Receding Horizon Stabilization and Disturbance Attenuation for Neural Networks With Time-Varying Delay

Partial-Neurons-Based Proportional-Integral Observer Design for Artificial Neural Networks: A Multiple Description Encoding Scheme

This article is concerned with a new partial-neurons-based proportional-integral observer (PIO) design problem for a class of artificial neural networks (ANNs) subject to bounded disturbances. For the purpose of improving the reliability of the data transmission, the multiple description encoding mechanisms are exploited to encode the measurement data into two identically important descriptions, and the encoded data are then transmitted to the decoders via two individual communication channels susceptible to packet dropouts, where Bernoulli-distributed stochastic variables are utilized to characterize the random occurrence of the packet dropouts. An explicit relationship is discovered that quantifies the influences of the packet dropouts on the decoding accuracy, and a sufficient condition is provided to assess the boundedness of the estimation error dynamics. Furthermore, the desired PIO parameters are calculated by solving two optimization problems based on two metrics (i.e., the smallest ultimate bound and the fastest decay rate) characterizing the estimation performance. Finally, the applicability and advantage of the proposed PIO design strategy are verified by means of an illustrative example.

Substability and Substabilization: Control of Subfully Actuated Systems

The region of attraction of the Lyapunov asymptotic stability at the origin is defined to be a ball centered at the origin, which is clearly simply connected and also bounded in the local case. In this article, the concept of substability is proposed, which allows "gaps" and "holes" in the region of attraction of the Lyapunov exponential stability, and also allows the origin to be a boundary point of the region of attraction. The concept is meaningful and useful in many practical applications, but is particularly made so with the control of single- and multi-order subfully actuated systems. Specifically, the singular set of a sub-FAS is first defined, and a substabilizing controller is then designed such that the closed-loop system is a constant linear one with an arbitrarily assignable eigen-polynomial, but with its initial values restricted within a so-called region of exponential attraction (ROEA). Consequently, the substabilizing controller drives all the state trajectories starting from the ROEA exponentially to the origin. The introduced concept of substabilization is of great importance because, on the one side, it is often practically useful since the designed ROEA is often large enough for certain applications, while on the other side, Lyapunov asymptotically stabilizing controllers can be further easily established based on substabilization. Several examples are given to demonstrate the proposed theories.

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.

Symmetry Control of Comfortable Vehicle Suspension Based on H∞

Suspension is an important part of intelligent and safe transportation; it is the balance point between the comfort and handling stability of a vehicle under intelligent traffic conditions. In this study, a control method of left-right symmetry of air suspension based on H∞ theory was proposed, which was verified under intelligent traffic conditions. First, the control stability caused by the active suspension control system running on uneven roads needs to be ensured. To address this issue, a 1/4 vehicle active suspension model was established, and the vertical acceleration of the vehicle body was applied as the main index of ride comfort. H∞ performance constraint output indicators of the controller contained the tire dynamic load, suspension dynamic stroke, and actuator control force limit. Based on the Lyapunov stability theory, an output feedback control law with H∞-guaranteed performance was proposed to constrain multiple targets. This way, the control problem was transformed into a solution to the Riccati equation. The simulation results showed that when dealing with general road disturbances, the proposed control strategy can reduce the vehicle body acceleration by about 20% and meet the requirements of an ultimate suspension dynamic deflection of 0.08 m and a dynamic tire load of 1500 N. Using this symmetrical control method can significantly improve the ride comfort and driving stability of a vehicle under intelligent traffic conditions.

Event-Triggered Adaptive Fuzzy Output-Feedback Control for Nonstrict-Feedback Nonlinear Systems With Asymmetric Output Constraint

This article addresses the event-triggered adaptive fuzzy output-feedback control problem for a class of nonstrict-feedback nonlinear systems with asymmetric and time-varying output constraints, as well as unknown nonlinear functions. By designing a linear observer to estimate the unmeasurable states, a novel event-triggered adaptive fuzzy output-feedback control scheme is proposed. The barrier Lyapunov function (BLF) and the error transformation technique are used to handle the output constraint under a completely unknown initial tracking condition. It is shown that with the proposed control scheme, all the solutions of the closed-loop system are semiglobally bounded, and the tracking error converges to a small set near zero, while the output constraint is satisfied within a predetermined finite time, even when the constraint condition is violated initially. Moreover, with the proposed event-triggering mechanism (ETM), the Zeno behavior can be strictly ruled out. An example is finally provided to demonstrate the effectiveness of the proposed control method.

