Robust Output Feedback MPC: An Interval-Observer Approach

Abstract

In this work, we address the problem of outputfeedback Model Predictive Control (MPC) of constrained, linear, discrete-time systems corrupted by additive perturbations on both state and output. The use of estimated variables in MPC is challenging and computationally expensive due to constraint satisfaction. To overcome this issue, the proposed approach incorporates interval observers on the MPC scheme to cope with uncertainty, leading to a novel, simple and very intuitive methodology providing robust constraint satisfaction with reduced computational complexity.

Robust Output Feedback MPC for LPV Systems Using Interval Observers

“…Following an idea conceived for linear systems [17], this section addresses the design of an interval predictor: an estimator that satisfies relation (2), but that requires only information on the system dynamics, the bounds on the matrices A and B and the bounds on the disturbances.…”

“…This implies point (1). For point (2), since the dynamics of Z k is nominal (i.e., completely known) under Assumption 3, we have that ISS in X f follows directly from the selection of the terminal ingredients (i.e., the choice of Ψ j , j = {1, 2, 3}, in Algorithm 1), which guarantees that Finally, for point (3), we have that the solution of OCP (17) implies that x k ∈ z k,0 , z k,0 ⊂ X due to relation (2) and u k = s k 0 ∈ U, under Assumption 6 and the discussed features of X f .…”

“…In the present paper, following an idea recently proposed for LTI systems [17], we present an alternative for robust output feedback MPC for LPV systems using interval observers (IO) [18]. These observers -while being a special class of set-membership estimators -provide a guaranteed estimation of the admissible values (i.e., intervals) of the states, by using input-output information at each instant of time.…”

Robust output feedback model predictive control of time‐delayed systems using interval observers

“…In this section, we will address the design of a static feedback controller for IP (12). This feedback will be used to derive the terminal ingredients for the MPC design, as we will discuss in the following.…”

“…In this sense, the contribution of this work is twofold: propose new interval estimators (an observer and a predictor) and develop an algorithm solving the output-feedback MPC problem for linear, discrete-time, time-delayed systems with both state and control constraints and additive perturbations. The proposed MPC algorithm follows a recent idea applied to linear time-invariant (LTI) systems 12 , in which the novelty relies on the use of interval observers (IO) 13 : an estimator that offers a computationally inexpensive way to compute the set-membership of the system states (in the form of intervals) with guaranteed stability.…”