A Semi-Algebraic Optimization Approach to Data-Driven Control of Continuous-Time Nonlinear Systems

Dai, Tianyu; Sznaier, Mario

doi:10.1109/lcsys.2020.3003505

Cited by 49 publications

(58 citation statements)

References 19 publications

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Section: Introductionmentioning

confidence: 99%

“…Recently, several methods have been developed for control synthesis [15,16]. One major difference is that [15,16] focus on polynomial dynamics, while our methods applies to more general systems. Another important difference is that we use a stronger notion of stability compared with [16].…”

Section: Introductionmentioning

confidence: 99%

“…One major difference is that [15,16] focus on polynomial dynamics, while our methods applies to more general systems. Another important difference is that we use a stronger notion of stability compared with [16]. Another line of research that is related to this work is optimal control synthesis based on generalized moment problems.…”

Section: Introductionmentioning

confidence: 99%

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A Convex Data-Driven Approach for Nonlinear Control Synthesis

2021

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We consider a class of nonlinear control synthesis problems where the underlying mathematical models are not explicitly known. We propose a data-driven approach to stabilize the systems when only sample trajectories of the dynamics are accessible. Our method is built on the density-function-based stability certificate that is the dual to the Lyapunov function for dynamic systems. Unlike Lyapunov-based methods, density functions lead to a convex formulation for a joint search of the control strategy and the stability certificate. This type of convex problem can be solved efficiently using the machinery of the sum of squares (SOS). For the data-driven part, we exploit the fact that the duality results in the stability theory can be understood through the lens of Perron–Frobenius and Koopman operators. This allows us to use data-driven methods to approximate these operators and combine them with the SOS techniques to establish a convex formulation of control synthesis. The efficacy of the proposed approach is demonstrated through several examples.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A Convex Data-Driven Approach for Nonlinear Control Synthesis

2021

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“…A point-to-point optimal control problem for bilinear systems is formulated in the recent work [22]. The datadriven control design for polynomial systems is the subject of [23], [24]. While [23] uses Rantzer's dual Lyapunov's theory and moments based techniques, [24] uses Lyapunov second method and a particular parametrization of the Lyapunov function to obtain SOS programs whose feasibility directly provide stabilizing controllers.…”

mentioning

confidence: 99%

“…The datadriven control design for polynomial systems is the subject of [23], [24]. While [23] uses Rantzer's dual Lyapunov's theory and moments based techniques, [24] uses Lyapunov second method and a particular parametrization of the Lyapunov function to obtain SOS programs whose feasibility directly provide stabilizing controllers. See [15] for additional results on the data-driven control design of polynomial systems based on Petersen's lemma.…”

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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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