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首页> 外文期刊>International Journal of Control >Sliding control of non-linear systems containing time-varying uncertainties with unknown bounds
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Sliding control of non-linear systems containing time-varying uncertainties with unknown bounds

机译：具有不确定范围的时变不确定性的非线性系统的滑模控制

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摘要

The sliding controller is very effective in dealing with system uncertainties defined in compact sets. If the bounds of the uncertainties are not available, the adaptive sliding controller might be designed. One restriction for the adaptive sliding scheme is that the unknown parameter should be constant, which is not always satisfied in practice. For a non-linear system with general uncertainties (i.e. time varying with unknown bounds), both the traditional sliding control and adaptive sliding control do not work properly. This paper proposes a new sliding control scheme for non-linear systems containing time-varying uncertainties with unknown bounds. The uncertainties are assumed to be piecewise continuous functions of time and satisfy the Dirichlet conditions. By representing these uncertainties in finite-term Fourier series, they can be estimated by updating the Fourier coefficients. Since the coefficients are time-invariant, update laws are easily obtained from the Lyapunov approach to guarantee output error convergence. Computer simulations are performed to show efficacy of the proposed schemes.
机译：滑动控制器在处理紧凑集中定义的系统不确定性方面非常有效。如果不确定性的界限不可用，则可以设计自适应滑动控制器。自适应滑动方案的一个限制是未知参数应为常数，这在实践中并不总是能满足。对于具有一般不确定性（即，时间随着未知范围变化的非线性系统），传统的滑动控制和自适应滑动控制均不能正常工作。本文提出了一种非线性系统的新的滑动控制方案，该系统包含具有未知范围的时变不确定性。假定不确定性是时间的分段连续函数，并且满足Dirichlet条件。通过用有限项傅立叶级数表示这些不确定性，可以通过更新傅立叶系数来估计它们。由于系数是随时间变化的，因此可以很容易地从Lyapunov方法获得更新定律，以确保输出误差收敛。进行计算机仿真以显示所提出方案的功效。

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