LQR and Genetic Algorithms: An Effective Duo for Assessing Control Expenditure and Performance in Dynamic Systems

In this work, a novel methodology is introduced that employs genetic algorithms to determine the optimal weighting matrices for a linear quadratic regulator controller. A method is presented to construct a multi-objective fitness function that allows one to give prioritisation to energy consumption or other performance metrics, such as rise time, settling time, and steady-state error. To validate the effectiveness of the proposed approach, we conducted simulation studies based on a model of an inverted pendulum on a cart system. The results show a reduction of up to 30.36% in the energy of the controller and a reduction of 20.27% in its maximum value when choosing to prioritise the energy expenditure of the controller over other performance metrics, without significantly compromising the convergence of the system states. The results encompass an effective way of optimising energy expenditure in non-linear controller designs.