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<p>This paper discusses the control of chaos in a one-dimensional control system based on the state-mapping network (SMN) and deep reinforcement learning (DRL). The concept of the SMN for the one-dimensional control system <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11071_2025_11669_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="125" /> </InlineMediaObject> <EquationSource Format="TEX">\(x_{t+1}=f(x_t)+u_t\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>x</mi> <mrow> <mi>t</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> <mo>=</mo> <mi>f</mi> <mrow> <mo stretchy="false">(</mo> <msub> <mi>x</mi> <mi>t</mi> </msub> <mo stretchy="false">)</mo> </mrow> <mo>+</mo> <msub> <mi>u</mi> <mi>t</mi> </msub> </mrow> </math></EquationSource> </InlineEquation> is introduced, and several properties of the network are proved. Subsequently, a control method based on the SMN is introduced, which is non-invasive and only requests arbitrarily small input in some special cases. Finally, a situation is addressed in which there is a lack of information about the system. A control method that combines the SMN with DRL is proposed. Numerical results demonstrate the effectiveness of this method.</p>

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Controlling chaos based on state-mapping network and deep reinforcement learning

  • 期刊论文

  • 发表日期：

    2025年8月2日

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  • Tongtao Liu,
  • Yongping Zhang

摘要

This paper discusses the control of chaos in a one-dimensional control system based on the state-mapping network (SMN) and deep reinforcement learning (DRL). The concept of the SMN for the one-dimensional control system \(x_{t+1}=f(x_t)+u_t\) x t + 1 = f ( x t ) + u t is introduced, and several properties of the network are proved. Subsequently, a control method based on the SMN is introduced, which is non-invasive and only requests arbitrarily small input in some special cases. Finally, a situation is addressed in which there is a lack of information about the system. A control method that combines the SMN with DRL is proposed. Numerical results demonstrate the effectiveness of this method.