are: (i) a novel constrained objective function for model learning with neural networks and the adjoining constrained optimization problem for learning the controller, and (ii) a primal-dual method to solve both these problems that has small duality gap.

The paper is organized as follows: Section \[sec:model\_learning\] describes the sufficiently accurate formulation for model learning and Sec. \[sec:control\] utilizes this learned model for designing controllers with state and action constraints. We demonstrate the efficacy of this approach on a challenging Ball-Paddle system in Sec. \[sec:experiments\].

Related Work {#sec:relatedwork}
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The idea of learning a model from data and using it to control systems is not new. PILCO [@deisenroth2011pilco] learns a probabilistic forward model with Gaussian Process Regression, and is later extended to Bayesian Neural Networks [@gal2016improving]. Guided Policy Search [@levine2014learning; @levine2016end] uses a Gaussian Mixture Model for use as an expert policy. Both formulate an optimization problem with the task of maximizing an expected reward. This allows a policy to be trained by backpropagating through the forward model. [@jordan1992forward] and [@gillespie2018learning] both learn neural network models. The latter then formulates a convex optimization problem by linearizing the neural network. However, it is has been observed that linearizing highly nonlinear systems often 