Assured Neural Network Architectures for Control and Identification of Nonlinear Systems
This provides assured neural network designs for control tasks, addressing a gap where current methods lack such guarantees, though it is incremental as it builds on existing TLL architecture results.
The paper tackles the problem of automatically designing ReLU neural network architectures with guarantees that they can control nonlinear systems to meet formal specifications, by bounding the number of affine functions needed based on Lipschitz continuity assumptions and linking this to a TLL architecture.
In this paper, we consider the problem of automatically designing a Rectified Linear Unit (ReLU) Neural Network (NN) architecture (number of layers and number of neurons per layer) with the assurance that it is sufficiently parametrized to control a nonlinear system; i.e. control the system to satisfy a given formal specification. This is unlike current techniques, which provide no assurances on the resultant architecture. Moreover, our approach requires only limited knowledge of the underlying nonlinear system and specification. We assume only that the specification can be satisfied by a Lipschitz-continuous controller with a known bound on its Lipschitz constant; the specific controller need not be known. From this assumption, we bound the number of affine functions needed to construct a Continuous Piecewise Affine (CPWA) function that can approximate any Lipschitz-continuous controller that satisfies the specification. Then we connect this CPWA to a NN architecture using the authors' recent results on the Two-Level Lattice (TLL) NN architecture; the TLL architecture was shown to be parameterized by the number of affine functions present in the CPWA function it realizes.