Modulation-Enhanced Excitation for Continuous-Time Reinforcement Learning via Symmetric Kronecker Products

This work introduces new results in continuous-time reinforcement learning (CT-RL) control of affine nonlinear systems to address a major algorithmic challenge due to a lack of persistence of excitation (PE). This PE design limitation has previously stifled CT-RL numerical performance and prevented these algorithms from achieving control synthesis goals. Our new theoretical developments in symmetric Kronecker products enable a proposed modulation-enhanced excitation (MEE) framework to make PE significantly more systematic and intuitive to achieve for real-world designers. MEE is applied to the suite of recently-developed excitable integral reinforcement learning (EIRL) algorithms, yielding a class of enhanced high-performance CT-RL control design methods which, due to the symmetric Kronecker product algebra, retain EIRL's convergence and closed-loop stability guarantees. Through numerical evaluation studies, we demonstrate how our new MEE framework achieves substantial improvements in conditioning when approximately solving the Hamilton-Jacobi-Bellman equation to obtain optimal controls. We use an intuitive example to provide insights on the central excitation issue under discussion, and we demonstrate the effectiveness of the proposed procedure on a real-world hypersonic vehicle (HSV) application.