Optimal control of inverted pendulums using finite element method

An alternative control scheme based on finite element method has been developed to solve optimal control problems in space and time domains. The nonlinear Lagrangian is expanded about a given trajectory configuration in terms of a correction vector. The equations of motion are derived retaining only upto quadratic terms. The cost function comprises of total absolute torsional impulse and equations of motion are the constraints. The control of simple and double inverted pendulums is presented here to show the validity of this method. These problems are also solved using the classical Riccati method for comparison.