Linear Matrix Inequality Technique Research Articles

Investigation on the stability of networked-control integrated energy systems for frequency regulations

This paper presents the stability analysis of integrated energy systems under network environment. The networked-control integrated energy systems involve time-delay in the control loop. These time-delays are time-invariant or time-varying in nature. Further, it affects the stability and dynamic performance of the integrated energy systems. In this paper stability analysis of networked-control integrated energy systems are done using Lyapunov–Krasovskii functional and linear matrix inequality techniques. The maximum amount of time-delay that establishes the stability of the integrated energy systems is determined and controller is designed with concern to the time-delay. The effect of electric vehicles and battery energy storage system in stability delay margins of integrated energy systems is also addressed and the numerical simulations are done to verify the effectiveness of the presented results.

Design of a robust and practicable SSI damping controller using H[formula omitted] technique for series compensated DFIG-based wind farms

This paper designs a robust and practicable subsynchronous interaction (SSI) damping controller using H∞ technique for the safe operation of series capacitor compensated wind farms (WFs) with doubly-fed induction generator (DFIG) wind turbines (WTs). Mixed sensitivity control design together with pole placement are formulated into a set of linear matrix inequalities (LMIs) to obtain the controller parameters. The LMI technique allows to include both desirable frequency and time domain specifications. The proposed damping controller is integrated into the WT controller (WTC) and receives the DFIG converter currents as inputs. The implementation of the proposed controller does not require any communication links between the WTs and WF secondary control layer. The controller output signals are applied to the inner control loops of DFIG converters and are dynamically limited for the desired fault-ride-through (FRT) performance. The effectiveness of the damping controller is verified through detailed electromagnetic transient (EMT) simulations. In these simulations, the complete medium-voltage (MV) collector grid is modeled with all details, and it is assumed that the wind speed at the location of each turbine follows a Gaussian distribution. The collected results confirm the accuracy of the modeling of the entire WF as an aggregated WT with the average wind speed.

Exponential Consensus of Multi-Agent Systems under Event-Triggered Impulsive Control with Actuation Delays.

This paper investigates the exponential consensus problem for a class of nonlinear leader-following multi-agent systems using impulsive control, where impulses are generated by the event-triggered mechanism and are subjected to actuation delays. It is proved that Zeno behavior can be avoided, and by employing the linear matrix inequality technique, some sufficient conditions for realizing exponential consensus of the considered system are derived. Actuation delay is an important factor affecting the consensus of the system, and our results show that increasing the actuation delay can enlarge the lower bound of the triggering interval, while it harms the consensus. To demonstrate the validity of the obtained results, a numerical example is provided.

Robust controller for artificial pancreas for patients with type-1 diabetes

The target of this paper is to design a simple and an efficient controller for artificial pancreas (AP) system for blood glucose (BG) regulation in type-1 diabetic mellitus (T1DM) patient. Bergman’s intravenous model is chosen for the controller design as the model is minimum ordered model of T1DM patient. A multi-objective output feedback controller has been designed for AP system considering robustness, disturbance rejection, and transient criterion. Considering H∞, pole-placement, and H2 constraints, a control algorithm has been developed and has been solved using linear matrix inequality (LMI) technique. As a testing platform of the intravenous model-based designed controller, UVa/Padova T1DM metabolic simulator has been chosen which uses subcutaneous insulin delivery method. The controller has been tested in the presence of unannounced meal disturbances. Experimental results show that the controller regulates BG level very efficiently with lesser amount of insulin and avoids hypoglycemia effect. In the presence of external noises like glucose sensor noise and insulin pump error, the robustness of the controller has been checked. The performance of the controller has been compared with compound internal model control (IMC) strategy reported earlier for same meal scenario. The designed multi-objective controller gives better performance metrices than compound IMC controller.

Adaptive event‐triggered pinning synchronization control for complex networks with random saturation subject to hybrid cyber‐attacks

SummaryThis research is concerned with the problem of pinning based output synchronization control for a complex networks with random saturation vulnerable to hybrid cyber‐attacks via an adaptive event‐triggered scheme (AETS). The output synchronization error systems are subject to suffer from deception attacks, replay attacks, and denial‐of‐service attacks. A novel hybrid cyber‐attack model is first constructed to integrate the three kinds of attacks into a synchronization of complex network. AETSs based on output synchronization errors with the consideration of hybrid cyber‐attacks, have been proposed to reduce the burden of communication. A pinning control strategy is used to decrease the control signal's input. By constructing a Lyapunov functional and using the linear matrix inequality technique, sufficient conditions are provided to ensure the output synchronization error system. Finally, a numerical simulation results are developed to illustrate the efficacy of the proposed theoretical methodology.

