In this brief, the output reachable estimation and safety verification problems for multilayer perceptron (MLP) neural networks are addressed. First, a conception called maximum sensitivity is introduced, class of MLPs whose activation functions monotonic functions, can be computed via solving convex optimization problems. Then, using simulation-based method, set problem formulated into chain Finally, an automated developed based on result. An application to robotic arm model with two joints...

In this technical note, a necessary and sufficient stability criterion for switched linear systems under dwell-time constraint is proposed by employing class of time-scheduled homogeneous polynomial Lyapunov functions with sufficiently large degree. The key feature nonconservative condition lies in its convexity the system matrices, which explicitly facilitates further extension to uncertain systems. Then, order obtain numerically testable condition, family LMI conditions are presented aid...

This survey presents an overview of verification techniques for autonomous systems, with a focus on safety-critical cyber-physical systems (CPS) and subcomponents thereof. Autonomy in CPS is enabling by recent advances artificial intelligence (AI) machine learning (ML) through approaches such as deep neural networks (DNNs), embedded so-called enabled components (LECs) that accomplish tasks from classification to control. Recently, the formal methods community has developed characterize...

The vulnerability of artificial intelligence (AI) and machine learning (ML) against adversarial disturbances attacks significantly restricts their applicability in safety-critical systems including cyber-physical (CPS) equipped with neural network components at various stages sensing control. This article addresses the reachable set estimation safety verification problems for dynamical embedded serving as feedback controllers. closed-loop system can be abstracted form a continuous-time...

This paper addresses the output reachable set estimation problem for continuous-time switched linear systems consisting of Hurwtiz stable subsystems. Based on a common Lyapunov function approach, is estimated by union bounding ellipsoids. Then, multiple functions with time-scheduled structure are employed to estimate under dwell-time constraint. Furthermore, safety verification uncertain investigated based result estimation. First, sufficient condition ensuring existence an approximate...

Neural networks have been widely used to solve complex real-world problems. Due the complicate, nonlinear, non-convex nature of neural networks, formal safety guarantees for output behaviors will be crucial their applications in safety-critical systems.In this paper, reachable set computation and verification problems a class consisting Rectified Linear Unit (ReLU) activation functions are addressed. A layer-by-layer approach is developed compute set. The formulated form manipulations union...

The event‐triggered control problem for switched linear system is addressed in this study. periodical sampling scheme and event‐triggering condition are incorporated the closed‐loop. feedback updates its value only at instants as long satisfied well. In addition, switchings allowed to occur meanwhile switching satisfied. Three equivalent sufficient conditions proposed ensure asymptotic stability of systems. particular, one has a promising feature affineness matrices, consequence, it extended...

In this note, the global exponential stability of discrete-time switched systems under arbitrary switching is investigated. First, for nonlinear systems, found to be equivalent existence an M-step sequence with sufficient length and a family Lyapunov functions, then criterion proposed nominal linear case in framework quadratic function. order extend handle uncertainties, condition which has promising feature that convex system matrices derived, leading robust uncertain systems. Moreover,...

In this article, the finite-time stability analysis and stabilisation for switched continuous linear system are addressed. Several sufficient conditions boundness of proposed in article. By comparing results, it is shown that more information about switching signal known, less conservative results can be derived. Then, based on static state dynamic output feedback controllers designed to stabilise systems. numerical examples given illustrate within

In this work, the reachable set estimation and safety verification problems for a class of piecewise linear systems equipped with neural network controllers are addressed. The is considered to consist Rectified Linear Unit (ReLU) activation functions. A layer-by-layer approach developed output computation ReLU networks. formulated in form manipulations union polytopes. Based on controllers, feedback control system can be estimated iteratively given finite-time interval. With set, performed...

Artificial neural networks (ANN) have displayed considerable utility in a wide range of applications such as image processing, character and pattern recognition, self-driving cars, evolutionary robotics, non-linear system identification control. While ANNs are able to carry out complicated tasks efficiently, they susceptible unpredictable errant behavior due irregularities that emanate from their complex structure. As result, there been reservations about incorporating them into...

This article investigates the stability of a class switched systems using dynamical dwell time approach. First, condition for whose subsystems are stable presented with approach, which is shown to be less conservative in switching law design than Then proposed approach extended both and unstable subsystems. Finally, some numerical examples given illustrate effectiveness results.

SUMMARY In this paper, we investigate the stability analysis problem of switched impulsive nonlinear systems and several stabilization problems discrete‐time linear are studied. First, sufficient conditions ensuring globally uniformly asymptotically system under arbitrary DDT (dynamical dwell time which defines length interval between two successive switchings) switching derived, respectively. case, first consider composed by stable subsystems, then extend results to case where not all...

In this technical note, the stability and failure tolerant control are investigated for linear time-invariant (LTI) systems with occasional controller failures. At first, a collection of non-convex sufficient conditions ensuring closed loop to be globally asymptotically stable is presented, which simple use but difficult consider purpose. To overcome this, time-scheduled Lyapunov function approach considered alternative convex obtained. Based on result, time-dependent failure-tolerant...