Controller design for robust invariance from noisy data

Bisoffi, Andrea; De Persis, Claudio; Tesi, Pietro

doi:10.48550/arxiv.2007.13181

Cited by 7 publications

(15 citation statements)

References 36 publications

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“…The first optimal control input u * (t) = u t|t is then applied to the system and problem ( 22) is solved in receding horizon fashion. (22) is feasible at each time step t, then the closed-loop system (8) under the controller (22) robustly satisfies the constraints in (9) at each time step t under the process and measurement noise w(t) ∈ Z w and v(t) ∈ Z v .…”

Section: Lemma 4 Given Input-state Trajectoriesmentioning

confidence: 99%

“…Moreover, the authors in [5] provide data-driven MPC with stability and robustness guarantees. Also, data-driven feedback controllers and stabilization are discussed in [9], [14], [25], [26]. Recent developments in the data-driven direction include robust controller synthesis from noisy input-state trajectories [6] and data-driven optimal control [13], [23].…”

Section: Introductionmentioning

confidence: 99%

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Robust Data-Driven Predictive Control using Reachability Analysis

Alanwar¹,

Stürz²,

Johansson³

2021

Preprint

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We present a robust data-driven control scheme for unknown linear systems with a bounded process and measurement noise. Instead of depending on a system model as in traditional predictive control, a controller utilizing datadriven reachable regions is proposed. The data-driven reachable regions are based on a matrix zonotope recursion and are computed based on only noisy input-output data of a trajectory of the system. We assume that measurement and process noise are contained in bounded sets. While we assume knowledge of these bounds, no knowledge about the statistical properties of the noise is assumed. In the noise-free case, we prove that the presented purely data-driven control scheme results in an equivalent closed-loop behavior to a nominal model predictive control scheme. In the case of measurement and process noise, our proposed scheme guarantees robust constraint satisfaction, which is essential in safety-critical applications. Numerical experiments show the effectiveness of the proposed data-driven controller in comparison to model-based control schemes.

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Section: Lemma 4 Given Input-state Trajectoriesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Robust Data-Driven Predictive Control using Reachability Analysis

Alanwar¹,

Stürz²,

Johansson³

2021

Preprint

View full text Add to dashboard Cite

show abstract

“…This has motivated a renewed interest in system analysis and control design methods relying on finite-length data sequences [1][2][3][4]. Several recent works propose to use raw measurements for representing discrete-time systems, and solving system analysis and control design problems [1,2,[5][6][7][8][9][10][11][12][13][14][15][16]. As mentioned in [1], the main feature of these approaches is to bypass explicit system identification that is usually required in standard control design.…”

Section: Introductionmentioning

confidence: 99%

“…All above works assume the availability of historical data, i.e., finite-length trajectories produced by the open-loop system and measured offline. The works [1,2,[8][9][10][11][12][13] consider system representations based on input-state historical data. Data-based parameterizations of linear state-feedback and linear quadratic regulators are developed in [1], under the assumption that historical input data are persistently exciting.…”

Section: Introductionmentioning

confidence: 99%

A Data-Driven Convex Programming Approach to Worst-Case Robust Tracking Controller Design

Xu,

Turan,

Guo

et al. 2021

Preprint

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This paper studies finite-horizon robust tracking control for discrete-time linear systems, based on input-output data. We leverage behavioral theory to represent system trajectories through a set of noiseless historical data, instead of using an explicit system model. By assuming that recent output data available to the controller are affected by noise terms verifying a quadratic bound, we formulate an optimization problem with a linear cost and LMI constraints for solving the robust tracking problem without any approximations. Our approach hinges on a parameterization of noise trajectories compatible with the data-dependent system representation and on a reformulation of the tracking cost, which enables the application of the Slemma. In addition, we propose a method for reducing the computational complexity and demonstrate that the size of the resulting LMIs does not scale with the number of historical data. Finally, we show that the proposed formulation can easily incorporate actuator disturbances as well as constraints on inputs and outputs. The performance of the new controllers is discussed through simulations.

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“…In contrast with traditional model-based approaches, datadriven and learning techniques for control invariance and stabilizability problems have recently been attracting significant attention [3]- [5]. Among them, a certain line of research leverages randomized methods for (controlled) invariance set estimation and set-membership verification [6]- [14].…”

Section: Introductionmentioning

confidence: 99%

Probabilistic stabilizability certificates for a class of black-box linear systems

Fabiani,

Margellos,

Goulart

2021

Preprint

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We provide out-of-sample certificates on the controlled invariance property of a given set with respect to a class of black-box linear systems. Specifically, we consider linear time-invariant models whose state space matrices are known only to belong to a certain family due to a possibly inexact quantification of some parameters. By exploiting a set of realizations of those undetermined parameters, verifying the controlled invariance property of the given set amounts to a linear program, whose feasibility allows us to establish an aposteriori probabilistic certificate on the controlled invariance property of such a set with respect to the nominal linear timeinvariant dynamics. The proposed framework is applied to the control of a networked system with unknown weighted graph.

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Controller design for robust invariance from noisy data

Cited by 7 publications

References 36 publications

Robust Data-Driven Predictive Control using Reachability Analysis

Robust Data-Driven Predictive Control using Reachability Analysis

A Data-Driven Convex Programming Approach to Worst-Case Robust Tracking Controller Design

Probabilistic stabilizability certificates for a class of black-box linear systems

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