A novel [formula omitted] control for T-S fuzzy systems with transform matching membership functions

This article studies H∞ optimization issue of Takagi-Sugeno (T-S) fuzzy systems with an improved transform matching membership functions (MFs) approach. Different from existing transform matching MFs control method, a polynomial disassembling strategy is first proposed for T-S fuzzy systems. Then, combining with parameterized linear matrix inequality (LMI) technique which can remove the inequality constraints between the MFs in systems and fuzzy controllers, sufficient conditions are presented to maintain asymptotic stability and desired H∞ performance for studied plants. Afterwards, a novel MFs online optimization algorithm is proposed for the first time to automatically adjust the values of scaling and bias parameters so as to realize better H∞ performance. In contrast to the traditional control using improved matching MFs, the practical behavior of disturbance attenuation index is reduced efficiently. Additionally, the proposed MFs online optimization algorithm is capable of sustaining the desired H∞ performance when the disturbance channels exist modeling errors, i.e., the practical disturbance attenuation index γ is still less than the preset value. For guaranteeing the convergence of cost function, sufficient condition is obtained based upon Lyapunov stability theory. Finally, two demonstrative simulations are presented to confirm the advantages and benefits of the novel MFs online optimization control strategy.

Evaluation of Ride Performance of Active Inerter-Based Vehicle Suspension System with Parameter Uncertainties and Input Constraint via Robust H∞ Control

In this study, we investigate a robust H∞ controller for a quarter-car model of an active inerter-based suspension system under parameter uncertainties and road disturbance. Its main objective is to improve the inherent compromises between ride quality, handling performance, suspension stroke, and energy consumption. Inerters have been extensively used to suppress unwanted vibrations from various kinds of mechanical structures. The advantage of inerter is that the realized ratio of equivalent mass (inertance relative to the mass of the primary structure) is greater than its actual mass ratio, resulting in higher performance for the same effective mass. First, the dynamics and state space of the active inerter-based suspension system were achieved for the quarter-car model with parameter uncertainties. In order to attain the defined objectives, and ensure that the closed-loop system achieves the prescribed disturbance attenuation level, the Lyapunov stability function, and linear matrix inequality (LMI) techniques have been utilized to satisfy the robust H∞ criterion. Furthermore, to limit the gain of the controller, some LMIs have been added. In the case of feasibility, sufficient LMI conditions by solving a convex optimization problem afford the stabilizing gain of the robust state-feedback controller. According to numerical simulations, the active inerter-based suspension system in the presence of parameter uncertainties and external disturbance performs much better than both a passive suspension with inerter and active suspension without inerter.

Event-triggered H∞ robust filtering for nonlinear semi-Markov switching systems

This paper studies the filtering problem for a class of discrete-time semi-Markov switching repeated scalar nonlinear systems with an event-triggered scheme. Considering the limitation of bandwidth, the mode-dependent event-triggered mechanism is introduced to determine whether the currently sampled sensor data is transmitted to the filter, in which the parameters of the event generator depend on the system mode. By means of a constructed time-varying Lyapunov function, the two stages of the systems jump instant and mode residence are analysed, and a linear matrix inequality technique is used to ensure the mean-square stability and performance of the filter error system. Accordingly, the co-design method of the mode-dependent time-varying filter and the event-triggered mechanism is derived for semi-Markov switching systems. Finally, a numerical simulation is given to illustrate the effectiveness and feasibility of the method proposed in this paper.

Leader-following consensus of semi-Markov jump nonlinear multi-agent systems under hybrid cyber-attacks

In this paper, the leader-following consensus issue is investigated for a class of nonlinear multi-agent systems with semi-Markov parameters subject to hybrid cyber-attacks. A semi-Markov chain is adopted to describe the variation of switching topologies caused by the complexity of the environment and makes the studied problem more general. Hybrid cyber-attacks consisting of denial-of-service attacks and deception attacks are described with the help of two groups of Bernoulli sequences which are assumed to be independent of each other. On this basis, a sufficient condition for the stability of the consensus error system is established by using linear matrix inequality techniques. Finally, the validity of the results obtained is verified by two numerical examples.

