<p>Finite-time prescribed performance tracking control for unknown time-varying delayed high-order nonlinear systems (HNSs) with unknown input dead zone is investigated in this paper. Fuzzy logical systems are employed to identify unknown uncertainties. An improved finite-time prescribed performance function is devised to ensure the error signal converges to any predefined residual set at any specified time. The output of unknown dead zone with high-order power <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11071_2024_10849_Article_IEq1.gif" Format="GIF" Height="21" Rendition="HTML" Resolution="72" Type="Linedraw" Width="64" /> </InlineMediaObject> <EquationSource Format="TEX">$u^{\vartheta _ n}(v(t))$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msup> <mi>u</mi> <msub> <mi>ϑ</mi> <mi>n</mi> </msub> </msup> <mrow> <mo stretchy="false">(</mo> <mi>v</mi> <mrow> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mrow> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation> is reconstructed as a friendly form, so that the real controller can be designed properly via adaptive estimation tactic. The time-varying delay is tackled by an improved Lyapunov–Krasovskii function. Moreover, the approximation errors and the conversion coefficient <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11071_2024_10849_Article_IEq2.gif" Format="GIF" Height="25" Rendition="HTML" Resolution="72" Type="Linedraw" Width="27" /> </InlineMediaObject> <EquationSource Format="TEX">$\frac{1}{\psi (u)}$</EquationSource> <EquationSource Format="MATHML"><math> <mfrac> <mn>1</mn> <mrow> <mi>ψ</mi> <mo stretchy="false">(</mo> <mi>u</mi> <mo stretchy="false">)</mo> </mrow> </mfrac> </math></EquationSource> </InlineEquation> are estimated via the adaptive parameters. Finally, the simulations show that the error signal converges to the prescribed set within the settling time and the control performance can be pledged.</p>

Prescribed performance fuzzy output tracking control for time-varying delayed high-order nonlinear systems with unknown input dead zone

期刊论文
发表日期：

2025年1月9日

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Junchang Zhai,
Huanqing Wang

摘要

Finite-time prescribed performance tracking control for unknown time-varying delayed high-order nonlinear systems (HNSs) with unknown input dead zone is investigated in this paper. Fuzzy logical systems are employed to identify unknown uncertainties. An improved finite-time prescribed performance function is devised to ensure the error signal converges to any predefined residual set at any specified time. The output of unknown dead zone with high-order power $u^{\vartheta _ n}(v(t))$ $u^{ϑ_{n}} (v (t))$ is reconstructed as a friendly form, so that the real controller can be designed properly via adaptive estimation tactic. The time-varying delay is tackled by an improved Lyapunov–Krasovskii function. Moreover, the approximation errors and the conversion coefficient $\frac{1}{\psi (u)}$ $\frac{1}{ψ (u)}$ are estimated via the adaptive parameters. Finally, the simulations show that the error signal converges to the prescribed set within the settling time and the control performance can be pledged.