A Continuous Asymptotic Tracking Control Strategy for
Uncertain Multi-Input Nonlinear Systems


In this paper, we present a novel continuous control mechanism that compensates for
uncertainty in a class of multi-input nonlinear systems. The control strategy is based on
limited assumptions on the structure on the system nonlinearities. A Lyapunov-based
stability argument is employed to prove semi-global asymptotic tracking. The control
mechanism has the interesting feature of "learning" the unknown system dynamics. For the
sake of clarity, the proposed control design is initially presented for a first-order,
single-input case. Using this result as a stepping stone, the design is then extended to
higher-order, multi-inout systems. Simulation results are included to illustrate performance
of the control.


The control of uncertain nonlinear dynamic systems is a topic that continues to challenge
control theoreticians. This topic is also of practical importance since many real-world systems
exhibit nonlinear dynamic behavior. To make matters even more difficult, in many practical cases,
the mathematical model is often poorly known or uncertain. To cope with the uncertainty issue,
an abundance of design tools have emerged during the last two decades that facilitate the systematic
construction of controllers for various classes of uncertain nonlinear systems. As one might expect,
the choice of a specific control design method is strongly influenced by the type of uncertainty
associated with the system model.

Simulation Results

____Figure 4: Control input for variable structure controller

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