Integral-Type Event-Triggered Model Predictive Control of Nonlinear Systems With Additive Disturbance

This article studies integral-type event-triggered model predictive control (MPC) of continuous-time nonlinear systems. An integral-type event-triggered mechanism is proposed by incorporating the integral of errors between the actual and predicted state sequences, leading to reduced average sampling frequency. Besides, a new and improved robustness constraint is introduced to handle the additive disturbance, rendering the MPC problem with a potentially enlarged initial feasible region. Furthermore, the feasibility of the designed MPC and the stability of the closed-loop system are rigorously investigated. Several sufficient conditions to guarantee these properties are established, which is related to factors, such as the prediction horizon, the disturbance bound, the triggering level, and the contraction rate for the robustness constraint. The effectiveness of the proposed algorithm is illustrated by numerical examples and comparisons.

Nonfragile H∞ State Estimation for Recurrent Neural Networks With Time-Varying Delays: On Proportional-Integral Observer Design

In this article, a novel proportional-integral observer (PIO) design approach is proposed for the nonfragile H_∞ state estimation problem for a class of discrete-time recurrent neural networks with time-varying delays. The developed PIO is equipped with more design freedom leading to better steady-state accuracy compared with the conventional Luenberger observer. The phenomena of randomly occurring gain variations, which are characterized by the Bernoulli distributed random variables with certain probabilities, are taken into consideration in the implementation of the addressed PIO. Attention is focused on the design of a nonfragile PIO such that the error dynamics of the state estimation is exponentially stable in a mean-square sense, and the prescribed H_∞ performance index is also achieved. Sufficient conditions for the existence of the desired PIO are established by virtue of the Lyapunov-Krasovskii functional approach and the matrix inequality technique. Finally, a simulation example is provided to demonstrate the effectiveness of the proposed PIO design scheme.

Memory-Event-Triggered H∞ Output Control of Neural Networks With Mixed Delays

This article investigates the problem of memory-event-triggered H∞ output feedback control for neural networks with mixed delays (discrete and distributed delays). The probability density of the communication delay among neurons is modeled as the kernel of the distributed delay. To reduce network communication burden, a novel memory-event-triggered scheme (METS) using the historical system output is introduced to choose which data should be sent to the controller. Based on a constructed Lyapunov-Krasovskii functional (LKF) with the distributed delay kernel and a generalized integral inequality, new sufficient conditions are formed by linear matrix inequalities (LMIs) for designing an event-triggered H∞ controller. Finally, experiments based on a computer and a real wireless network are executed to confirm the validity of the developed method.

Functional Nonlinear Model Predictive Control Based on Adaptive Dynamic Programming

This paper presents a functional model predictive control (MPC) approach based on an adaptive dynamic programming (ADP) algorithm with the abilities of handling control constraints and disturbances for the optimal control of nonlinear discrete-time systems. In the proposed ADP-based nonlinear MPC (NMPC) structure, a neural-network-based identification is established first to reconstruct the unknown system dynamics. Then, the actor-critic scheme is adopted with a critic network to estimate the index performance function and an action network to approximate the optimal control input. Meanwhile, as the MPC strategy can effectively determine the current control by solving a finite horizon open-loop optimal control problem, in the proposed algorithm, the infinite horizon is decomposed into a series of finite horizons to obtain the optimal control. In each finite horizon, the finite ADP algorithm solves the optimal control problem subject to the terminal constraint, the control constraint, and the disturbance. The uniform ultimate boundedness of the closed-loop system is verified by the Lyapunov approach. Finally, the ADP-based NMPC is conducted on two different cases and the simulation results demonstrate the quick response and strong robustness of the proposed method.

