Control of a Non Observable Double Inverted Pendulum Using a Novel Active Learning Method Based State Estimator

In this paper a novel fuzzy approach exploiting Active Learning Method is employed in order to estimate the immeasurable states required to control a non-observable double inverted pendulum. Active Learning Method (ALM) is a fuzzy modeling method which exploits Ink Drop Spread (IDS) as its main engine. IDS is a universal fuzzy modeling technique which is very similar to the way human brain processes different phenomena. The ALM system is trained by the data obtained from Linear Quadratic Regulator (LQR) controller. LQR uses an optimal control approach which under certain conditions guarantees robustness. Instead of an expert's knowledge, the LQR controller output is used as a priori knowledge to train ALM. The application of ALM method is then investigated in conditions where some states of system like the upper angle of the pendulum and its angular velocity are not available and the proposed system is not observable. The fact of practical non-observablity of this system obliges us to use an open-loop state estimator to estimate the missing states. Instead, a novel state estimator using ALM is introduced which shows practical superiority in estimation.