Tracking Control for Affine Time-Varying Nonlinear Systems with Bounds

Nam H. Nguyen, Tung X. Vu, Hung V. Nguyen

Abstract


In practice, there exist systems with high nonlinearity and time-varying functions. Time-varying nonlinear systems (TVNS) present inherent challenges due to their high nonlinearity and time-varying nature, especially when unknown input disturbance and model uncertainties occur. In this work, a class of single input single output (SISO) uncertain affine TVNS is considered for tracking controller design in the presence of unknown disturbance, in which both the disturbance and model uncertainties are assumed to be bounded. Based on these bounds, a tracking controller will be proposed for first-order uncertain TVNS with unknown input disturbance, and then it is extended for second-order uncertain affine TVNS with unknown input disturbance. Unlike other existing works, the proposed controller does not use fuzzy systems, neural networks or any adaptive mechanism to cope with uncertainties and disturbances. It only uses the bounds of disturbance and model uncertainties, the information of tracking error to compute the control signal, and Lyapunov stability theory is applied to analyze stability of the closed-loop system. In addition, the convergence rate of tracking error can be adjusted by tuning parameters. Some numerical simulations with a first-order system and a model of inverted pendulum are given to verify the developed controller. These systems are uncertain and disturbed by unknown external signals and the proposed controller does not know this information but the tracking error still converges to a small circle containing the origin. The proposed controller can be extended for higher-order systems or MIMO systems such as robotic manipulators.


Keywords


Nonlinear Systems; Time-Varying Systems; Input Disturbance; Boundedness; Robust Control; Model Uncertainties.

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References


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DOI: https://doi.org/10.18196/jrc.v5i4.22077

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