Output Tracking for Nonlinear Systems with Singular Points

Abstract

Some of the well-known linear results on output tracking have been generalized to include nonlinear control systems by removing from the state space a codimension one submanifold of "singular points." These points do not exist in the linear case, but in nonlinear tracking applications the system trajectory can begin at or pass through "singular points." The purpose of this paper is to study nonlinear output tracking with singular points.

Trajectory following method on output tracking of non-linear non-minimum phase systems

“…This controller is different with controller in [3,4,5,6] and designed based on gradient descent control algorithm. Like controller which is designed based on input-output linearized technique, the stability of gradient descent control algorithm depends on the stability of internal dynamics of the system.…”

“…Recently, output tracking problems on nonlinear nonminimum phase systems have been investigated intensively. The stable inversion proposed in [3,4] is an iterative solution to the tracking problem with unstable zero dynamics. This method requires the system to have well defined relative degree and hyperbolic zero dynamics, i.e.…”

Non-linear feedback control of the ZI powertrain

“…In literature several methods can be found that deal with the control of certain types of those systems, for example Chen and Balance (2002), Devasia et al (1996), Hauser et al (1992), Herrmann et al (2001), Hirschorn and Davis (1987), Huang and Yuan (2002), Isidori (1995), Leith and Leithead (2001), Okou et al (1999), and Yamada and Yuzawa (2002). Some of these methods deal with the problem of systems having ill-defined relative degree, others deal with the problem of systems being non-minimum phase (NMP).…”

Tracking through singularities using sliding mode differentiators

“…Several methods have been proposed to deal with this problem, such as those in [11,14] for exact tracking through singularities, where the concepts of degree and rank of singularity are introduced. In [7,8], by extending some results of Krener [13] the problem is studied by showing that if an approximated system is found, then, under certain conditions on the approximations and the zero dynamics of the system, the control law calculated for the approximated system guarantees a bounded tracking error and bounded internal variables when applied to the original system.…”

“…In [1] an image-based approach to perform visual control for differential-drive robots is performed. The system presents singularities which are treated as in [11]. In [18], for underactuated robots, singular points are neglected, resulting in an inaccurate tracking.…”