Exponential stabilization for sampled-data neural-network-based control systems

Sampled-Data Control for Exponential Synchronization of Delayed Inertial Neural Networks With Aperiodic Sampling and State Quantization

This article is devoted to dealing with exponential synchronization for inertial neural networks (INNs) with heterogeneous time-varying delays (HTVDs) under the framework of aperiodic sampling and state quantization. First, by taking the effect of aperiodic sampling and state quantization into consideration, a novel quantized sampled-data (QSD) controller with time-varying control gain is designed to tackle the exponential synchronization of INNs. Second, considering the available information of the lower and upper bounds of each HTVD, a refined Lyapunov-Krasovskii functional (LKF) is proposed. Meanwhile, an improved looped-functional method is utilized to fully capture the characteristic of practical sampling patterns and further relax the positive definiteness requirement for LKF. Consequently, less conservative exponential synchronization conditions with extra flexibility are derived. Finally, a numerical example is employed to demonstrate the effectiveness and advantages of the proposed synchronization method.

Runtime Safety Monitoring of Neural-Network-Enabled Dynamical Systems

Complex dynamical systems rely on the correct deployment and operation of numerous components, with state-of-the-art methods relying on learning-enabled components in various stages of modeling, sensing, and control at both offline and online levels. This article addresses the runtime safety monitoring problem of dynamical systems embedded with neural-network components. A runtime safety state estimator in the form of an interval observer is developed to construct the lower bound and upper bound of system state trajectories in runtime. The developed runtime safety state estimator consists of two auxiliary neural networks derived from the neural network embedded in dynamical systems, and observer gains to ensure the positivity, namely, the ability of the estimator to bound the system state in runtime, and the convergence of the corresponding error dynamics. The design procedure is formulated in terms of a family of linear programming feasibility problems. The developed method is illustrated by a numerical example and is validated with evaluations on an adaptive cruise control system.

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 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.

Sampled-Data State Estimation of Reaction Diffusion Genetic Regulatory Networks via Space-Dividing Approaches

A novel state estimator is designed for genetic regulatory networks with reaction-diffusion terms in this study. First, the diffusion space (where mRNA and protein exist) is divided into several parts and only a point, a line, or a plane, etc., is measured in every subspace to reduce the measurement cost effectively. Then, samplers and network-induced time delay are considered to meet the network transmission requirement. A new criterion to ensure that the estimation error converges to zero is established by using the Lyapunov functional combined with Wirtinger's inequality, reciprocally convex approach, and Halanay's inequality; furthermore, the estimator's parameters are derived by solving linear matrix inequalities. Finally, two simulation examples (including one-dimensional and two-dimensional spaces) are presented to demonstrate the developed scheme's applicability.

Energy-to-Peak State Estimation for Switched Neutral-Type Neural Networks With Sector Condition via Sampled-Data Information

In this article, the energy-to-peak state estimation problem is investigated for a class of switched neutral neural networks subject to the external perturbations with bounded energy. Both the values of the measurement outputs and switching signal of the subsystems are only available for the controllers at the discrete sampling instants. Unlike the results for nonswitched neural networks, the coexistence of the switching and sampling actions directly causes the asynchronous phenomena between the indexes of subsystems and their corresponding controllers. To address this situation, the piecewise time-dependent Lyapunov-Krasovskii functional and slow switching mechanism are introduced. Under the developed theorem conditions, we prove that the designed state estimator exponentially tracks the true value of the neural state with the accessible sampled-data information. Also, the influence of the exogenous perturbations on the peak value of the estimation error is constrained at a prescribed level. Finally, a neutral cellular neural network with switching parameters is employed to substantiate the effectiveness and applicability of the theoretical results.

Synchronization for Quantized Semi-Markov Switching Neural Networks in a Finite Time

Finite-time synchronization (FTS) is discussed for delayed semi-Markov switching neural networks (S-MSNNs) with quantized measurement, in which a logarithmic quantizer is employed. The stochastic phenomena of structural and parametrical changes are modeled by a semi-Markov process whose transition rates are time-varying to depend on the sojourn time. Practical systems subject to unpredictable structural changes, such as quadruple-tank process systems, are described by delayed S-MSNNs. A key issue under the consideration is how to design a feedback controller to guarantee the FTS between the master system and the slave system. For this purpose, by using the weak infinitesimal operator, sufficient conditions are constructed to realize FTS of the resulting error system over a finite-time interval. Then, the solvability conditions for the desired finite-time controller can be determined under a linear matrix inequality framework. Finally, the theoretical findings are illustrated by the quadruple-tank process model.

Estimation of Domain of Attraction for Aperiodic Sampled-Data Switched Delayed Neural Networks Subject to Actuator Saturation

In this paper, for the case of the asynchronous switching caused by that subsystem's switching occuring during a sampling interval, the domain of attraction estimation problem is investigated for aperiodic sampled-data switched delayed neural networks (ASDSDNNs) subject to actuator saturation. A parameters-dependent time-scheduled Lyapunov functional consisting of a novel looped-functional is constructed using segmentation technology and linear interpolation. By employing this novel functional and using an average dwell time (ADT) approach, exponential stability criteria are proposed for polytopic uncertain ASDSDNNs subject to actuator saturation. And a relationship between ADT and sampling period is revealed for ASDSDNNs. As a corollary, exponential stability criteria are proposed for nominal ASDSDNNs subject to actuator saturation. Furthermore, by describing the domain of attraction as a time-varying ellipsoid determined by the time-scheduled Lyapunov matrix, the proposed theoretical conditions are transformed into a linear matrix inequality (LMI)-based multi-objective optimization problem. The dynamic estimates of the domain of attraction for ASDSDNNs are solved. Numerical simulation examples are provided to illustrate the effectiveness of the proposed method.

