Synthesizing Stable Reduced-Order Visuomotor Policies for Nonlinear Systems via Sums-of-Squares Optimization

Understand

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.