Optimized multiobjective H∞ control applied to inverted pendulum

This paper introduces several practical aspects of designing multiobjective problems such as H_∞ controllers. We present a procedure to obtain a controller with two degree of freedom (DOF). First we stabilize the nominal system by a conventional controller like LQR We use genetic algorithm to optimize LQR controller, too. This part of our controller leads to low cost of control input effort, and then we enforce other objectives in the framework of LMI optimization. This procedure leads to less energy consumption in comparison with using LMI methods alone. We design and implement this approach in an inverted pendulum as one of the most commonly nonlinear studied systems in the control area and can be considered as a benchmark for evaluating controlling methodologies.