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Nonlinear Model Predictive Control of Inverted Pendulum Using Iterative Steepest Descent Algorithm

This paper presents nonlinear model predictive control (NMPC) for nonlinear systems and apply to the inverted pendulum. There is distinction between the optimal control and NMPC. The optimal control aims to minimize the cost function over the finite horizon and applies the control input to the system. On the other hand, NMPC employs the state feedback and updates the control input at each time step. At each sampling time, the control design of NMPC is formulated as a two-point boundary-value (TPBV) problem. When the optimal control law is calculated, only the first control input is applied to the controlled system. We employ an iterative steepest descent algorithm to solve the TPBV problem. Numerical results show comparison between the optimal control and NMPC applied to the inverted pendulum.