Reliably-stabilizing piecewise-affine neural network controllers

• URL: http://arxiv.org/abs/2111.07183v1
• Date: Sat, 13 Nov 2021 20:01:43 GMT
• Title: Reliably-stabilizing piecewise-affine neural network controllers
• Authors: Filippo Fabiani, Paul J. Goulart
• Abstract summary: 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 that preserve the desirable properties of a given MPC scheme.
• Score: 5.203329540700177
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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 worst-case 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 a ReLU-based approximation of an MPC control law.

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