Learning multi-step prediction models for receding horizon control

Terzi, Enrico; Fagiano, Lorenzo; Farina, Marcello; Scattolini, Riccardo

doi:10.23919/ecc.2018.8550494

Cited by 15 publications

(40 citation statements)

References 26 publications

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“…With the cheap availability of large data-sets and the advent of more and more powerful identification and learning techniques, recent years have seen a renaissance of research activity in this area, and in particular on robust methods. From the learning side, new and powerful Set Membership (SM) identification methods, see [6,16,30,31], have been developed to identify a model for the system with guaranteed prediction error bounds, suitable for robust control design. From the control side, MPC algorithms, robust with respect to model disturbances, have been studied from several standpoints, and considering different characterizations of the model and its associated uncertainty, see e.g.…”

Section: Introductionmentioning

confidence: 99%

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

et al. 2019

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A comprehensive approach addressing identification and control for learningbased Model Predictive Control (MPC) for linear systems is presented. The design technique yields a data-driven MPC law, based on a dataset collected from the working plant. The method is indirect, i.e. it relies on a model learning phase and a model-based control design one, devised in an integrated manner. In the model learning phase, a twofold outcome is achieved: first, different optimal p-steps ahead prediction models are obtained, to be used in the MPC cost function; secondly, a perturbed state-space model is derived, to be used for robust constraint satisfaction. Resorting to Set Membership techniques, a characterization of the bounded model uncertainties is obtained, which is a key feature for a successful application of the robust control algorithm. In the control design phase, a robust MPC law is proposed, able to track piece-wise constant reference signals, with guaranteed recursive feasibility and convergence properties. The controller embeds multistep predictors in the cost function, it ensures robust constraints satisfaction thanks to the learnt uncertainty model, and it can deal with possibly unfeasible reference values. The proposed approach is finally tested in a numerical example.

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Section: Introductionmentioning

confidence: 99%

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

et al. 2019

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“…(32) The terms multiplyingτ ip andd i converge to their limit (see (30)) from below, while the term τ imax {j, o} χ i,p converges to zero from above as → ∞. Thus, in general it is possible that τ i p+j >τ i∞ for some and j.…”

Section: E Infinite-horizon Simulation Error Boundmentioning

confidence: 99%

“…We now introduce two new results that solve this issue, allowing one to derive a convergent estimated i ≈d 0i , as well as estimates of the system order and, additionally, of the impulse response decay trend. The main conceptual innovation with respect to the preliminary results of [30] is to analyze not only each value of λ ip separately, but also the course of this quantity as a function of the horizon p. Theorem 1. If Assumptions 2-5 hold, then, for any arbitrarily small η > 0, ∃N < ∞ such that…”

Section: B Theoretical Properties Of the Multi-step Error Boundmentioning

confidence: 99%

“…If Θ ip is unbounded, then this indicates that the data collected from the system are not informative enough, and new data should be acquired. In [30], the set Θ ip was taken as FPS for the predictors pertaining to the horizon p. Here, we provide a further refinement by adding the constraints on the estimated decay trend obtained in Section III-C. Let us define the polytope:…”

Section: Feasible Parameter Sets and Finite-horizon Simulation Errmentioning

confidence: 99%

“…In a way similar toε 0 ip , it is not possible to exactly compute the bound (23) using a finite data set. Thus, we introduce an estimateτ ip (θ ip ), which, under Assumption 5, converges to τ ip (θ ip ) from below as the number of data points increases, see [30]. Such an estimate is then inflated by a scalar γ > 1 to account for the uncertainty due to the usage of a finite data set:…”

Section: Feasible Parameter Sets and Finite-horizon Simulation Errmentioning

confidence: 99%

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Set Membership Identification of Linear Systems With Guaranteed Simulation Accuracy

Lauricella

Fagiano

2020

IEEE Trans. Automat. Contr.

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The problem of model identification for linear systems is considered, using a finite set of sampled data affected by a bounded measurement noise, with unknown bound. The objective is to identify one-step-ahead models and their accuracy in terms of worst-case simulation error bounds. To do so, the Set Membership identification framework is exploited. Theoretical results are derived, allowing one to estimate the noise bound and system decay rate. Then, these quantities and the data are employed to define the Feasible Parameter Set (FPS), which contains all possible models compatible with the available information.Here, the estimated decay rate is used to refine the standard FPS formulation, by adding constraints that enforce the desired converging behavior of the models' impulse response. Moreover, guaranteed simulation error bounds for an infinite future horizon are derived, improving over recent results pertaining to finite simulation horizon only. These bounds are the basis for a result and method to guarantee asymptotic stability of the identified model. Finally, the desired one-step-ahead model is identified by means of numerical optimization, and the related simulation error bounds are evaluated. Both input-output and state-space model structures are addressed. The approach is showcased on a numerical example and on real-world experimental data of the roll rate dynamics of an autonomous glider.

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Minimum time learning model predictive control

Rosolia

Borrelli

2020

Intl J Robust & Nonlinear

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In this paper we present a Learning Model Predictive Control (LMPC) strategy for linear and nonlinear time optimal control problems. Our work builds on existing LMPC methodologies and it guarantees finite time convergence properties for the closed-loop system. We show how to construct a time varying safe set and terminal cost function using closed-loop data. The resulting LMPC policy is time varying and it guarantees recursive constraint satisfaction and non-decreasing performance.Computational efficiency is obtained by convexifing the time varying safe set and time varying terminal cost function. We demonstrate that, for a class of nonlinear system and convex constraints, the convex LMPC formulation guarantees recursive constraint satisfaction and non-decreasing performance. Finally, we illustrate the effectiveness of the proposed strategies on minimum time obstacle avoidance and racing examples.

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Learning multi-step prediction models for receding horizon control

Cited by 15 publications

References 26 publications

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

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

Set Membership Identification of Linear Systems With Guaranteed Simulation Accuracy

Minimum time learning model predictive control

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