Dual Control of Exploration and Exploitation for Auto-Optimisation Control with Active Learning

The quest for optimal operation in environments with unknowns and uncertainties is highly desirable but critically challenging across numerous fields. This paper develops a dual control framework for exploration and exploitation (DCEE) to solve an auto-optimisation problem in such complex settings. In general, there is a fundamental conflict between tracking an unknown optimal operational condition and parameter identification. The DCEE framework stands out by eliminating the need for additional perturbation signals, a common requirement in existing adaptive control methods. Instead, it inherently incorporates an exploration mechanism, actively probing the uncertain environment to diminish belief uncertainty. An ensemble based multi-estimator approach is developed to learn the environmental parameters and in the meanwhile quantify the estimation uncertainty in real time. The control action is devised with dual effects, which not only minimises the tracking error between the current state and the believed unknown optimal operational condition but also reduces belief uncertainty by proactively exploring the environment. Formal properties of the proposed DCEE framework like convergence are established. A numerical example is used to validate the effectiveness of the proposed DCEE. Simulation results for maximum power point tracking are provided to further demonstrate the potential of this new framework in real world applications.