MBPOA-based LQR controller and its application to the double-parallel inverted pendulum system

As the performance of Linear Quadratic Regulator (LQR) controllers greatly depends on its weighting matrices, i.e. Q and R, designing these two matrices is one of the most important components in the LQR problem which is a tedious and challenging work in the applications of LQR. Hence, a novel LQR approach based on the Pareto-based Multi-objective Binary Probability Optimization Algorithm (MBPOA) is proposed in this paper, in which MBPOA is utilized to search for the optimal weighting matrices to relieve the effort of parameter settings and improve the control performance according to the pre-defined objective functions. By combining LQR with MBPOA, the optimal controllers can be obtained easily and effortless. Moreover, the control performance can be adjusted further conveniently to meet the requirements of applications as a set of Pareto-optimal LQR controllers is offered. The simulation and experiment results on the double-parallel inverted pendulum system demonstrate the effectiveness and efficiency of the developed MBPOA-based LQR method. Considering the characteristics such as robustness, the optimal dynamic performance and easy implementation without prior knowledge, the MBPOA-based LQR is a promising control approach for engineering applications.