Stability Analysis of Optimal Adaptive Control using Value Iteration with Approximation Errors
This addresses stability guarantees in control systems for robotics or autonomous applications, but it appears incremental as it builds on existing value iteration methods.
The paper analyzes the stability of adaptive optimal control systems during learning with value iteration, accounting for approximation errors, and provides estimates for the region of attraction to ensure trajectories remain valid.
Adaptive optimal control using value iteration initiated from a stabilizing control policy is theoretically analyzed in terms of stability of the system during the learning stage without ignoring the effects of approximation errors. This analysis includes the system operated using any single/constant resulting control policy and also using an evolving/time-varying control policy. A feature of the presented results is providing estimations of the \textit{region of attraction} so that if the initial condition is within the region, the whole trajectory will remain inside it and hence, the function approximation results remain valid.