Learning safe neural network controllers with barrier certificates

Abstract

We provide a new approach to synthesize controllers for nonlinear continuous dynamical systems with control against safety properties. The controllers are based on neural networks (NNs). To certify the safety property we utilize barrier functions, which are represented by NNs as well. We train the controller-NN and barrier-NN simultaneously, achieving a verification-in-the-loop synthesis. We provide a prototype tool nncontroller with a number of case studies. The experiment results confirm the feasibility and efficacy of our approach.

An Iterative Scheme of Safe Reinforcement Learning for Nonlinear Systems via Barrier Certificate Generation

“…In this section, we first depict an example of three dimension nonlinear continuous system to show our algorithm by synthesizing a safe DNN controller for it, and then present an experimental evaluation of our algorithm over a set of benchmark examples by comparing with a DNN controller learning framework called nncontroller in [39].…”

“…We have implemented a safe controller synthesis tool called SRLBC based on Algorithm 2, with Tensorflow 1.14 for the DNN controller synthesis and a Matlab package PENBMI [22] for barrier certificate generation. Table 1 shows the performance evaluation of our SRLBC and nncontroller in [39] on 12 continuous systems. All experiments are conducted on a machine running Windows 10 with 16 GB RAM, a 3.20 GHz AMD Ryzen 7 3700X CPU, and an NVIDIA GeForce GTX 1650 super GPU.…”

“…The main research on this topic is through reachable set estimation of DNN-controlled systems, which can only deal with time bounded safety property [11,12,18,19,37]. On the other hand, other than formally verifying synthesized DNN controllers, more recent works have been proposed to learn DNN controllers for dynamical systems with safety guarantees [8,39,40]. For example, a verification-in-the-loop DNN controller training algorithm is presented in [8], which integrates RL framework with user-provided control barrier functions (CBFs) for reward function encoding, combined with SMT based formal CBF checking; a correctness-by-design method is proposed in [39] that first learns DNN controllers and barrier certificates simultaneously using supervised learning, and then performs posterior formal verification of barrier certificates via SMT solvers.…”

“…Meanwhile, the barrier certificates in our approach are computed by numerical optimization method, which is more efficient than the SMT based method in [8]. Compared with [39], our method is based on RL framework and thus has better data sampling efficiency than the meshing-based data set generation in [39] for supervised learning. Besides, our method is iterative so that can utilize intermediate learned results to guide learning in the next iteration, rather than restarting from scratch as in [39] when a learned barrier certificate failed formal checking.…”

“…Compared with [39], our method is based on RL framework and thus has better data sampling efficiency than the meshing-based data set generation in [39] for supervised learning. Besides, our method is iterative so that can utilize intermediate learned results to guide learning in the next iteration, rather than restarting from scratch as in [39] when a learned barrier certificate failed formal checking. Thanks to these advantages, our method has really good performance in efficiency and scalability even for problems with dimension up to 12. The main contributions of this paper are summarized as follows:…”