State Feedback Controller Gain Research Articles

Further analysis of stabilization of neutral type singular systems with mixed time‐varying delays and multiple random states

AbstractIn this paper, the stabilization problem of neutral type singular systems (NTSSs) with mixed time‐varying delays and multiple random states is further analyzed. Lyapunov Krasovskill functional (LKF) and generalized Itô formula, together with linear matrix inequality (LMI), are used to represent a new stability criterion for NTSSs with mixed time‐varying delays (MTVDs) in multiple random states. First, the regularity, impulse free, and stochastic stability of the system are satisfied by designing a state feedback controller (SFC). Second, on the basis of Leibniz Newton formula, the stability criterion is also feasible by integrating zero value equation technology, and then combined with singular decomposition, the gain of SFC is obtained. Finally, our paper is a further analysis of the latest literature, so two numerical examples are used to verify the feasibility and effectiveness of this method.

Dynamic event-triggered consensus control for nonlinear multi-agent systems under DoS attacks.

In this paper, we investigated leader-following consensus control for nonlinear multi-agent systems (MASs) experiencing denial-of-service (DoS) attacks. We proposed a distributed control strategy incorporating an adaptive scheme and a state feedback control gain to eliminate the effects of system nonlinear dynamics and uncertainties. In addition, we introduced a dynamic event-triggered control (DETC) to minimize the utilization of communication resources. Finally, we provided simulation results to show the validity of the proposed approach.

Asynchronous Switching Control of Discrete Time Delay Linear Switched Systems Based on MDADT

Ideally, switching between subsystems and controllers occurs synchronously. In other words, whenever a subsystem requires switching, its corresponding sub-controller will be promptly activated. However, in reality, due to network delays, system detection, etc., the activation of candidate controllers frequently lags, which causes issues with asynchronous switching between controllers and subsystems. This asynchronous switching problem may affect system performance and even make the system unstable because the state between the subsystem and the controller may be inconsistent, resulting in the controller not being able to control the subsystem correctly. To keep the system stable while using asynchronous switching, this work suggests an asynchronous control technique for a class of discrete linear switching systems with time delay based on the mode-dependent average dwell time (MDADT). First, we construct a state feedback controller and establish a closed-loop system. In the asynchronous and synchronous intervals of subsystems and controllers, different Lyapunov functions are selected, and sufficient conditions for exponential stability and the H∞ performance of the closed-loop system under asynchronous switching are obtained. In addition, using the MDADT switching strategy, the relevant parameters of each subsystem are designed and the corresponding state–feedback controller gain matrix can be obtained. Finally, a switching system with three subsystems is shown. The approach is confirmed by simulating it using the average dwell time (ADT) switching strategy and the MDADT switching strategy separately.

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.

New Development in Quadratic L2 Performance of Switched Uncertain Stochastic Systems

Global quadratic stability and L2 performance in probability (quadratic stability and L2 gain γ in probability: abbreviated as GQL2(γ)-P) is studied for switched systems consisting of linear stochastic subsystems with norm-bounded uncertainties. Under the assumption that there is no single subsystem achieving GQL2(γ)-P, it is shown that if there exists a convex combination of subsystems achieving GQL2(γ)-P, then a state-dependent switching law, based on the convex combination of subsystems, is proposed under which the switched system achieves GQL2(γ)-P. Then, the discussion is extended to the case involving state feedback controller gain. A numerical example and the application to DC–DC boost converters are provided to demonstrate the proposed design condition and the algorithm.

