Reachable Set Estimation for Markovian Jump Neural Networks With Time-Varying Delays

Asynchronous adaptive event-triggered fault detection for delayed Markov jump neural networks: A delay-variation-dependent approach

This paper presents a delay-variation-dependent approach to fault detection of a discrete-time Markov jump neural network (MJNN) with a time-varying delay and mismatched modes. The goal is to detect the potential fault of delayed MJNNs by constructing an appropriate adaptive event-triggered and asynchronous H∞ filter. By choosing a delay-product-type Lyapunov-Krasovskii (L-K) functional with a delay-dependent matrix and exploiting some matrix polynomial inequalities, bounded real lemmas (BRLs) are obtained on the existence of suitable adaptive event generator and filters. These BRLs are dependent not only on the delay bounds but also on the delay variation rate. Simulation results are given to show the validity of the proposed theoretical method.

Sampled-Data Synchronization of Stochastic Markovian Jump Neural Networks With Time-Varying Delay

In this article, sampled-data synchronization problem for stochastic Markovian jump neural networks (SMJNNs) with time-varying delay under aperiodic sampled-data control is considered. By constructing mode-dependent one-sided loop-based Lyapunov functional and mode-dependent two-sided loop-based Lyapunov functional and using the Itô formula, two different stochastic stability criteria are proposed for error SMJNNs with aperiodic sampled data. The slave system can be guaranteed to synchronize with the master system based on the proposed stochastic stability conditions. Furthermore, two corresponding mode-dependent aperiodic sampled-data controllers design methods are presented for error SMJNNs based on these two different stochastic stability criteria, respectively. Finally, two numerical simulation examples are provided to illustrate that the design method of aperiodic sampled-data controller given in this article can effectively stabilize unstable SMJNNs. It is also shown that the mode-dependent two-sided looped-functional method gives less conservative results than the mode-dependent one-sided looped-functional method.

Reachable Set Estimation of Delayed Markovian Jump Neural Networks Based on an Improved Reciprocally Convex Inequality

This brief investigates the reachable set estimation problem of the delayed Markovian jump neural networks (NNs) with bounded disturbances. First, an improved reciprocally convex inequality is proposed, which contains some existing ones as its special cases. Second, an augmented Lyapunov-Krasovskii functional (LKF) tailored for delayed Markovian jump NNs is proposed. Thirdly, based on the proposed reciprocally convex inequality and the augmented LKF, an accurate ellipsoidal description of the reachable set for delayed Markovian jump NNs is obtained. Finally, simulation results are given to illustrate the effectiveness of the proposed method.

Almost Sure Stabilization of Continuous-Time Jump Linear Systems via a Stochastic Scheduled Controller

This article addresses the almost surely exponential (ASE) stabilization problem of continuous-time jump systems realized by a stochastic scheduled controller. In this study, a stochastic scheduled controller based on the anytime algorithm is proposed. It is able to cope with the situation where no controller is added to subsystems during some time slices. Sufficient conditions for the existence of such a controller are established by applying novel techniques to its stochastic transfer matrix, and they are all presented with solvable forms. Particularly, both dwell times of the jump signal and distribution properties of stochastic scheduling are considered and proved to have played positive roles in obtaining better performance and applications. Two special situations about no jump systems with constant and varied dwell times are further studied, respectively. A practical example is offered so as to verify the effectiveness and superiority of the methods proposed in this study.

Active Learning for Estimating Reachable Sets for Systems With Unknown Dynamics

This article presents a data-driven method for computing reachable sets where active learning (AL) is used to reduce the computational burden. Set-based methods used to estimate reachable sets typically do not scale well with the state-space dimension, or rely heavily on the existence of a model. If such a model is not available, it is simple to generate state trajectory data by numerically simulating black-box oracles of systems (whose dynamics are unknown) from sampled initial conditions. Using these data samples, the estimation of reachable sets can be posed as a classification problem, wherein AL can intelligently select samples that are most informative and least similar to previously labeled samples. By exploiting submodularity, the actively learned samples can be selected efficiently, with bounded suboptimality. Our proposed framework is illustrated by estimating the domains of attractions of model predictive controllers (MPCs) and reinforcement learners. We also consider a scenario where there are two oracles that differ with respect to evaluation costs and labeling accuracy. We propose a framework to reduce the dependency of the expensive oracle in labeling samples using disagreement-based AL (DBAL). The potential of the DBAL algorithm is demonstrated on a solver selection problem for real-time MPC.

