通过平方和优化为非线性系统综合稳定的降阶视觉运动策略
Synthesizing Stable Reduced-Order Visuomotor Policies for Nonlinear Systems via Sums-of-Squares Optimization
AI总结：
本文结合 Lyapunov 分析与平方和优化，为含学习感知模块的视觉反馈非线性系统综合可证明稳定的降阶多项式策略，并在摆和四旋翼上验证其抗噪稳定效果。
摘要：
我们提出一种方法，用于为控制仿射非线性系统综合动态的降阶输出反馈多项式控制策略；当反馈控制回路中使用视觉观测和一个经过学习的感知模块时，该策略可保证运行时对目标状态的稳定性。我们利用 Lyapunov 分析来形式化此类策略的综合问题。该问题在策略参数以及用于证明策略稳定性的 Lyapunov 函数方面是非凸的。为近似求解该问题，我们提出两种方法：第一种方法求解一系列平方和优化问题，以迭代改进一个按构造即可证明稳定的策略；第二种方法直接对多项式策略的参数执行基于梯度的优化，并在事后验证其闭环稳定性。我们扩展了该方法，以在存在观测噪声时提供稳定性保证；这种噪声在现实中来源于学习型感知模块的误差。我们在包括摆和四旋翼飞行器在内的若干欠驱动非线性系统上评估了所提方法，结果表明，在从图像控制这些系统时，我们的保证可转化为经验稳定性，而基线方法可能无法可靠地使系统稳定。
英文摘要：
We present a method for synthesizing dynamic, reduced-order output-feedback polynomial control policies for control-affine nonlinear systems which guarantees runtime stability to a goal state, when using visual observations and a learned perception module in the feedback control loop. We leverage Lyapunov analysis to formulate the problem of synthesizing such policies. This problem is nonconvex in the policy parameters and the Lyapunov function that is used to prove the stability of the policy. To solve this problem approximately, we propose two approaches: the first solves a sequence of sum-of-squares optimization problems to iteratively improve a policy which is provably-stable by construction, while the second directly performs gradient-based optimization on the parameters of the polynomial policy, and its closed-loop stability is verified a posteriori. We extend our approach to provide stability guarantees in the presence of observation noise, which realistically arises due to errors in the learned perception module. We evaluate our approach on several underactuated nonlinear systems, including pendula and quadrotors, showing that our guarantees translate to empirical stability when controlling these systems from images, while baseline approaches can fail to reliably stabilize the system.
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