Nonlinear Adaptive Model Predictive Control via Immersion and Invariance Stabilizability

Abstract

Adaptive control systems are designed to achieve the desired control performance when plant parameters are unknown or possibly slow-changing. In this paper, we propose an adaptive model predictive control (MPC) algorithm for a class of nonlinear input affine systems. The key idea is to combine the MPC algorithm with the adaptive Immersion and Invariance (I&I) control method. That is, MPC is used to calculate the input satisfying the assumption in the adaptive I&I control method and then the parameter update law in I&I depends on the state, estimated parameter, and input determined by the MPC algorithm. This strategy allows us to estimate the unknown parameters online and produce the control input at the same time. To modify the I&I method, we show a stability theorem for a linearly parameterized plant and then, numerical examples are given to demonstrate its effectiveness.