Event-Based Pinning Synchronization Control for Discrete-Time Delayed Complex Cyber-Physical Networks Under All-Around Attacks

This paper is concerned with the problem of pinning synchronization control for a class of nonlinear discrete-time delayed complex cyber-physical networks under all-around attacks. To handle the all-around attacks, a constrained hybrid attacks model is established, which incorporates the pattern feature of false data injection attacks and physical attacks. By utilizing the Lyapunov stability theory and the linear matrix inequality technique, a novel dynamic event-triggering pinning synchronization control scheme is developed to cope with the synchronization control task. Subsequently, sufficient conditions are obtained to guarantee that the closed-loop error dynamics are ultimately exponentially bounded. Furthermore, the design procedure of the synchronization controller is presented for the considered complex cyber-physical networks subject to all-around attacks. Finally, an illustrative example is delivered to demonstrate the effectiveness of the proposed method.

Sampling-Position-Based Event-Triggering Consensus of Nonlinear Second-Order Agents

In this brief, we study the consensus seeking problems for second-order nonlinear multi-agent systems with unavailable velocity measurements. An event-triggered control strategy is developed based on causally sampled position data only, which can reduce the controller update frequencies significantly and avoid continuous communications effectively. Some sufficient conditions for achieving consensus are obtained in light of Lyapunov-Krasovskii stability theory and linear matrix inequality technique.

Distributed Filtering Under Constrained Bit Rate Over Wireless Sensor Networks: Dealing With Bit Rate Allocation Protocol

This article is concerned with the distributed filtering issue for linear discrete-time systems under bounded noises and constrained bit rate over wireless sensor networks. The communication between different sensor nodes is implemented via a wireless digital communication network with limited bandwidth. A bit rate constraint, which is subject to the so-called bandwidth allocation strategy, is placed to quantify the effect of the network bandwidth on the distributed filtering performance. An improved coding–decoding procedure is proposed to enable each node to decode messages from its neighbor nodes. Based on this procedure, a decoded-innovation-based distributed filtering scheme is put forward and a sufficient condition is established to ensure that the filtering error dynamics is ultimately bounded. Subsequently, a relationship between the bit rate and certain specific filtering performance is discovered. The desired parameters of the distributed filter are determined via solving two optimization problems whose objectives are actually the filtering performance indices including the smallest ultimate bound and the fastest decay rate. Furthermore, the codesign issue of the bit rate allocation protocol and the filter gain is converted into the mixed integer nonlinear programming problem, which is solved by means of the particle swarm optimization algorithm and the linear matrix inequality technique. Finally, numerical simulations on three scenarios are provided to verify the validity of the proposed distributed filtering approach.

Event-Triggered Quantized Input-Output Finite-Time Synchronization of Markovian Neural Networks

This paper addresses the event-triggered input-output finite-time mean square synchronization for uncertain Markovian jump neural networks with partly unknown transition rates and quantization. Considering the limited network resources, an event-triggered technique and a logarithmic quantizer are both provided. The error system model with uncertainty is established in the unified framework. Then, based on Lyapunov functional approach, interesting results are presented to guarantee the properties of the input-output finite-time mean square synchronization for the error systems. Furthermore, some solvability conditions are induced for the desired input-output finite-time mean square synchronization controller under linear matrix inequality techniques. Eventually, the theoretical finding’s efficiency is shown by an example.

Data-based [formula omitted]gain optimal control for discrete-time system with unknown dynamics

This paper considers the L2gain optimal problem for a class of discrete-time linear time-invariant with state-disturbance feedback controller and unknown system dynamic. Firstly, for a given stabilizing control policy, we establish the relation between the L2gain and a sequence of lower triangle Toeplitz matrices. Meanwhile, we show that the upper bound of optimal L2gain is proportional to the linear correlation degree between the input and disturbance matrices. Secondly, to overcome the obstacle arising from the unknown system dynamics, a data-based reinforcement learning scheme is developed for the optimal control policy by using linear matrix inequality technique and Q-learning with policy iteration. Under certain conditions, we prove that either the reinforcement learning process ends in a finite number of iterations, or the L2gain sequence is strictly monotonically convergent along the iteration axis provided that the disturbance data set can fully activate the closed-loop system. Finally, simulations are given to illustrate the effectiveness of our findings.