X-ray cone-beam computed tomography geometric artefact reduction based on a data-driven strategy

Cone-beam computed tomography (CBCT) enables three-dimensional imaging of the internal structure of objects in a non-invasive way with high accuracy. Practical misalignment of the CBCT system causes geometric artefacts in reconstructed images, which seriously degrades image quality in ways such as detail loss and decreased spatial resolution. This leads to inaccurate distinction of defects in detection, especially in precise industrial fields like aerospace and instrument manufacturing. This paper presents a method to reduce the geometric artefacts based on a data-driven strategy, which is an end-to-end modified fully convolutional neural network (M-FCNN). The designed M-FCCN contains five convolution layers and five deconvolution layers for feature extraction and output image rebuilding, respectively. In addition, the pooling layer is not used in the designed M-FCNN, considering the preservation of details in the reconstructed image. In this M-FCCN, artefact images with different features have been trained separately. After training, the M-FCNN can be applied to directly reduce geometric artefacts in the reconstructed image. The designed M-FCNN has been demonstrated with different types of synthetic data and has achieved accurate results. It is also validated with practical data, including carbon composite and medical oral phantoms with comparable quality to phantom-based methods, proving that it is an effective way to reduce geometric artefacts in the image domain by means of a data-driven strategy.

Event-Triggered Stabilization of Neural Networks With Time-Varying Switching Gains and Input Saturation

This paper investigates the event-triggered stabilization of neural networks (NNs) subject to input saturation. The main core lies in the design of a novel controller with time-varying switching gains and the associated switching event-triggered condition (ETC). The ETC is essentially a switching between the aperiodic sampling and continuous event trigger. The control gains of the designed controller are composed of an exponentially decaying term and two gain matrices. The two gain matrices are required to be switched when the switching between the aperiodic sampling and continuous event trigger is met. By employing the generalized sector condition and switching Lyapunov function, several sufficient conditions that ensure the local exponential stability of the NNs are formulated in terms of linear matrix inequalities (LMIs). Both the exponentially decaying term and switching gains improve the feasible region of LMIs, and then they are helpful to enlarge the set of admissible initial conditions, the threshold in ETC, and the average waiting time. Together with several optimization problems, two numerical examples are employed to validate the effectiveness of our results.

A Novel Finite-Sum Inequality-Based Method for Robust $H_\infty$ Control of Uncertain Discrete-Time Takagi-Sugeno Fuzzy Systems With Interval-Like Time-Varying Delays

This paper is concerned with the problem of robust ${H}_{\infty}$ control of an uncertain discrete-time Takagi-Sugeno fuzzy system with an interval-like time-varying delay. A novel finite-sum inequality-based method is proposed to provide a tighter estimation on the forward difference of certain Lyapunov functional, leading to a less conservative result. First, an auxiliary vector function is used to establish two finite-sum inequalities, which can produce tighter bounds for the finite-sum terms appearing in the forward difference of the Lyapunov functional. Second, a matrix-based quadratic convex approach is employed to equivalently convert the original matrix inequality including a quadratic polynomial on the time-varying delay into two boundary matrix inequalities, which delivers a less conservative bounded real lemma (BRL) for the resultant closed-loop system. Third, based on the BRL, a novel sufficient condition on the existence of suitable robust ${H}_{\infty}$ fuzzy controllers is derived. Finally, two numerical examples and a computer-simulated truck-trailer system are provided to show the effectiveness of the obtained results.

Robust Distributed Predictive Control of Waterborne AGVs-A Cooperative and Cost-Effective Approach

Waterborne autonomous guided vessels (waterborne AGVs) moving over open waters experience environmental uncertainties. This paper proposes a novel cost-effective robust distributed control approach for waterborne AGVs. The overall system is uncertain and has independent subsystem dynamics but coupling objectives and state constraints. Waterborne AGVs determine their actions in a parallel way, while still minimizing an overall cost function and respecting coupling constraints robustly by communicating within a neighborhood. Our first contribution is the proposal of the system robustness level for the cost-effective robust distributed model predictive control (RDMPC) for waterborne AGVs. Cost-effective RDMPC models the price of robustness by explicitly considering uncertainty and system characteristics in a tube-based robust control framework. The second contribution is an efficient integrated branch & bound (B&B) and the alternating direction method of multipliers (ADMMs) algorithm for solving the cost-effective RDMPC problem. The algorithm exploits special ordered variable sets and combining branching criteria with intermediate ADMM results conducting smart search in B&B. Simulation results demonstrate the effectiveness of the proposed approach for cooperative distributed waterborne AGVs with cost-effective robustness.

