Memory State Feedback Research Articles

L2-gain analysis and fault-tolerant control of nonlinear discrete time-delay saturated switched systems with memory state feedback

For nonlinear discrete time-delay saturated switched systems with memory feedback, the problem of actuator failure with external disturbances is studied. First, we propose a sufficient condition for the existence of a fault-tolerant state feedback law with memory by using the switched Lyapunov function (SLF) strategy, which ensures that the closed-loop system has a maximum tolerant disturbance capacity by solving the optimization problem. Then, the minimum upper bound on the [Formula: see text]-gain is estimated by solving the optimization problem. Finally, the reliability of the proposed method is verified by examples.

A new [formula omitted] control method of singular time-delay systems based on a variable memory state feedback

This paper is concerned with the H∞ control problem of singular time-delay systems. A variable memory state feedback is established with state decomposition. It is verified that this feedback including the traditional memory and memoryless state feedbacks as special cases, and thus it is more general than these existing feedback strategies Based on the proposed feedback, a new H∞ control method with better performance level is derived. Moreover, the yielded computational complexity is lower. The superiority is confirmed by two given examples.

Robust stabilization for uncertain discrete–time singular Markovian jump systems with time–varying delays

AbstractThe stabilization problem for uncertain discrete‐time singular Markovian jump systems (DSMJSs) with time‐varying delays is comprehensively covered in this paper. An updated Lyapunov–Krasovskii functional is presented via a discrete state decomposition method. With the help of this constructed Lyapunov–Krasovskii functional, some delay‐ and mode‐dependent sufficient conditions for the open‐loop DSMJSs are derived. Based on these circumstances, a memory mode‐dependent state feedback control is used to create a closed‐loop DSMJS with parameter uncertainties that is regular and causal. And then, the stochastically admissible conditions are attained. Through the exact calculation of each decomposition component for the designed memory state feedback controller, the intended memory state feedback controller settings are determined. It should be mentioned that the algorithm suggested in this article expands the controller design's feasibility and flexibility. The numerical results show how the approach is superior to previous ones, and the given results are less conservative.

A memory state-feedback controller via random pocket dropouts for multi-agent systems with external disturbance

This study explores the challenge of achieving consensus in multi-agent systems (MASs) when facing the random packet dropouts and disturbances. It employs memory state-feedback control (MSFC) in the context of undirected graphs and specified leader agents. The analysis focuses on mean square consensus, considering MASs within strongly connected networks or networks with undirected spanning trees. The MSFC approach is developed to ensure asymptotic consensus despite packet dropouts and also to reduce the impact of disturbances. Specifically, the consensus analysis leverages the Lyapunov-Krasovskii functional (LKF) framework, and the necessary conditions for implementing the proposed MSFC are established using linear matrix inequalities (LMIs). The system, augmented with an H ∞ attenuation level is guaranteed to achieve asymptotic mean-square stability according to the provided criteria. In conclusion, two examples are provided to illustrate the effectiveness and practicality of the proposed control mechanism.

A novel memory stabilization controller design for descriptor Markovian jump systems with time-varying delays

This paper is focused on the stochastic stability and controller design of descriptor Markovian jump systems with time-varying delays. For achieving this goal, systems are decomposed into differential-algebraic equations firstly. A modified mode-dependent Lyapunov-Krasovskii functional (LKF) and a memory state feedback controller are constructed on the basis of the state decomposition. Then, combining the auxiliary functions integral inequality and the extended reciprocally convex matrix inequality (ERCMI), an ameliorative stochastic stability criterion is obtained. Based on this novel stability condition, the designed controller is used to make sure the closed-loop systems are stochastically stable. Finally, the effectiveness of presented results is confirmed with some numerical examples.