Reachable Set Estimation for Markovian Jump Neutral-Type Neural Networks With Time-Varying Delays

The reachable set estimation problem for a class of Markovian jump neutral-type neural networks (MJNTNNs) with bounded disturbances and time-varying delays is tackled in this article. With the aid of the delay partitioning method, a novel stochastic Lyapunov-Krasovskii functional containing triple integral terms is constructed in mode-dependent augmented form. To begin with, transition probabilities of the concerned Markovian jump neural networks (NNs) are considered to be completely known. By employing the integral inequality approach and reciprocally convex combination method, it is proved that all state trajectories which start from the origin by bounded inputs can be constrained by an ellipsoid-like set if a group of linear matrix inequalities (LMIs) is feasible. Then, the free-connection weighting matrix technique is utilized to handle the case of partially known transition probabilities. As byproducts, some sufficient conditions are also obtained to guarantee the stochastic stability of the concerned NNs. The validity of the theoretical analysis is confirmed by numerical simulations.

Reachable Set Estimation for Neural Network Control Systems: A Simulation-Guided Approach

The vulnerability of artificial intelligence (AI) and machine learning (ML) against adversarial disturbances and attacks significantly restricts their applicability in safety-critical systems including cyber-physical systems (CPS) equipped with neural network components at various stages of sensing and control. This article addresses the reachable set estimation and safety verification problems for dynamical systems embedded with neural network components serving as feedback controllers. The closed-loop system can be abstracted in the form of a continuous-time sampled-data system under the control of a neural network controller. First, a novel reachable set computation method in adaptation to simulations generated out of neural networks is developed. The reachability analysis of a class of feedforward neural networks called multilayer perceptrons (MLPs) with general activation functions is performed in the framework of interval arithmetic. Then, in combination with reachability methods developed for various dynamical system classes modeled by ordinary differential equations, a recursive algorithm is developed for over-approximating the reachable set of the closed-loop system. The safety verification for neural network control systems can be performed by examining the emptiness of the intersection between the over-approximation of reachable sets and unsafe sets. The effectiveness of the proposed approach has been validated with evaluations on a robotic arm model and an adaptive cruise control system.

Event-Based Dissipative Filtering of Markovian Jump Neural Networks Subject to Incomplete Measurements and Stochastic Cyber-Attacks

In this article, the dissipativity-based filtering of the Markovian jump neural networks subject to incomplete measurements and deception attacks is investigated by adopting an event-triggered communication strategy, where the attackers are supposed to occur in a random fashion but obey the Bernoulli distribution. Consider that the information of the system mode is transmitted to the filter over the communication network that is vulnerable to external attacks, which may lead to the undesired performance of the resulting system by injecting malicious information from the attackers. As a result, the filter has difficulty completing information from the original system. Besides, an event-triggered communication mechanism is introduced to reduce the communication frequency between data transmission due to the limited network resources, and different triggering conditions corresponding to different jump modes are developed. Then, based on the above considerations, the sufficient condition is derived to ensure the stochastic stability and dissipativity of the resulting augmented system although the deception attacks and incomplete information exist. A numerical simulated example is provided to verify the theoretical analysis.

Reachable Set Estimation for Discrete-Time Markovian Jump Neural Networks With Generally Incomplete Transition Probabilities

This paper is concerned with the problem of reachable set estimation for discrete-time Markovian jump neural networks with generally incomplete transition probabilities (TPs). This kind of TP may be exactly known, merely known with lower and upper bounds, or unknown. The aim of this paper is to derive a precise reachable set description for the considered system via the Lyapunov-Krasovskii functional (LKF) approach. By constructing an augmented LKF, using an equivalent transformation method to deal with the unknown TPs and utilizing the extended reciprocally convex matrix inequality, and the free matrix weighting approach to estimate the forward difference of the constructed LKF, several sufficient conditions that guarantee the existence of an ellipsoidal reachable set are established. Finally, a numerical example with simulation results is given to demonstrate the effectiveness and superiority of the proposed results.

Quasi-Synchronization of Discrete-Time Lur'e-Type Switched Systems With Parameter Mismatches and Relaxed PDT Constraints

This paper investigates the problem of quasi-synchronization for a class of discrete-time Lur'e-type switched systems with parameter mismatches and transmission channel noises. Different from the previous studies referring to the persistent dwell-time (PDT) switching signals, the average dwell-time (ADT) constraints combined with the PDT are considered simultaneously in this paper to relax the limitation of dwell-time requirements and to improve the flexibility of the PDT switching signal design. By virtue of the semi-time-varying (STV) Lyapunov function, the synchronization criteria for transmitter-receiver systems in a switched version are obtained to satisfy a prescribed synchronization error bound. An estimate of the synchronization error bound is provided via the reachable set approach and, further, an explicit description of the error bounds is given. Then, sufficient conditions on the existence of STV observers are derived with a predetermined error bound, and the corresponding observer gains are calculated via solving a group of linear matrix inequalities. Finally, the effectiveness and validness of the developed theoretical results are demonstrated via a numerical example.