Positiveness and Finite-Time Control of Dual-Switching Poisson Jump Networked Control Systems With Time-Varying Delays and Packet Drops

This article studies the stochastically finite-time <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$L_{2}$</tex-math></inline-formula> control problem for the time-varying delay positive dual-switching Poisson jump networked control systems (TVD-PDSPJ-NCSs) with packet drops. A key issue is that the TVD-PDSPJ-NCSs do not specify the jumping sequence of working processing modes. First, the TVD-PDSPJ-NCSs are modeled for the first time by considering the non-negative total amount of data, work processing modes jumping, and data transmission channel switching of the NCSs. Then, a proper finite-time state feedback controller is designed for the TVD-PDSPJ-NCSs so that the closed-loop dual-switching Poisson jump NCSs are positive, stochastically finite-time bounded, and fulfill the specified <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$L_{2}$</tex-math></inline-formula> disturbance attenuation performance simultaneously. By means of stochastic Lyapunov–Krasovskii functional methods, some sufficient conditions in the form of linear matrix inequalities are derived to obtain the finite-time state feedback controller gain. Furthermore, the optimal solution of the switching law is obtained such that the regulator can select the optimal data transmission channel according to the degree of packet drops. Finally, an application example is given to show the feasibility and validity of the proposed results.

Finite-time reliable sampled-data control for fractional-order memristive neural networks with quantisation

ABSTRACT This paper addresses the reliable finite-time stabilisation problem for a class of fractional-order memristor neural networks under sampled-data controller influenced by the quantisation signal and actuator failures. Precisely, the framework of observer has been initiated for estimating unmeasured state and remunerate the actuator faults with nonlinearities in the controller. Precisely, quantiser is incorporated in the network can reduce the process of transmitting data. Subsequently, activation function approach bringing together with traditional indirect Lyapunov theory endows some sufficient conditions in the frame of linear matrix inequalities to assure the finite-time stabilisation criterion for the addressed neural networks under the proposed reliable sampled-data control. Explicitly, the state feedback control and observer gain matrices are attained by solving the developed linear matrix inequalities. Convincingly, two numerical simulations are explored to substantiate the excellence and potentiality of the developed control law.

Trust-based fault detection and robust fault-tolerant control of uncertain cyber-physical systems against time-delay injection attacks

Control systems need to be able to operate under uncertainty and especially under attacks. To address such challenges, this paper formulates the solution of robust control for uncertain systems under time-varying and unknown time-delay attacks in cyber-physical systems (CPSs). A novel control method able to deal with thwart time-delay attacks on closed-loop control systems is proposed. Using a descriptor model and an appropriate Lyapunov functional, sufficient conditions for closed-loop stability are derived based on linear matrix inequalities (LMIs). A design procedure is proposed to obtain an optimal state feedback control gain such that the uncertain system can be resistant under an injection time-delay attack with variable delay. Furthermore, various fault detection frameworks are proposed by following the dynamics of the measured data at the system's input and output using statistical analysis such as correlation analysis and K-L (Kullback-Leibler) divergence criteria to detect attack's existence and to prevent possible instability. Finally, an example is provided to evaluate the proposed design method's effectiveness.

Minimum variance control of chaos in a hyperchaotic memristor based oscillator using online particle swarm optimization

This paper introduces a new hyperchaotic oscillator base on a new boundary-restricted Hewlett-Packard memristor model. Firstly, the complex system is designed based on a memristor-based hyperchaotic real system, and its properties are analyzed by means of Lyapunov exponents, Lyapunov dimension and phase portraits diagrams. Secondly, a simple feedback control based on the minimum variance control technique is designed to stabilize the hyperchaotic oscillator system, which is one of the new developed approaches for controlling the chaos in high-dimensional hyperchaotic systems. In this method, the time series variance is considered for designing and calculating the state feedback control gain. Furthermore, the state feedback control is designed so that to minimize the variance as a cost function, followed by developing an online optimization technique using the particle swarm optimization method in order to calculate the state feedback control based on the minimum variance strategy. Then, the application of this method is examined on a hyperchaotic memristor-based oscillator. Finally, the sensitivity of the proposed method is evaluated in different initial conditions that greatly influence the hyperchaotic dynamics. Considering that the optimization is online, simulation results show highly good effectiveness of the presented technique in controlling the chaos in high-dimensional hyperchaotic oscillators

Robust stability analysis of uncertain fractional order neutral-type delay nonlinear systems with actuator saturation

In this paper, we study the robust stability of uncertain fractional order (FO) nonlinear systems having neutral-type delay and input saturation. From the Lyapunov–Krasovskii functional, sufficient criteria on asymptotic robust stability of such FO systems with the help of linear matrix inequalities are specified to compute the gain of state-feedback controller. An optimization is also derived using the cone complementarity linearization method for finding the controller gains subject to maximizing the domain of attraction. The main results are confirmed via numerical examples.