Synchronization of complex dynamical networks subjected to actuator faults and periodic scaling attacks using probabilistic time-varying delays

In this paper, the synchronization problem of complex dynamical networks (CDNs) subjected to actuator faults and periodic scaling attacks using probabilistic time-varying delays is investigated. In order to handle the fault effects in actuators of proposed complex networks, an actuator fault model is considered. The major objective of this paper is to construct a memory state feedback controller with time-varying actuator faults that are asymptotically synchronized in the mean square sense to defend against periodic scaling attacks. By establishing suitable Lyapunov-Krasovskii functionals and applying Wirtinger-based integral inequality, sufficient conditions are derived in terms of linear matrix inequalities (LMIs) for the proposed system. Moreover, a time-varying delay is supposed to depend on probabilistic distribution conditions. Thus, the resulting criteria that emerge are based on the amount of the delay as well as the probability that the delay will have values at certain intervals. At last, the efficiency of our proposed work is demonstrated by two numerical simulations.

Robust stabilization for an autonomous underwater vehicle motion based on descriptor time-delay model

This article introduces a new technique for stabilizing autonomous underwater vehicles in the descriptor model. Autonomous underwater vehicle stabilization is limited by several constraints, including time-variable uncertainty, time delay, and disturbances. The interaction of descriptor system requirements and the issues mentioned above adds complexities. This study outlines the delay-dependent [Formula: see text] robust stability achieved through memory-less and memory state feedback. Furthermore, a less conservative sufficient condition is obtained for admissibility using a new delay-dependent linear matrices inequality. Autonomous underwater vehicle is regular, impulse-free, and stable under all permissible conditions and satisfies prescribed [Formula: see text] performance conditions via a Lyapunov functional approach. The method applies to neutral and retarded dynamics with discrete and distributed time delays.

RobustH∞Control of DC Motor in the Presence of Input Delay and Disturbance by the Predictor‐Based Method

In this study, the speed control of a DC motor with input delay and external disturbance is investigated. A delay‐dependent memory state feedback robust predictor‐basedH∞ controller that formerly has presented is utilized. Sufficient LMIs conditions provide the stabilizing gain of the predictor‐based controller. The first‐order model of a DC motor has been studied previously using PID and STA (super twisting algorithm) methods. However, in this paper, the delay‐dependent robustH∞ controller is used on both the first and second orders of the DC motor. Finally, the predictor‐basedH∞ controller is compared to the PID controller and the commonH∞ controller as well. The simulation results show that the proposed method has been more useful and efficient.

Fuzzy Weighted Memory Event-Triggered Control for Networked Control Systems Subject to Deception Attacks

This paper considers the event-triggered control problem for a class of Networked Control Systems (NCS) subject to transmission delays and stochastic deception attacks. A new fuzzy weighted memory event-triggered mechanism is proposed to reduce the network bandwidth consumption and data transmission rates. In this context, a new fuzzy weighted memory state feedback controller is proposed to stabilize the closed-loop NCS. Considering the security problem of NCS, a randomly occurring deception attack model is employed, assuming bounded malicious signals injected by the attacker. Based on a suitable Lyapunov-Krasovskii functional, a design methodology is proposed, in terms of linear matrix inequalities, to synthesize both trigger parameters and NCS controller gains. Finally, a numerical example is considered to illustrated the effectiveness of proposed results, compared to previous ones from the literature.

An exponential stabilization criterion for switched delayed interval type-2 fuzzy systems under admissible edge-dependent average dwell time mechanism

This paper addresses the exponential stabilization of the switched interval type-2 fuzzy (IT-2F) time-delay systems under admissible edge-dependent average dwell time (AEDADT) scheme with a non-fragile memory state feedback controller. The IT-2F model depicts uncertain nonlinear systems where the lower and upper membership functions characterize the uncertain parameters. Unlike the previous works that relied on average dwell time (ADT), this work employs the concepts of slow switching and fast switching based on the AEDADT property for both stable and unstable modes. The main reason behind the integration is that fast switching has a great feature in restricting the unstable subsystems. Furthermore, in most nonlinear systems, the feedback control rate is realized by memoryless state feedback control. However, a time lag occurs between system state and control response. Therefore, a non-fragile memory state feedback controller is chosen to ensure the globally uniformly exponential stability condition for proposed nonlinear systems through the linear matrix inequalities (LMI) approach. A mode-dependent average dwell time (MDADT) switching scheme is compared with the described switching rule and derived the superiority of obtained results. The results demonstrate that the AEDADT switching rule is more flexible and achieves tighter bounds than the MDADT property. Finally, numerical simulations and comparisons are provided to illustrate the capability of proposed theoretical results.

