Practical Study of Derivative-Free Observer-Based Nonlinear Adaptive Predictive Control

Abstract This chapter is devoted to the study and the implementation of model predictive control (MPC) based on state observers for nonlinear multivariable systems. First, we focused on the implementation of a linearized predictive controller in the presence of state estimation using the second-order divided difference filter, which is an extended Kalman filter alternative. The state observer presents a simplicity of implementation because no Jacobian matrices’ calculations are required. In addition, it adopts the Cholesky factorization for covariance matrices’ construction to increase stability. The limits of this technique are outlined and discussed, namely, the convergence of both the observer and the controller. To overcome previous limits, we developed an adaptive MPC scheme-based observer for nonlinear multivariable systems, which effectively increases the control-loop performances. The adaptive scheme consists of the design of an output error model to minimize the error between the model and the system outputs to improve the desired performances in term of state estimation, setpoint tracking, and perturbation rejection.