Nonlinear Parameters and State Estimation for Adaptive Nonlinear Model Predictive Control Design

Abstract

This paper deals with an adaptive nonlinear model predictive control (NMPC) based estimator in cases of mismatch modeling, presence of perturbations and/or parameter variations. Thus, we propose an adaptive nonlinear predictive controller based on the second-order divided difference filter (DDF) for multivariable systems. The controller uses a nonlinear state-space model for parameters and state estimation and for the control law synthesis. Two nonlinear optimization layers are included in the proposed algorithm. The first optimization problem is based on the output error (OE) model with a tuning factor, and it is dedicated to minimize the error between the model and the system at each sample time by estimating unknown parameters when assuming that all system states are available. The second optimization layer is used by the centralized nonlinear predictive controller to generate the control law which minimizes the error between future setpoints and future outputs along the prediction horizon. The proposed algorithm leads to a good tracking performance with an offset-free output and an effectiveness in perturbation attenuation. Practical results on a real setup show the reliability of the proposed approach.

RETRACTED: Constrained cuckoo search algorithm and Takagi-Sugeno fuzzy models for predictive control

“…Other works have proposed changes to the PSO algorithm, for example: The adaptive PSO has been successfully applied to the optimal self-tuning PID controller (Djoewahir et al, 2013) and a multivariable predictive control scheme formulated by using the TS fuzzy modeling method and a new constrained multiobjective PSO algorithm (Thamallah et al, 2018). In Salhi and Bouani (2016), Salhi and Bouani (2017) and Thom et al (2018), the authors used fmincon Matlab function-based interior point algorithm to solve the predictive optimization problem. The perturbed PSO-based approach for MPC parameters tuning have been used and successfully applied to the control of a nonlinear system (Derouich et al, 2016).…”

Handling Model Plant Mismatch in State Estimation Using a Multiple-Model-Based Approach

“…An alternative approach, as described in ref , is to reduce model plant mismatch by updating the system parameters at each time step by solving an optimization problem. This approach provides diagnostic information through the updated parameter estimates but has a high computational load as an optimization problem must be solved at each time step.…”

Switched Offline Multiple Model Predictive Control with Polyhedral Invariant Sets

“…Moreover, the heavy online computation burden causes the poor performance in real time. 1,2 Many researches use the technique of linearization to handle the nonlinear process. 3−5 However, for these nonlinear systems with a wide operating region, one linear MPC cannot be efficient unless the system always works in a small region around the operating point.…”

“…Nevertheless, the nonlinear MPC (NMPC) technique is far away from mature in both theory and application, which limits the existing MPC algorithm to linear or quasi-linear systems. Moreover, the heavy online computation burden causes the poor performance in real time. , …”