Robust predictive control with data-based multi-step prediction models

Abstract

This note extends a recently proposed algorithm for model identification and robust model predictive control (MPC) of asymptotically stable, linear time-invariant systems subject to process and measurement disturbances. Independent output predictors for different horizon values are estimated with Set Membership methods. It is shown that the corresponding prediction error bounds are the least conservative in the considered model class. Then, a new multi-rate robust MPC algorithm is developed, employing said multi-step predictors to robustly enforce constraints and stability against disturbances and model uncertainty, and to reduce conservativeness. A simulation example illustrates the effectiveness of the approach.

Learning-based predictive control for linear systems: A unitary approach

“…the one-step-ahead guaranteed prediction error bound, iterating it over time with the same model matrices, and eventually addingd. This alternative bound has been pro- posed in out previous works [31] and [32]. It can be noted that the proposed approach achieves a guaranteed bound on the prediction error that is half the one obtained from the integration ofτ 1 (θ (1) * ) +d, thus reducing conservativeness significantly.…”

“…A numerical example is finally reported. Preliminary results on the learning and control synthesis algorithms developed in this paper have been reported in [31], and [32]. In this paper, we propose a novel offline method to learn the uncertainty model to be used in the control design phase, together with a new MPC design to deal with the tracking of (possibly infeasible) piecewise constant reference signals, we derive the full proofs of all the theoretical results concerning learning and control design, and we merge our preliminary work into a unitary and holistic vision of the interplay between learning and control for MPC.…”

Learning-Based Model Predictive Control: Toward Safe Learning in Control

“…Fagiano et al (14) reviewed the method and contrasted it with scenario MPC, which we briefly touch on in Section 3.2.1. Terzi et al (50)(51)(52) discussed the use of models mapping an entire input sequence to a state sequence over the prediction horizon for autoregressive exogenous models using set-membership identification. For polytopic state-space linear time-invariant systems in the general form of Equation 12, Di Cairano (53) and Zhou et al ( 54) presented an MPC approach in which, similarly to the method of Aswani et al (37), the model is improved for performance, but the model uncertainty sets T are not updated over time.…”

Learning multi-step prediction models for receding horizon control

“…A collection of multi-step models derived for all p ∈ [1, p] provides an estimated sequence of future system outputs, up to the prediction horizon p < ∞, together with an associated sequence of guaranteed uncertainty intervals τ p (θ p ). These models can be then embedded in a robust finite-horizon optimal control problem to be solved in a receding-horizon approach, thus realizing a MPC law based on multi-step predictions [5]. Three important reasons to consider multi-step models are: 1. the model identification procedure results in convex optimization problems, as opposed to the nonlinear programs arising when identifying one-step-ahead models with an output-error (i.e.…”

“…In (5), the notation • indicates specific measured values of a quantity. φp (i) are the measured instances of the regressor ϕ p ∈ Φ p , and ỹp (i) the corresponding measured values of noise-corrupted outputs p steps in the future, i.e.…”