Robust local stabilization of discrete time-varying delayed state systems under saturating actuators

This paper deals with discrete time-varying systems with state-delayed and saturating actuators. A robust state feedback control gain is designed through convex methods ensuring the local stability of the time-varying system with interval time-varying state delay. The estimate of the set of admissible initial conditions is characterized by three convex sets allowing less conservative estimates. Through two numerical examples, we compare our approach with others in the literature and illustrate the better behavior of the proposed methods.

Optimal state feedback controller for three tank cylindrical interacting system using Grey Wolf Algorithm

This article presents, optimal state feedback controller for three tank cylindrical interacting system was proposed to maintain set point in the tank. Grey Wolf Optimization Algorithm used to describe the optimal tuning of state feedback controller. Generally, optimal state feedback controller reduces fluctuation state with lowest control energy. Gain of the optimal state feedback controller used to reduce the fluctuation state to minimum value. By adding integrator, the measured value of the tank moves towards set point. Linear quadratic regulator is a multivariable state feedback control and it depends on the state of the system. The controller performance enhanced by suitable range of Q and R value. The proposed technique uses heuristic algorithm for tuning the state feedback gain directly. The results show that the developed control technique given better performance.

Robust gain-scheduling static output-feedback [formula omitted] control of vehicle lateral stability with heuristic approach

This paper presents a velocity-dependent static output-feedback control method to improve the vehicle lateral stability and handling performance. The uncertainties of longitudinal velocity, tire cornering stiffness and actuator saturation are taken into account. Considering the unmeasurable state in practice, a robust gain-scheduling output-feedback H∞ controller is designed based on the measurable velocity. By employing a two-stage heuristic approach, the output-feedback controller gain is obtained based on the state-feedback controller gain, which would be more favorable in application. The simulation results with two steering maneuvers indicate the effectiveness of the proposed method.

Model Based Robust Predictive Control of Ship Roll/Yaw Motions with Input Constraints

A robust H∞-type state feedback model predictive control (H∞-SFMPC) with input constraints is proposed to optimize the control performance during the ship sailing. Specifically, the approach employed in this paper is able to optimize the closed-loop performance with respect to an H∞-type cost function which predicts the system performance based on the actual model instead of the ideal model. As a result, the effect caused by disturbances is attenuated. The state feedback control gain for the control input of the rudder-fin joint roll/yaw control system is obtained by solving a constrained convex optimization problem in terms of linear matrix inequalities. Simulations are carried out, which reveal that the proposed approach has outstanding control performance. Furthermore, it is found that the approach also has significant robustness with respect to parameter uncertainties.

Event-Triggered Control for Switched Systems in Network Environments

This paper is concerned with event-triggered control for a switched system in network environments. Firstly, a novel event-triggering communication scheme with switching features is proposed. The switching features are taken into full consideration to guarantee the current sampled data to be transmitted if a switch occurs between the last sampling instant and the current sampling instant. The newly proposed event-triggering scheme is advantageous in dealing with switched networked control systems. Secondly, under the event-triggering scheme, an asynchronously switched time-delay system model is established by taking into account effects of network-induced delays. Finally, a mode-dependent state feedback controller gain and event generator parameters co-design method is proposed for the asynchronously switched time-delay system. System performance analysis demonstrates the effectiveness of the proposed methods.

