A Moments Based Approach to Designing MIMO Data Driven Controllers for Switched Systems

Dai, Tianyu; Sznaier, Mario

doi:10.1109/cdc.2018.8619361

Cited by 55 publications

(71 citation statements)

References 18 publications

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“…Studying how our approach can be used to systematically address control problems via data-dependent LMIs could be very rewarding, and lead to a methodical inclusion of data to analyze and design control systems. A great leap forward will come from systematically extending the methods of this paper to systems where identification is challenging, such as switched [17] and nonlinear systems. The results of this paper show that our approach is concretely promising for nonlinear systems, but we have only touched the surface of this research area.…”

Section: Discussionmentioning

confidence: 99%

“…control theory [6], iterative feedback tuning [7], and virtual reference feedback tuning [8]. This topic is now attracting more and more researchers, with problems ranging from PIDlike control [9] to model reference control and output tracking [10], [11], [12], [13], [14], predictive [15], [16], robust [17] and optimal control [18], [19], [20], [21], [22], [23], [24], the latter being one of the most frequently considered problems. The corresponding techniques are also quite varied, ranging from dynamics programming to optimization techniques and algebraic methods.…”

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confidence: 99%

See 1 more Smart Citation

Formulas for Data-Driven Control: Stabilization, Optimality, and Robustness

Persis

Tesi

2020

IEEE Trans. Automat. Contr.

619

711

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In a paper by Willems and coauthors it was shown that persistently exciting data can be used to represent the inputoutput behavior of a linear system. Based on this fundamental result, we derive a parametrization of linear feedback systems that paves the way to solve important control problems using data-dependent Linear Matrix Inequalities only. The result is remarkable in that no explicit system's matrices identification is required. The examples of control problems we solve include the state and output feedback stabilization, and the linear quadratic regulation problem. We also discuss robustness to noise-corrupted measurements and show how the approach can be used to stabilize unstable equilibria of nonlinear systems.

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Section: Discussionmentioning

confidence: 99%

mentioning

confidence: 99%

Formulas for Data-Driven Control: Stabilization, Optimality, and Robustness

Persis

Tesi

2020

IEEE Trans. Automat. Contr.

619

711

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show abstract

“…This calls for strengthening Assumption 3 in the sense of Definition 2. 4 Assumption 4: |d| ≤ δ for some known δ > 0. Assumption 4 is indeed stronger than Assumption 3 in the sense that it implies Assumption 3 once we set ∆ := δ √ T I s .…”

Section: A Process Disturbances: Noisy Data and Robust Invariancementioning

confidence: 99%

Learning Controllers from Data via Approximate Nonlinearity Cancellation

Persis¹,

Rotulo²,

Tesi³

2022

Preprint

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We introduce a method to deal with the data-driven control design of nonlinear systems. We derive conditions to design controllers via (approximate) nonlinearity cancellation. These conditions take the compact form of data-dependent semidefinite programs. The method returns controllers that can be certified to stabilize the system even when data are perturbed and disturbances affect the dynamics of the system during the execution of the control task, in which case an estimate of the robustly positively invariant set is provided. I. INTRODUCTIONA Utomating the control design process is important to cope with complex dynamical plants whose dynamics is poorly known. Data-driven control is a notable example of such an automated synthesis. Namely, data-driven control refers to the procedure of designing controllers for an unknown system starting solely from measurements collected from the plant and some priors about the plant itself (linear vs. nonlinear parametrization, nature of the noise, etc.). In this paper we study the problem of designing controllers for nonlinear systems from data.Related literature. System identification followed by control design for the identified system is a classical way to indirectly perform data-driven control [1]. By direct data-driven control instead it is meant a procedure in which no intermediate step of identifying the system model is taken, earlier examples being the iterative feedback tuning (IFT) [2], and the virtual reference feedback tuning (VRFT) [3]. Recent times have seen a renewed interest in direct data-driven control, viewed as compact data-dependent conditions which, once verified, automatically return controllers without explicitly identifying the plant. One of the focus points in these data-driven control results is how to deal with perturbations and noise affecting the data and the resulting noise-induced uncertainty. Assuming a process noise with bounded ∞ norm, [4] defines a set of system's matrices pairs consistent with the data and, using an extended Farkas' lemma, derives conditions under which stability of all systems in the set hold. These conditions can be checked using polynomial optimization techniques.The papers [5], [6] highlight the relevance of a result in [7], about representing the behavior of a linear time-invariant system via a single input-output trajectory, and use this result to develop data-enabled, rather than model-based, predictive control, providing probabilistic guarantees on performance for systems subject to stochastic disturbances.C. De Persis and M. Rotulo are with ENTEG and the J.

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“…Although such approaches have been extended to the control of more complex systems, such as linear parameter-varying (LPV) systems 35,36 or nonlinear systems with bounded disturbances, 37,38 they have never been extended to the control of hybrid/switching systems, in which both the local behavior and the operating condition of the plant are unknown. To the best of our knowledge, the only approach in the literature for data-driven control of switched systems has been recently presented in, 39 in which the problem of finding a switching static regulator for state feedback is solved within a set-membership framework through the solution of a polynomial optimization problem. This approach relies on Lyapunov arguments to formulate the design problem and to prove the stability of the closed-loop system.…”

Section: Introductionmentioning

confidence: 99%

Direct data‐driven design of switching controllers

Breschi

Formentin

2019

Intl J Robust & Nonlinear

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Switching linear models can be used to represent the behavior of hybrid, time-varying, and nonlinear systems, while generally providing a satisfactory trade-off between accuracy and complexity. Although several control design techniques are available for such models, the effect of modeling errors on the closed-loop performance has not been formally evaluated yet. In this paper, a data-driven synthesis scheme is thus introduced to design optimal switching controllers directly from data, without needing a model of the plant. In particular, the theory will be developed for piecewise affine controllers, which have proven to be effective in many real-world engineering applications. The performance of the proposed approach is illustrated on some benchmark simulation case studies.

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A Moments Based Approach to Designing MIMO Data Driven Controllers for Switched Systems

Cited by 55 publications

References 18 publications

Formulas for Data-Driven Control: Stabilization, Optimality, and Robustness

Formulas for Data-Driven Control: Stabilization, Optimality, and Robustness

Learning Controllers from Data via Approximate Nonlinearity Cancellation

Direct data‐driven design of switching controllers

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