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Data-driven control has rapidly matured into a powerful complement to classical model-based paradigms. Among the most successful approaches are nonparametric, trajectory-centric methods built on Willems et al.’s fundamental lemma and model-free reinforcement learning (RL) schemes. In this survey, we reverse the usual presentation order to reflect their differing assumptions and scopes. First, this paper provides a unified treatment of fundamental lemma-based methods, which require knowledge of the system structure (LTI or suitably lifted nonlinear) but offer rigorous guarantees by replacing explicit model identification with input-output trajectory representations. This paper covers state-feedback synthesis for both linear and nonlinear systems, extensions to model predictive control that directly leverage data, and recent advances in data-driven state estimation under noise-free and noisy measurements. This paper then turns to RL-based control, which lifts the structural constraints entirely — trading formal stability proofs for broad applicability to complex and uncertain cyber-physical energy systems (CPESs) dynamics. This paper reviews key RL architectures, policy-and value-based algorithms, and their practical challenges in energy applications. Recognizing the network-induced vulnerabilities of modern grids, this paper also surveys data-driven defense strategies against Denial-of-Service and false-data-injection attacks, from anomaly detection to resilient control. To illustrate practical impact, this paper steps through case studies ranging from canonical generator benchmarks to high-fidelity, grid-connected wind-turbine simulations, demonstrating both trajectory-based controllers and RL agents. This paper concludes by outlining future directions: integrating learning-augmented control with fundamental lemma frameworks, enhancing robustness to network effects, and embedding data-driven models in large-scale optimization for next-generation CPESs.
Liu et al. (Wed,) studied this question.