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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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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We consider the stabilization problem of a discrete-time system that switches among a finite set of unknown linear subsystems under unknown switching signal. To this end, we propose a method that uses data to directly design a control mechanism without any explicit identification step. Our approach is online, meaning that the data are collected over time while the system is evolving in closed-loop, and are directly used to iteratively update the controller. A major benefit of the proposed online implementation is therefore the ability of the controller to automatically adjust to changes in the operating mode of the system. We show that the proposed control mechanism guarantees exponential stability of the closed-loop switched system under sufficiently slow switching. The effectiveness of the approach is illustrated via a numerical example.