Related papers: Reach-SDP: Reachability Analysis of Closed-Loop Sy…
In recent years, Neural Networks (NNs) have been employed to control nonlinear systems due to their potential capability in dealing with situations that might be difficult for conventional nonlinear control schemes. However, to the best of…
Backward reachability analysis is essential to synthesizing controllers that ensure the correctness of closed-loop systems. This paper is concerned with developing scalable algorithms that under-approximate the backward reachable sets, for…
Safety is a critical concern for the next generation of autonomy that is likely to rely heavily on deep neural networks for perception and control. Formally verifying the safety and robustness of well-trained DNNs and learning-enabled…
Reachability analysis of hybrid systems has been used as a safety verification tool to assess offline whether the state of a system is capable of remaining within a designated safe region for a given time horizon. Although it has been…
Neural networks can be used as approximations of several complex control schemes such as model predictive control. We show in this paper which properties deep neural networks with rectifier linear units as activation functions need to…
The problem of computing the reachable set for a given system is a quintessential question in nonlinear control theory. While previous work has yielded a plethora of approximate and analytical methods for determining such a set, these…
The literature on reachability analysis methods for neural networks currently only focuses on uncertainties on the network's inputs. In this paper, we introduce two new approaches for the reachability analysis of neural networks with…
Despite their success in massive engineering applications, deep neural networks are vulnerable to various perturbations due to their black-box nature. Recent study has shown that a deep neural network can misclassify the data even if the…
The maximization of reach-avoid probabilities for stochastic systems is a central topic in the control literature. Yet, the available methods are either restricted to low-dimensional systems or suffer from conservative approximations. To…
Reachability analysis is a formal method to guarantee safety of dynamical systems under the influence of uncertainties. A substantial bottleneck of all reachability algorithms is the necessity to adequately tune specific algorithm…
We consider the safety evaluation of discrete time, stochastic systems over a finite horizon. Therefore, we discuss and link probabilistic invariance with reachability as well as reach-avoid problems. We show how to efficiently compute…
Robust control problems have significant practical implications since external disturbances can significantly impact the performance of control methods. Existing robust control methods excel at control-affine systems but fail at neural…
This paper presents a specification-guided safety verification method for feedforward neural networks with general activation functions. As such feedforward networks are memoryless, they can be abstractly represented as mathematical…
Neural network (NN) dynamics models and control policies achieve strong performance in robotics, but providing sound guarantees under uncertainty remains difficult, especially for closed-loop NN systems. Existing reachability tools provide…
A supervised learning framework is proposed to approximate a model predictive controller (MPC) with reduced computational complexity and guarantees on stability and constraint satisfaction. The framework can be used for a wide class of…
This paper presents Verisig, a hybrid system approach to verifying safety properties of closed-loop systems using neural networks as controllers. Although techniques exist for verifying input/output properties of the neural network itself,…
Recent advances in machine learning technologies and sensing have paved the way for the belief that safe, accessible, and convenient autonomous vehicles may be realized in the near future. Despite tremendous advances within this context,…
We present a stochastic model predictive control framework for nonlinear systems subject to unbounded process noise with closed-loop guarantees. First, we provide a conceptual shrinking-horizon framework that utilizes general probabilistic…
A matrix optimization problem over an uncertain linear system on finite horizon (abbreviated as MOPUL) is studied, in which the uncertain transition matrix is regarded as a decision variable. This problem is in general NP-hard. By using the…
The Neural Network (NN), as a black-box function approximator, has been considered in many control and robotics applications. However, difficulties in verifying the overall system safety in the presence of uncertainties hinder the…