用在线高斯过程保证非线性系统学习中的安全与高效探索
Safe Exploration for Nonlinear Processes Using Online Gaussian Process Learning
- 基于实时学习的高斯过程捕捉未知非线性，结合线性近似实现安全控制
- 安全集扩大约30%，高斯过程误差从1.11降至0.03，实现高效学习
- 适合需要高可靠性、在不确定环境中进行安全探索的工程场景
本文提出一种针对部分已知动力学的非线性系统安全数据驱动控制框架。该方法在在线学习过程中确保系统稳定性和约束满足，仅需一个可稳定化的线性近似作为初始假设。未建模的非线性动态通过实时学习的高斯过程残差项捕捉。安全性通过基于李雅普诺夫理论推导的概率控制不变集来保障，确保高概率稳定性。控制输入由一个凸二次规划计算得出，以最大化信息获取同时遵守概率安全约束。该框架提供有限样本安全保证，并允许随着不确定性降低而自适应扩展不变集。数值结果验证了该方法的有效性：在模型不确定性下实现了安全且信息丰富的探索，安全集扩大约30%，高斯过程均方根误差从1.11降至0.03。
原文摘要 · Abstract (English)
This paper proposes a safe data-driven control framework for nonlinear systems with partially known dynamics. The method ensures stability and constraint satisfaction during online learning, assuming only a stabilizable linear approximation of the process is available. Unmodeled nonlinear dynamics are captured by a Gaussian process residual learned in real time. Safety is enforced through a probabilistic control-invariant set derived from Lyapunov theory, guaranteeing high-probability stability. A convex quadratic program computes control inputs that maximize information gain while respecting probabilistic safety constraints. The framework provides finite-sample safety guarantees and allows adaptive expansion of the invariant set as uncertainty decreases. Numerical results validate the approach, demonstrating safe and informative exploration under model uncertainty: the safe set expands by about 30% while the Gaussian process root-mean-square error drops from 1.11 to 0.03.
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