Synchronization of complex dynamical networks with random coupling delay and actuator faults

This paper addresses the issue of passivity-based synchronization problem for a family of Markovian jump neutral complex dynamical networks (NCDNs) with coupling delay and actuator faults. Also, by considering the effect of random fluctuation in complex dynamical network systems, the occurrence of coupling delay are taken in terms of a stochastic distribution, which obeys the Bernoulli distribution. To handle the fault effects in actuators of proposed complex network systems, an actuator fault model is considered. The main objective of this paper is to develop a robust state feedback controller such that for all possible actuator failures and random coupling delays, all nodes of the proposed Markovian jump NCDNs is globally asymptotically synchronized to the reference node in mean square sense and guarantee the output strict passivity performance. By developing a suitable Lyapunov-Krasovskii functional and utilizing the Wirtinger-based integral inequality, the required a set of sufficient conditions for the synchronization of proposed system is established in form of linear matrix inequalities. Finally, three numerical examples including a 3-dimensional Lorenz chaotic model are provided to demonstrate the correctness and superiority of the proposed control scheme.

Extended Dissipativity Analysis for Markovian Jump Neural Networks With Time-Varying Delay via Delay-Product-Type Functionals

This paper investigates the problem of extended dissipativity for Markovian jump neural networks (MJNNs) with a time-varying delay. The objective is to derive less conservative extended dissipativity criteria for delayed MJNNs. Toward this aim, an appropriate Lyapunov-Krasovskii functional (LKF) with some improved delay-product-type terms is first constructed. Then, by employing the extended reciprocally convex matrix inequality (ERCMI) and the Wirtinger-based integral inequality to estimate the derivative of the constructed LKF, a delay-dependent extended dissipativity condition is derived for the delayed MJNNs. An improved extended dissipativity criterion is also given via the allowable delay sets method. Based on the above-mentioned results, the extended dissipativity condition of delayed NNs without Markovian jump parameters is directly derived. Finally, three numerical examples are employed to illustrate the advantages of the proposed method.

Asynchronous and Resilient Filtering for Markovian Jump Neural Networks Subject to Extended Dissipativity

The problem of asynchronous and resilient filtering for discrete-time Markov jump neural networks subject to extended dissipativity is investigated in this paper. The modes of the designed resilient filter are assumed to run asynchronously with the modes of original Markov jump neural networks, which accord well with practical applications and are described through a hidden Markov model. Due to the fluctuation of the filter parameters, a resilient filter taking into account parameter uncertainty is adopted. Being different from the norm-bound type of uncertainty which has been studied in a considerable number of the existing literatures, the interval type of uncertainty is introduced so as to describe uncertain phenomenon more accurately. By means of convex optimal method, the gains of filter are derived to guarantee the stochastic stability and extended dissipativity of the filtering error system under the wave of the filter parameters. Considering the limited computing power of MATLAB solver, a relatively simple simulation is exploited to verify the effectiveness and merits of the theoretical findings where the relationships among optimal performance index, uncertain parameter σ , and asynchronous rate are revealed.

Output Reachable Set Estimation and Verification for Multilayer Neural Networks

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, and for a class of MLPs whose activation functions are monotonic functions, the maximum sensitivity can be computed via solving convex optimization problems. Then, using a simulation-based method, the output reachable set estimation problem for neural networks is formulated into a chain of optimization problems. Finally, an automated safety verification is developed based on the output reachable set estimation result. An application to the safety verification for a robotic arm model with two joints is presented to show the effectiveness of the proposed approaches.

Reachable set estimation for Markovian jump neural networks with time-varying delay

This paper is concerned with the reachable set estimation for Markovian jump neural networks with time-varying delay and bounded peak inputs. The objective is to find a description of a reachable set that is containing all reachable states starting from the origin. In the framework of Lyapunov-Krasovskii functional method, an appropriate Lyapunov-Krasovskii functional is constructed firstly. Then by using the Wirtinger-based integral inequality and the extended reciprocally convex matrix inequality, an ellipsoidal description of the reachable set for the considered neural networks is derived. Finally, a numerical example with simulation results is provided to verify the effectiveness of our results.