An improved model-free adaptive control for nonlinear systems: An LMI approach

This paper proposes two model-free adaptive control (MFAC) schemes by using the linear matrix inequality (LMI) approach for the single-input single-output (SISO) and multi-input multi-output nonlinear (MIMO) systems, respectively. For each control scheme, with the aid of the dynamic linearization technique, the nonlinear system is transformed into an equivalent linear data model. In such a transformation, the nonlinear characteristic of systems is compressed into a time-varying parameter. Then, with the help of the introduction of the observer method, the tracking control problem can be converted into an optimization problem and the controller parameters can be obtained by using the LMI technique. This conversion cannot only reduce the complexity of the stability analysis but also find the appropriate controller parameters, especially for the MIMO case. Finally, three examples with comparisons are provided to illustrate the validity of the devised MFAC schemes.

Resilient event-triggered stabilization for uncertain Markovian jump delayed neural networks under time-window-based aperiodic DoS attacks

In this paper, the problem of robustly stable in mean square of uncertain Markovian jump neural networks (UMJNNs) with time-varying delays under time-window-based aperiodic denial-of-service (DoS) attacks is investigated. First, a new class of portrayal is proposed for DoS attacks, that is, fixed time-window-based non-periodic DoS attacks. In addition, a resilient event-triggered communication scheme (RETCS) is designed between sensors and controllers to reduce “unnecessary” waste of network resources under the proposed non-periodic DoS attack. Then, a new model of UMJNNs with time-varying delays considering non-periodic DoS attacks is developed on this basis. Second, a new single Lyapunov function is constructed in this paper for non-periodic DoS attacks. In addition, the stability criteria of UMJNNs with time-varying delays are obtained based on Lyapunov stability theory and the linear matrix inequality technique. Then, the criterion for co-designing the trigger parameters of RETCS and the gain matrix of the controller is proposed. Finally, the validity of the obtained result is illustrated by two examples.

Sliding-Mode Synchronization Control of Complex-Valued Inertial Neural Networks With Leakage Delay and Time-Varying Delays

This work explores the synchronization problem of two nonidentical complex-valued inertial neural networks (CVINNs) considering time-varying delays, leakage delay, and external disturbances. The entire analysis does not use reduced-order conversion, nor does it involve the separation of real and imaginary parts, but directly focuses on the original system. First, an integral sliding-mode surface suitable for the system is proposed. Second, the efficient sliding-mode control laws are designed, under which the state trajectories of the closed-loop dynamic error systems can be driven onto the predefined sliding-mode surface in finite time. Then, not requiring the time-varying delays to be differentiable, by constructing innovative Lyapunov–Krasovskii functionals, the synchronization criteria are obtained in the forms of the linear matrix inequality techniques. Eventually, for the systems with different types of activation functions, the corresponding numerical verification and comparison are carried out.

Dissipative Sliding-Mode Synchronization Control of Uncertain Complex-Valued Inertial Neural Networks: Non-Reduced-Order Strategy

This study investigates the dissipative synchronization of uncertain complex-valued inertial neural networks with external disturbances using sliding mode control (SMC). In the absence of both variable substitution as well as the equivalent transformations of real- and complex-valued systems, this study focuses directly on the original complex-valued inertial system. First, a suitable integral switching surface (SS) function is proposed. Second, by constructing innovative Lyapunov-Krasovskii functionals and applying the Wirtinger-based integral inequality and reciprocally convex approach, a synchronization criterion is derived on the basis of the linear matrix inequality technique to ensure that the sliding mode dynamics are stable and dissipative. Then, an SMC law and an adaptive SMC law are designed, and the accessibility analysis of the predefined SS is provided. Numerical verifications as well as the superiority and practicality analysis of the proposed approach are provided through four examples.

Stability of T-S fuzzy system under non-fragile sampled-data [formula omitted] control using augmented Lyapunov-Krasovskii functional

This article is concerned with the non-fragile sampled-data control for T-S fuzzy system with parameter uncertainties. Firstly, a novel augmented Lyapunov-Krasovskii functional with sufficient sampled-data information is constructed. And a novel h(t)-depended exponential stability criterion with H∞ performance is gotten by reciprocally convex matrix inequality. Beyond that, compared with the existing methods, the gain matrices for non-fragile sampled-data controller expected are less conservative by linear matrix inequality technique. And numerical examples are provided to support the viability and validity of the results.

Special issue on “Optimal design and operation of energy systems”

Special issue on “Optimal design and operation of energy systems”