RMPC for Uncertain Nonlinear Systems With Non-Additive Dynamic Disturbances and Noisy Measurements

Sami El-Ferik

doi:10.1109/access.2020.2975535

Abstract

In this paper, we present a robust, model-predictive control scheme for the general class of uncertain and constrained discrete-time nonlinear systems subject to noisy measurements. The relationships between the system's dynamics, uncertainties, disturbances and the measurement noise are nonlinear and not necessarily additive. In particular, the disturbance is the output of an uncertain system with an unknown input. This study serves the threefold ultimate objective of ensuring robust satisfaction of the state constraints, recursive feasibility and stability. To satisfy state constraints, the proposed algorithms adopt a constraints tightening approach using the restricted constraint sets computed online. Several bounds on the prediction level and rate are derived and the size of the terminal region is maximized using polytopic linear differential inclusions (PLDI). An explicit bound on the maximum allowable disturbance for recursive feasibility is also derived based on optimization of the one-step ahead controllable set to the terminal region. The disturbance and uncertainties are non-vanishing and therefore only Input-to-state practical stability (ISpS) can be ensured. A simulation example demonstrates the efficacy of the mathematical framework and algorithms developed in this work.

Highlights

Model predictive control (MPC) is a moving horizon control approach that has been recognized as the most used control strategy for systems under inputs and state constraints
MPC is a model-based control and can be called either linear or nonlinear depending on the nature of the model used in the prediction of the system’s dynamics
CONTRIBUTION In this paper, we extend the work initially developed in [35] and consider the system to be affected by an external dynamic disturbance having its own exo-system dynamic model

Summary

INTRODUCTION

Model predictive control (MPC) is a moving horizon control approach that has been recognized as the most used control strategy for systems under inputs and state constraints. In this approach (see for example [11], [18], [31]), the constrained finite horizon open loop OCP is solved at each time instant while considering the worst possible realizations of the uncertainty for any possible disturbances. This results in adopting a pessimistic control actions applied repeatedly. Most of the available literature either for nominal-MPC or Tube-based MPC have considered different constraint tightening approaches for systems with additive uncertainties ( [12], [17]).

NOTATION

DETERMINATION OF XMPC

ROBUST STABILITY

SIMULATION EXAMPLE

CONCLUSION