A common problem affecting neural network (NN) approximations of model predictive control (MPC) policies is the lack of analytical tools to assess the stability of the closed-loop system under the action of the NN-based controller. We present a general procedure to quantify the performance of such a controller, or to design minimum complexity NNs with rectified linear units (ReLUs) that preserve the desirable properties of a given MPC scheme. By quantifying the approximation error between NN-based and MPC-based state-to-input mappings, we first establish suitable conditions involving two key quantities, the worstcase error and the Lipschitz constant, guaranteeing the stability of the closed-loop system. We then develop an offline, mixed-integer optimization-based method to compute those quantities exactly. Together these techniques provide conditions sufficient to certify the stability and performance of an ReLU-based approximation of an MPC control law

Reliably-stabilizing piecewise-affine neural network controllers

Filippo Fabiani;
2022-01-01

Abstract

A common problem affecting neural network (NN) approximations of model predictive control (MPC) policies is the lack of analytical tools to assess the stability of the closed-loop system under the action of the NN-based controller. We present a general procedure to quantify the performance of such a controller, or to design minimum complexity NNs with rectified linear units (ReLUs) that preserve the desirable properties of a given MPC scheme. By quantifying the approximation error between NN-based and MPC-based state-to-input mappings, we first establish suitable conditions involving two key quantities, the worstcase error and the Lipschitz constant, guaranteeing the stability of the closed-loop system. We then develop an offline, mixed-integer optimization-based method to compute those quantities exactly. Together these techniques provide conditions sufficient to certify the stability and performance of an ReLU-based approximation of an MPC control law
2022
Mixed-integer (MI) linear optimization, model predictive control (MPC), neural networks (NNs)
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11771/25790
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