用符号约束提升深度模型的物理可解释性与控制稳定性
Modeling and Control of Deep Sign-Definite Dynamics with Application to Hybrid Powertrain Control
- 通过符号约束构建满足物理规律的深度动态模型
- 实现预测控制的凸优化，保证唯一解和光滑控制输入
- 在三水箱与混合动力系统中验证更强泛化能力
数据驱动控制越来越多依赖于复杂系统中的深度模型，而这些系统的机理模型难以获取。为确保可靠部署，学习到的动力学必须符合物理结构，并支持可处理的最优控制。本文引入符号约束——即雅可比矩阵元素的符号限制——作为单调性、正性和符号定性的统一描述。对于可精确线性化的深度动力学，我们给出了结构条件和神经网络参数化方式，使这些约束能被构造性地满足。相同结构使得模型预测控制可表述为凸二次规划或凸松弛，从而获得唯一最优解和Lipschitz连续的控制律。在三水箱系统和混合动力传动系统上的应用表明，相比非凸方法，该方法具有更优的外推性能和更平滑的控制输入。
原文摘要 · Abstract (English)
Data-driven control increasingly relies on deep models for complex systems whose first-principles models are difficult to obtain. For reliable deployment, however, learned dynamics should respect physical structure and lead to tractable optimal control. We introduce sign constraints, namely sign restrictions on Jacobian entries, as a unified description of monotonicity, positivity, and sign-definiteness. For exactly linearizable deep dynamics, we provide structural conditions and neural-network parameterizations that enforce these constraints by construction. The same structure also allows model predictive control to be formulated as a convex quadratic program or as a convex relaxation, yielding a unique optimizer and a Lipschitz continuous control law. Applications to a three-tank system and a hybrid powertrain demonstrate that the proposed approach offers improved extrapolation performance and smoother control inputs compared with competing nonconvex formulations.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。