Adaptive Variants of Optimal Feedback Policies
This addresses the challenge of adapting pre-learned policies to real-world variations for control systems, though it appears incremental as it builds on existing optimal feedback and adaptive control frameworks.
The paper tackles the problem of maintaining optimal feedback policies for uncertain nonlinear systems during transfer learning and sim-to-real applications, achieving convergence to zero cost and near-optimal performance in the mountain car problem despite parametric uncertainty.
The stable combination of optimal feedback policies with online learning is studied in a new control-theoretic framework for uncertain nonlinear systems. The framework can be systematically used in transfer learning and sim-to-real applications, where an optimal policy learned for a nominal system needs to remain effective in the presence of significant variations in parameters. Given unknown parameters within a bounded range, the resulting adaptive control laws guarantee convergence of the closed-loop system to the state of zero cost. Online adjustment of the learning rate is used as a key stability mechanism, and preserves certainty equivalence when designing optimal policies without assuming uncertainty to be within the control range. The approach is illustrated on the familiar mountain car problem, where it yields near-optimal performance despite the presence of parametric model uncertainty.