A Stochastic Sampling Mechanism for Time-Varying Formation of Multiagent Systems With Multiple Leaders and Communication Delays

The time-varying formation problem for multiagent systems (MASs) with stochastic sampling and multiple leaders is studied in this paper, in which communication delays are taken into account. All the agents are divided into the set of the follower group and the set of the leader group. Under the proposed stochastic sampling mechanism for time-varying formation of the MASs with communication delays, the followers are driven to achieve time-varying formation where the center of the formation is the convex combination of the states of the leaders. In the theoretical analysis, sufficient conditions for the MASs achieving time-varying formation in mean square under stochastic sampling with multiple leaders and communication delays are derived. Moreover, some corollaries are also given in this paper. Finally, the theoretical analysis is verified by a given simulation example.

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.

Stability Analysis and Application for Delayed Neural Networks Driven by Fractional Brownian Noise

This paper deals with two types of the stability problem for the delayed neural networks driven by fractional Brownian noise (FBN). The existence and the uniqueness of the solution to the main system with respect to FBN are proved via fixed point theory. Based on Hilbert-Schmidt operator theory and analytic semigroup principle, the mild solution of the stochastic neural networks is obtained. By applying the stochastic analytic technique and some well-known inequalities, the asymptotic stability criteria and the exponential stability condition are established. Both numerical example and practical application for synchronization control of multiagent system are provided to illustrate the effectiveness and potential of the proposed techniques.

Stabilization of Neural-Network-Based Control Systems via Event-Triggered Control With Nonperiodic Sampled Data

This paper focuses on a problem of event-triggered stabilization for a class of nonuniformly sampled neural-network-based control systems (NNBCSs). First, a new event-triggered data transmission mechanism is designed based on the nonperiodic sampled data. Different from the previous works, the proposed triggering scheme enables the NNBCSs design to enjoy the advantages of both nonuniform and event-triggered sampling schemes. Second, under the nonperiodic event-triggered data transmission scheme, the nonperiodic sampled-data three-layer fully connected feedforward neural-network (TLFCFFNN)-based event-triggered controller is constructed, and the resulting closed-loop TLFCFFNN-based event-triggered control system is modeled as a state delay system based on time-delay system modeling approach. Then, the stability criteria for the closed-loop system is formulated using Lyapunov-Krasovskii functional approach. Third, the sufficient conditions for the codesign of the TLFCFFNN-based controller and triggering parameters are given in terms of solvability of matrix inequalities to guarantee the asymptotical stability of the closed-loop system and an upper bound on the given cost function while reducing the updates of the controller. Finally, three numerical examples are provided to illustrate the effectiveness and benefits of the proposed results.

On Stabilization of Quantized Sampled-Data Neural-Network-Based Control Systems

This paper investigates the problem of stabilization of sampled-data neural-network-based systems with state quantization. Different with previous works, the communication limitation of state quantization is considered for the first time. More specifically, it is assumed that the sampled state measurements from sensor to the controller are quantized via a quantizer. To reduce conservativeness, a novel piecewise Lyapunov-Krasovskii functional (LKF) is constructed by introducing a line-integral type Lyapunov function and some useful terms that take full advantage of the available information about the actual sampling pattern. Based on the new LKF, much less conservative stabilization conditions are derived to obtain the maximal sampling period and the minimal guaranteed cost control performance. The desired quantized sampled-data three-layer fully connected feedforward neural-network-based controllers are designed by a linear matrix inequality approach. A search algorithm is given to find the optimal values of tuning parameters. The effectiveness and advantage of proposed method are demonstrated by the numerical simulation of an inverted pendulum.

Analysis and synthesis of networked control systems: A survey of recent advances and challenges

A networked control system (NCS) is a control system which involves a communication network. In NCSs, the continuous-time measurement is usually sampled and quantized before transmission. Then, the measurement is transmitted to the remote controller via the communication channel, during which the signal may be delayed, lost or even sometimes not allowed for transmission due to the communication or energy constraints. In recent years, the modeling, analysis and synthesis of networked control systems (NCSs) have received great attention, which leads to a large number of publications. This paper attempts to present an overview of recent advances and unify them in a framework of network-induced issues such as signal sampling, data quantization, communication delay, packet dropouts, medium access constraints, channel fading and power constraint, and present respective solution approaches to each of these issues. We draw some conclusions and highlight future research directions in end.

Discontinuous Lyapunov approach to state estimation and filtering of jumped systems with sampled-data

This paper is concerned with the sampled-data state estimation and H(∞) filtering for a class of Markovian jump systems with the discontinuous Lyapunov approach. The system measurements are sampled and then transmitted to the estimator and filter in order to estimate the state of the jumped system under consideration. The corresponding error dynamics is represented by a system with two types of delays: one is from the system itself, and the other from the sampling period. As the delay due to sampling is discontinuous, a corresponding discontinuous Lyapunov functional is constructed, and sufficient conditions are established so as to guarantee both the asymptotic mean-square stability and the H(∞) performance for the filtering error systems. The explicit expressions of the desired estimator and filter are further provided. Finally, two simulation examples are given to illustrate the design procedures and performances of the proposed method.