Reliably-stabilizing piecewise-affine neural network controllers
This addresses the lack of analytical tools for stability assessment in neural network controllers, which is critical for safety-critical control systems, though it is incremental as it builds on existing MPC and NN methods.
The paper tackles the problem of certifying stability for neural network approximations of model predictive control policies by establishing conditions based on approximation error and Lipschitz constant, and develops an offline mixed-integer optimization method to compute these quantities exactly, enabling reliable stability guarantees.
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.