Using Q-Learning and Genetic Algorithms to Improve the Efficiency of Weight Adjustments for Optimal Control and Design Problems

In traditional optimal control and design problems, the control gains and design parameters are usually derived to minimize a cost function reflecting the system performance and control effort. One major challenge of such approaches is the selection of weighting matrices in the cost function, which are usually determined via trial-and-error and human intuition. While various techniques have been proposed to automate the weight selection process, they either can not address complex design problems or suffer from slow convergence rate and high computational costs. We propose a layered approach based on Q-learning, a reinforcement learning technique, on top of genetic algorithms (GA) to determine the best weightings for optimal control and design problems. The layered approach allows for reuse of knowledge. Knowledge obtained via Q-learning in a design problem can be used to speed up the convergence rate of a similar design problem. Moreover, the layered approach allows for solving optimizations that cannot be solved by GA alone. To test the proposed method, we perform numerical experiments on a sample active-passive hybrid vibration control problem, namely adaptive structures with active-passive hybrid piezoelectric networks. These numerical experiments show that the proposed Q-learning scheme is a promising approach for automation of weight selection for complex design problems.