Robust-Adaptive Interval Predictive Control for Linear Uncertain Systems

TL;DR

This paper develops a robust adaptive predictive control method for linear systems with uncertainties, ensuring stability and constraint satisfaction despite disturbances and unknown parameters, demonstrated through numerical simulations.

Contribution

It introduces a novel control framework combining interval predictors with model predictive control for uncertain linear systems, ensuring robustness and feasibility.

Findings

Ensures recursive feasibility of the control scheme.

Guarantees asymptotic stability under uncertainties.

Validated effectiveness through numerical simulations.

Abstract

We consider the problem of stabilization of a linear system, under state and control constraints, and subject to bounded disturbances and unknown parameters in the state matrix. First, using a simple least square solution and available noisy measurements, the set of admissible values for parameters is evaluated. Second, for the estimated set of parameter values and the corresponding linear interval model of the system, two interval predictors are recalled and an unconstrained stabilizing control is designed that uses the predicted intervals. Third, to guarantee the robust constraint satisfaction, a model predictive control algorithm is developed, which is based on solution of an optimization problem posed for the interval predictor. The conditions for recursive feasibility and asymptotic performance are established. Efficiency of the proposed control framework is illustrated by numeric simulations.