UFIR Filtering for GPS-Based Tracking over WSNs with Delayed and Missing Data

In smart cities, vehicles tracking is organized to increase safety by localizing cars using the Global Positioning System (GPS). The GPS-based system provides accurate tracking but is also required to be reliable and robust. As a main estimator, we propose using the unbiased finite impulse response (UFIR) filter, which meets these needs as being more robust than the Kalman filter (KF). The UFIR filter is developed for vehicle tracking in discrete-time state-space over wireless sensor networks (WSNs) with time-stamped data discretely delayed on k-step-lags and missing data. The state-space model is represented in a way such that the UFIR filter, KF, and H∞ filter can be used universally. Applications are given for measurement data, which are cooperatively transferred from a vehicle to a central station through several nodes with k-step-lags. Better tracking performance of the UFIR filter is shown experimentally.

Aperiodic Robust Model Predictive Control for Constrained Continuous-Time Nonlinear Systems: An Event-Triggered Approach

The event-triggered control is a promising solution to cyber-physical systems, such as networked control systems, multiagent systems, and large-scale intelligent systems. In this paper, we propose an event-triggered model predictive control (MPC) scheme for constrained continuous-time nonlinear systems with bounded disturbances. First, a time-varying tightened state constraint is computed to achieve robust constraint satisfaction, and an event-triggered scheduling strategy is designed in the framework of dual-mode MPC. Second, the sufficient conditions for ensuring feasibility and closed-loop robust stability are developed, respectively. We show that robust stability can be ensured and communication load can be reduced with the proposed MPC algorithm. Finally, numerical simulations and comparison studies are performed to verify the theoretical results.

State Estimation for Static Neural Networks With Time-Varying Delays Based on an Improved Reciprocally Convex Inequality

This brief is concerned with the problem of neural state estimation for static neural networks with time-varying delays. Notice that a Luenberger estimator can produce an estimation error irrespective of the neuron state trajectory. This brief provides a method for designing such an estimator for static neural networks with time-varying delays. First, in-depth analysis on a well-used reciprocally convex approach is made, leading to an improved reciprocally convex inequality. Second, the improved reciprocally convex inequality and some integral inequalities are employed to provide a tight upper bound on the time-derivative of some Lyapunov-Krasovskii functional. As a result, a novel bounded real lemma (BRL) for the resultant error system is derived. Third, the BRL is applied to present a method for designing suitable Luenberger estimators in terms of solutions of linear matrix inequalities with two tuning parameters. Finally, it is shown through a numerical example that the proposed method can derive less conservative results than some existing ones.

O(t-α)-synchronization and Mittag-Leffler synchronization for the fractional-order memristive neural networks with delays and discontinuous neuron activations

This paper investigates O(t^-α)-synchronization and adaptive Mittag-Leffler synchronization for the fractional-order memristive neural networks with delays and discontinuous neuron activations. Firstly, based on the framework of Filippov solution and differential inclusion theory, using a Razumikhin-type method, some sufficient conditions ensuring the global O(t^-α)-synchronization of considered networks are established via a linear-type discontinuous control. Next, a new fractional differential inequality is established and two new discontinuous adaptive controller is designed to achieve Mittag-Leffler synchronization between the drive system and the response systems using this inequality. Finally, two numerical simulations are given to show the effectiveness of the theoretical results. Our approach and theoretical results have a leading significance in the design of synchronized fractional-order memristive neural networks circuits involving discontinuous activations and time-varying delays.

Sampled-Data Stabilization for Fuzzy Genetic Regulatory Networks with Leakage Delays

This paper deals with the sampled-data stabilization problem for Takagi-Sugeno (T-S) fuzzy genetic regulatory networks with leakage delays. A novel Lyapunov-Krasovskii functional (LKF) is established by the non-uniform division of the delay intervals with triplex and quadruplex integral terms. Using such LKFs for constant and time-varying delay cases, new stability conditions are obtained in the T-S fuzzy framework. Based on this, a new condition for the sampled-data controller design is proposed using a linear matrix inequality representation. A numerical result is provided to show the effectiveness and potential of the developed design method.