A Robust Hybrid of a Feedback Linearization Technique and an Interval Type-2 Fuzzy Control System for the Flapping Angle Dynamics of a Biomimetic Aircraft

We introduce a new configuration of a robust and adaptive autopilot system for a model-scale flapping-wing aircraft. The system is specifically designed to achieve high performance flapping angle tracking in the face of large uncertainties. To describe the dynamics of the system, we leverage the benefits of both first principle modeling and data-driven approach (system identification technique). We introduce a high-performance robust and adaptive nonlinear control system by means of a feedback linearization (FL) technique, supported with an interval Type-2 fuzzy system due to its ability to accommodate the footprint-of-uncertainties (FoUs). While the first stage of our nonlinear control system is to cancel some predictable nonlinearities using an FL technique, the second phase of control is to accommodate the existing uncertainties in the system by way of an interval Type-2 fuzzy control technique, e.g., due to imperfect cancelation and modeling errors. This way, the stability and the robustness of the closed-loop control system can be guaranteed. We quantify the relative merit of our hybrid control system with respect to an FL technique, supported with a fixed gain state feedback controller and a Type-1 fuzzy system. Lastly, we also conduct stability analysis of the overall closed-loop control system.

Resilient Event-Triggered Controller Synthesis of Networked Control Systems Under Periodic DoS Jamming Attacks.

In this paper, the event-based controller synthesis problem for networked control systems under the resilient event-triggering communication scheme (RETCS) and periodic denial-of-service (DoS) jamming attacks is studied. First, a new periodic RETCS is designed under the assumption that the DoS attacks imposed by power-constrained pulsewidth-modulated jammers are partially identified, that is, the period of the jammer and a uniform lower bound on the jammer's sleeping periods are known. Second, a new state error-dependent switched system model is constructed, including the impacts of the RETCS and DoS attacks. According to this new model, the exponential stability criteria are derived by using the piecewise Lyapunov functional. In these criteria, the relationship among DoS parameters, the triggering parameters, the sampling period, and the decay rate is quantitatively characterized. Then, a criterion is also proposed to obtain the explicit expressions of the triggering parameter and event-based state feedback controller gain simultaneously. Finally, the obtained theoretical results are verified by a satellite yaw-angles control system.

Observer-based [formula omitted] control design for singular switching semi-Markovian jump systems with random sensor delays

This paper studies the problem of H∞ control design for a class of singular switching semi-Markovian jump systems, in which the transition rates of jumping process are uncertain and the output measurements suffer from random sensor delays. Firstly, a Luenberger observer is designed to estimate the system state components, based on which an error dynamic is obtained. Then, stochastic stability analysis for the overall closed-loop system is given based on the upper and lower bounds of transition rates. Further, the state feedback controller gain matrices are given by solving a set of sufficient conditions in terms of strict linear matrix inequalities (LMIs), which also guarantee the closed-loop system to be stochastically stabilizable and has a prescribed H∞ performance index γ. Finally, a numerical example is provided to verify the effectiveness of the obtained result.

Resilient load frequency control design: DoS attacks against additional control loop

Resilient load frequency control (LFC) design problem is concerned for a multi-area power system with uncertainty and physical constraint under denial-of-service (DoS) attacks and transmission delay. LFC scheme consists of a local PI control loop and additional control loop to be designed. PI control loop is subjected to constant transmission delay while additional control loop is subjected to DoS attacks. We characterize DoS attacks by attack frequency, uniform lower bound of sleep interval and uniform upper bound of attack interval. Considering DoS attacks and time delay, we describe LFC system dynamic by a switched delay system model. Further, a stability criterion is derived by using delay system method and switched system method. Under the criterion, a design method is presented to solve state feedback control gain. Finally, numerical simulations are given to verify the validness of our proposed design method.

Stabilization of Discrete-Time Delayed Systems in Presence of Actuator Saturation Based on Wirtinger Inequality

This paper examines the stability analysis of discrete-time control systems particularly during the event of actuator saturation and time-varying state delay. With the help of Wirtinger inequality along with Lyapunov-Krasovskii functional gain of state feedback controller is determined for stabilization of above system. The saturation nonlinearity is represented in the terms of convex hull. A new linear matrix inequality (LMI) criterion is settled with reciprocally convex combination based inequality which is dependent on delay. The proposed criterion is less conservative in concern to increase the delay bound and a controller is also simulated for real time problem of missile control system in this paper. It is also attained that projected stability criterion is less conservative compared to other outcomes. Furthermore, an optimization procedure together with LMI constraints has been proposed to maximize the attraction of domain.