...Bidhayak Goswami; Anindya Chatterjee We consider linear time-invariant dynamic systems in the single-input, single-output (SISO) framework. In particular, we consider stabilization of an inverted pendulum on a cart using a force on the cart. This system is easy to stabilize with pendulum angle...

... direction, with the purpose of keeping the pendulum balanced upright. Inverted pendulum system The results of numerical simulations of the nonlinear model (Eq. 1 ) with the delayed force (11) and the dynamic friction model (Eqs. 5 , 6 ) are summarized in the top graph of Fig. 7 with a zoom...

... Furuta pendulum at the upright position. pendulums force control optimal control nonlinear control systems Riccati equations matrix algebra stability Internal Forces Nonlinear Optimal Regulator Projection Method State-Dependent Ricatti Equation Inverted Pendulum To build...

... of a simplified pendulum model, is checked satisfying the necessary condition of Maximum Principle, and is experimentally verified using the rotating type pendulum. Inverted Pendulum Nonlinear Systems Nonlinear Optimization Time Optimal Control Pendulums are known to have intrinsically interesting...