Finite-Time Stabilization and Adaptive Control of Memristor-Based Delayed Neural Networks

Finite-time stability problem has been a hot topic in control and system engineering. This paper deals with the finite-time stabilization issue of memristor-based delayed neural networks (MDNNs) via two control approaches. First, in order to realize the stabilization of MDNNs in finite time, a delayed state feedback controller is proposed. Then, a novel adaptive strategy is applied to the delayed controller, and finite-time stabilization of MDNNs can also be achieved by using the adaptive control law. Some easily verified algebraic criteria are derived to ensure the stabilization of MDNNs in finite time, and the estimation of the settling time functional is given. Moreover, several finite-time stability results as our special cases for both memristor-based neural networks (MNNs) without delays and neural networks are given. Finally, three examples are provided for the illustration of the theoretical results.Finite-time stability problem has been a hot topic in control and system engineering. This paper deals with the finite-time stabilization issue of memristor-based delayed neural networks (MDNNs) via two control approaches. First, in order to realize the stabilization of MDNNs in finite time, a delayed state feedback controller is proposed. Then, a novel adaptive strategy is applied to the delayed controller, and finite-time stabilization of MDNNs can also be achieved by using the adaptive control law. Some easily verified algebraic criteria are derived to ensure the stabilization of MDNNs in finite time, and the estimation of the settling time functional is given. Moreover, several finite-time stability results as our special cases for both memristor-based neural networks (MNNs) without delays and neural networks are given. Finally, three examples are provided for the illustration of the theoretical 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.

Filtering of Discrete-Time Switched Neural Networks Ensuring Exponential Dissipative and $l_{2}$ - $l_{\infty }$ Performances

This paper studies delay-dependent exponential dissipative and l₂ - l_∞ filtering problems for discrete-time switched neural networks (DSNNs) including time-delayed states. By introducing a novel discrete-time inequality, which is a discrete-time version of the continuous-time Wirtinger-type inequality, we establish new sets of linear matrix inequality (LMI) criteria such that discrete-time filtering error systems are exponentially stable with guaranteed performances in the exponential dissipative and l₂ - l_∞ senses. The design of the desired exponential dissipative and l₂ - l_∞ filters for DSNNs can be achieved by solving the proposed sets of LMI conditions. Via numerical simulation results, we show the validity of the desired discrete-time filter design approach.

Fault Estimation Observer Design for Discrete-Time Takagi-Sugeno Fuzzy Systems Based on Homogenous Polynomially Parameter-Dependent Lyapunov Functions

This paper investigates the problem of robust fault estimation (FE) observer design for discrete-time Takagi-Sugeno fuzzy systems via homogenous polynomially parameter-dependent Lyapunov functions. First, a novel framework of the fuzzy FE observer is established with the help of a maximum-minimum-priority-based switching mechanism. Then, for every activated switching case, a targeted result is achieved by the aid of exploring an important property of improved homogenous polynomials. Since the helpful information of the underlying system can be duly updated and effectively utilized at every sampled point, the conservatism of previous results is availably reduced. Furthermore, the proposed result is further improved by eliminating those redundant terms of the introduced matrix-valued variables. Simulation results based on a discrete-time nonlinear truck-trailer model are provided to show the advantages of the theoretic result that is developed in this paper.

Stability of Markovian Jump Generalized Neural Networks With Interval Time-Varying Delays

This paper examines the problem of asymptotic stability for Markovian jump generalized neural networks with interval time-varying delays. Markovian jump parameters are modeled as a continuous-time and finite-state Markov chain. By constructing a suitable Lyapunov-Krasovskii functional (LKF) and using the linear matrix inequality (LMI) formulation, new delay-dependent stability conditions are established to ascertain the mean-square asymptotic stability result of the equilibrium point. The reciprocally convex combination technique, Jensen's inequality, and the Wirtinger-based double integral inequality are used to handle single and double integral terms in the time derivative of the LKF. The developed results are represented by the LMI. The effectiveness and advantages of the new design method are explained using five numerical examples.

A PD-Like Protocol With a Time Delay to Average Consensus Control for Multi-Agent Systems Under an Arbitrarily Fast Switching Topology

This paper is concerned with the problem of average consensus control for multi-agent systems with linear and Lipschitz nonlinear dynamics under a switching topology. First, a proportional and derivative-like consensus algorithm for linear cases with a time delay is designed to address such a problem. By a system transformation, such a problem is converted to the stability problem of a switched delay system. The stability analysis is performed based on a proposed Lyapunov-Krasoversusii functional including a triple-integral term and sufficient conditions are obtained to guarantee the average consensus for multi-agent systems under arbitrary switching. Second, extensions to the Lipschitz nonlinear cases are further presented. Finally, numerical examples are given to illustrate the effectiveness of the results.