[论文解读] Robust Adaptive Learning Control for a Class of Non-affine Nonlinear Systems

Shuai Gao, Dong Shen+1 more|arXiv (Cornell University)|Feb 1, 2026

Iterative Learning Control Systems被引用 0

一句话总结

该论文为不确定的非仿射非线性系统开发了一种鲁棒自适应学习控制（AILC）方案，系统具有高相对阶和非重复干扰，利用梯度下降参数自适应和状态估计实现跟踪误差收敛到零的邻域。通过迭代求解得到一个隐式控制输入以便实施，并给出收敛保证和仿真。

ABSTRACT

We address the tracking problem for a class of uncertain non-affine nonlinear systems with high relative degrees, performing non-repetitive tasks. We propose a rigorously proven, robust adaptive learning control scheme that relies on a gradient descent parameter adaptation law to handle the unknown time-varying parameters of the system, along with a state estimator that estimates the unmeasurable state variables. Furthermore, despite the inherently complex nature of the non-affine system, we provide an explicit iterative computation method to facilitate the implementation of the proposed control scheme. The paper includes a thorough analysis of the performance of the proposed control strategy, and simulation results are presented to demonstrate the effectiveness of the approach.

研究动机与目标

• Motivate the control of uncertain non-affine nonlinear systems encountered in practice.
• Develop a direct adaptive iterative learning control (AILC) framework for high relative degree, non-affine systems.
• Provide a robust scheme handling time-varying unknown parameters and bounded disturbances.
• Guarantee convergence of tracking error to a neighborhood of zero and analyze the impact of disturbances and numerical input approximation.

提出的方法

• Represent the non-affine system as x_k(t+ρ)=F(X_k(t),u_k(t),t)+w_k(t) with F(X,u,t)=θ(t)ᵀ f(X,u).
• Use a gradient descent parametric adaptation law (GDPA) to estimate θ(t) from tracking residuals.
• Introduce a state estimator to reconstruct unmeasurable states for the high relative-degree system.
• Form an implicit AILC input by solving θ̂_k(t)ᵀ f(X_k^e(t),u_k(t))=r_k(t+ρ) and implement it via a contraction-mapping based iterative procedure.
• Implement an iteration-based explicit approximation u_k^p(t) converging to the implicit input, with a stopping criterion for practical use.
• Provide a Lyapunov-like convergence analysis showing limsup e_k(t+ρ) within a disturbance-dependent ball.

实验结果

研究问题

• RQ1 Can a direct adaptive learning control (AILC) framework be designed for non-affine nonlinear systems with high relative degree and non-repetitive disturbances?
• RQ2 How can unknown time-varying parameters θ(t) and unmeasured states be estimated robustly within the AILC to achieve convergence?
• RQ3 What is the impact of disturbances, relative degree, and numerical approximation error of the implicit control input on tracking accuracy?
• RQ4 How to compute an explicit implementable control input from an implicit AILC formulation?
• RQ5 Does the proposed method extend to iteration-varying reference trajectories and provide convergence guarantees?

主要发现

• A feasible ideal control input u_k^* exists for zero-disturbance cases, obtained as the fixed point of a contraction mapping.
• The GDPA law with dead-zone and projection ensures bounded parameter estimation and tracking error convergence to a neighborhood of zero.
• An explicit iterative approximation u_k^p(t) converges to the implicit AILC input u_k(t), with a computable stopping criterion for desired accuracy.
• Theorem 1 proves limsup of tracking error bounded by w plus terms dependent on initial estimation error and disturbances.
• Corollaries show perfect tracking in disturbance-free cases and special simplifications when relative degree ρ=1 or disturbances vanish.
• Simulation results (two examples) illustrate effectiveness and compare with DDILC.