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We develop data-driven reinforcement learning (RL) control designs forinput-affine nonlinear systems. We use Carleman linearization to express thestate-space representation of the nonlinear dynamical model in the Carlemanspace, and develop a real-time algorithm that can learn nonlinearstate-feedback controllers using state and input measurements in theinfinite-dimensional Carleman space. Thereafter, we study the practicality ofhaving a finite-order truncation of the control signal, followed by itsclosed-loop stability analysis. Finally, we develop two additional designs thatcan learn structured as well as sparse representations of the RL-basednonlinear controller, and provide theoretical conditions for ensuring theirclosed-loop stability. We present numerical examples to show how our proposedmethod generates closed-loop responses that are close to the optimalperformance of the nonlinear plant. We also compare our designs to otherdata-driven nonlinear RL control methods such as those based on neuralnetworks, and illustrate their relative advantages and drawbacks.

Reinforcement Learning-based Control of Nonlinear Systems using Carleman Approximation: Structured and Unstructured Designs