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In this paper, we consider the problem of automatically designing a RectifiedLinear Unit (ReLU) Neural Network (NN) architecture that is sufficient toimplement the optimal Model Predictive Control (MPC) strategy for an LTI systemwith quadratic cost. Specifically, we propose AReN, an algorithm to generateAssured ReLU Architectures. AReN takes as input an LTI system with quadraticcost specification, and outputs a ReLU NN architecture with the assurance thatthere exist network weights that exactly implement the associated MPCcontroller. AReN thus offers new insight into the design of ReLU NNarchitectures for the control of LTI systems: instead of training aheuristically chosen NN architecture on data -- or iterating over manyarchitectures until a suitable one is found -- AReN can suggest an adequate NNarchitecture before training begins. While several previous works were inspiredby the fact that both ReLU NN controllers and optimal MPC controller are bothContinuous, Piecewise-Linear (CPWL) functions, exploiting this similarity todesign NN architectures with correctness guarantees has remained elusive. AReNachieves this using two novel features. First, we reinterpret a recent resultabout the implementation of CPWL functions via ReLU NNs to show that a CPWLfunction may be implemented by a ReLU architecture that is determined by thenumber of distinct affine regions in the function. Second, we show that we canefficiently over-approximate the number of affine regions in the optimal MPCcontroller without solving the MPC problem exactly. Together, these resultsconnect the MPC problem to a ReLU NN implementation without explicitly solvingthe MPC and directly translates this feature to a ReLU NN architecture thatcomes with the assurance that it can implement the MPC controller. We showthrough numerical results the effectiveness of AReN in designing an NNarchitecture.

AReN: Assured ReLU NN Architecture for Model Predictive Control of LTI Systems