$k$-Step Look-Ahead Active Concurrent Learning-Based Dual Control of Exploration and Exploitation for Auto-Optimization

This study introduces a $k$ -step look-ahead active concurrent learning-based dual control of exploration and exploitation (KSLCL-DCEE) framework designed to address the challenges of auto-optimization in systems with unknown references and environments, inherently balancing parameter estimation and optimal reference tracking. The KSLCL-DCEE algorithm incorporates two loops that employ future gradients of the cost function to generate the subsequent control command by looking ahead $k$ -steps: the inner loop generates $k$ -step look-ahead gradients (i.e., estimated reference trajectory), while the outer loop utilizes the gradient at the $k$ th step to generate the dual control commands which act on a general linear system. Active concurrent learning with a modified learning rate in the initial period is introduced to relax the reliance on the condition of persistent excitation and achieve faster convergence. A comprehensive stability analysis of KSLCL-DCEE is provided. The effectiveness and performance of KSLCL-DCEE are demonstrated through numerical studies and applications on photovoltaic (PV) arrays.