SINGULARITY OF BACKSTEPPING CONTROL FOR NON-LINEAR SYSTEMS

     The back-stepping procedure is one of the tools, which allows for control law synthesis in non-linear smooth systems. [Krstic et al. 951] defined a class of non-linear system (called pure feedback systems), for which it is possible to apply the back-stepping procedure. The control laws in modem control theory are complex. They are designed to be implemented on microprocessor controllers, where the control law is evaluated numerically. However, this procedure applied to pure-feedback systems results sometimes in a numerically ill-conditioned control law. In some circumstances, a singularity (division by zero) appears in the derived control law. Singularity-free, a subclass of pure feedback systems is defined, and an appropriate proof is given. The problem of singularity is illustrated by two examples from the reference paper, designed using Matlab and performance is evaluated. In one of them, the singularity is present. In the second case, the plant belongs to the singularity-free sub-class of pure-feedback systems.

Reference Paper: Singularity of Backstepping Control for Non-Linear Systems
Author’s Name: Wiktor Bolek and Jerzy Sasisadek
Source: IEEE
Year:2002
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