Scholarlink

<p>This paper investigates the adaptive tracking control problem for AutoRegressive Moving Average (ARMA) systems with quantized observations, explicitly focusing on reference signals composed of non-periodic sequences. The authors propose an adaptive tracking control scheme integrating an adaptive controller with a stochastic approximation-type estimation algorithm. Different from the control scheme for Finite Impulse Response (FIR) systems, the estimation part not only estimates the unknown system parameters but also the unknown system outputs. Next, based on the certainty equivalent principle, the adaptive controller is designed using the above two estimates instead of the actual parameters and system outputs. To tackle the inherent coupling between the two estimates, the authors introduce a novel approach that combines the Lyapunov function method with a backward-shifted polynomial method featuring time-varying coefficients. This approach assists in establishing the mean square convergence of the estimates with a convergence rate of <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(O\left({1\over{k}}\right)\)</EquationSource> <EquationSource Format="MATHML"><math display="block"> <mi>O</mi> <mrow> <mo>(</mo> <mrow> <mfrac> <mn>1</mn> <mrow> <mi>k</mi> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> </math></EquationSource> </InlineEquation> under suitable conditions of the step size coefficient. Additionally, this paper shows that the designed adaptive control law can achieve asymptotically optimal tracking of non-periodic reference signals in the mean square sense. Finally, a numerical simulation is presented to validate the theoretical results obtained in this paper.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Adaptive Tracking Control for ARMA Models with Quantized Observations Under Non-Periodic Reference Signals

  • 期刊论文

  • 发表日期：

    2026年2月17日

查看全文
  • Chuiliu Kong,
  • Ying Wang

摘要

This paper investigates the adaptive tracking control problem for AutoRegressive Moving Average (ARMA) systems with quantized observations, explicitly focusing on reference signals composed of non-periodic sequences. The authors propose an adaptive tracking control scheme integrating an adaptive controller with a stochastic approximation-type estimation algorithm. Different from the control scheme for Finite Impulse Response (FIR) systems, the estimation part not only estimates the unknown system parameters but also the unknown system outputs. Next, based on the certainty equivalent principle, the adaptive controller is designed using the above two estimates instead of the actual parameters and system outputs. To tackle the inherent coupling between the two estimates, the authors introduce a novel approach that combines the Lyapunov function method with a backward-shifted polynomial method featuring time-varying coefficients. This approach assists in establishing the mean square convergence of the estimates with a convergence rate of \(O\left({1\over{k}}\right)\) O ( 1 k ) under suitable conditions of the step size coefficient. Additionally, this paper shows that the designed adaptive control law can achieve asymptotically optimal tracking of non-periodic reference signals in the mean square sense. Finally, a numerical simulation is presented to validate the theoretical results obtained in this paper.