Adaptive Model Predictive Control for a Class of Nonlinear Single-Link Flexible Joint Manipulator

The major concern and basic requirement for control engineers, besides stability and trajectory tracking, is to consider and utilize available resources efficiently. It involves restriction of the energy consumption and associated costs in the presence of system constraints. Recently, such optimal control schemes and techniques that are constructed on the mathematical model of the system have been productively realized, both for linear and nonlinear systems, and are termed as Model Predictive Control (MPC). This paper deals with an Adaptive MPC for a nonlinear nonminimum phase single-link flexible joint manipulator (SFJM) system with constraints on the input control effort, states, and output. The non-linear system model is linearized along its trajectory. At each sampling interval, the quadratic optimization problem is solved. The optimum input control effort is implemented in Receding Horizon fashion. This meaningfully diminishes the computational burden involved in solving complex nonlinear differential equations and the associated non-convex optimization problem. The adaptive MPC offers performance which is comparable to Nonlinear Model Predictive Control (NMPC). In this paper, the closed-loop stability of the overall control scheme is presented, and its performance is matched to the general Linear MPC and NMPC. The simulation results show the superiority of the performance of adaptive MPC over linear MPC with a significant decrease in computational burden as compared to NMPC.