaptive fuzzy asymptotically tracking control scheme was designed for full state constrained nonlinear system with unknown control direction.…”

“…In 1983, Nussbaum put forward the Nussbaum-gain technology, which solved the controller design problem of nonlinear system with unknown signs of control coefficients [13]. Based on this, a great deal of works have been done by scholars in recent years, which greatly promote the development of nonlinear systems with unknown control direction both in theory and application [14,15,16,17,18]. By using the Nussbaum gain technology, article [14] investigated the adaptive tracking control problem for a class of strict-feedback nonlinear systems with unknown control direction.…”