A variable memory state feedback and its application to robust control of uncertain singular time-delay systems

A variable memory state feedback and its application to robust control of uncertain singular time-delay systems

Robust predictive control of a supercavitating vehicle based on time-delay characteristics and parameter uncertainty

Supercavitating vehicle can realize high-speed underwater sailing. However, the nonlinear force and time-delay characteristics caused by the tail flapping the cavity wall become the main challenge of the vehicle controller design. Aiming at time-delay characteristics, the nonlinear of planing force, cavity radius perturbation and parameter uncertainty, the paper establishes a time-delay linear-parameter-varying (LPV) model and designs a robust predictive controller with anti-interference performance. In the process of predictive controller design, the variable quadratic function is used to achieve the robustness of the vehicle and reduce the conservatism of the controller design. Meanwhile, the memory state feedback is used to solve the problems of cavitation radius perturbation, control constraints, vehicle parameter uncertainty and external disturbance. The simulation results show that the controller has strong robustness against the disturbance of external parameters, and can guarantee the stability of the system.

State estimation and frequency stabilization of multi‐area power systems via fault‐alarm approach

AbstractThis work is mainly focused on designing hybrid memory state feedback load frequency control law for a class of multi‐area power systems against transmission delays, parameter uncertainties, actuator faults, and load disturbances via fault‐alarm approach. More specifically, the load disturbances are prompted by the incorporation of abundance amount of renewable energy resources, namely, photo voltaic and wind power. Additionally, the power system takes the effect of actuator faults into account, which is unavoidable and exists at any instant of time. Thus, to stabilize the addressed system, the fault‐alarm approach is exploited to develop the hybrid control law. Particularly, the state dynamics are well estimated by the aid of residual observer to detect the faulty condition of actuators. Also, by following the algorithm of fault detection, the spontaneous alert from the alarm is accomplished. Further, in consideration of appropriate Lyapunov–Krasovskii functional, the stability conditions having linear matrix inequality form are derived and which affirms the asymptotic stability of the power systems. Precisely, the controller gain matrices are obtained by solving the developed sufficient conditions. Eventually, the simulation results of two‐area interconnected power systems are presented to examine the applicability and advantage of the proposed theoretical result.

Robust non-fragile memory feedback control for multi-weighted complex dynamical networks with randomly occurring gain fluctuations

This paper deals with the robust observer-based synchronisation problem for a class of complex dynamic networks subject to multi-weights, time-varying coupling delay and external disturbance. Specifically, the gain fluctuation appears in the proposed controller and is represented in terms of a random variable obeying the Bernoulli distribution. The main objective of this paper is to design a non-fragile memory state feedback controller such that the resulting error system is stochastically synchronised under a prescribed performance level . First, a Luenberger-type state observer is constructed to estimate the state variables of the addressed system. Second, by constructing an appropriate Lyapunov–Krasovskii functional and using Wirtinger-based integral inequality techniques, the required set of sufficient conditions for the synchronisation of the proposed system is established in the form of linear matrix inequalities. In the end, two numerical examples are provided to demonstrate the validity and feasibility of the developed theoretical results.

Robust stability and memory state feedback control for a class of switched nonlinear systems with multiple time-varying delays

This study is concerned with the stability analysis and the feedback stabilization problems for a class of uncertain switched nonlinear systems with multiple time-varying delays. Unusually, more general time delays, which depend on the subsystem number, are considered. In this regard, by constructing a novel common Lyapunov function, using the aggregation techniques and the Borne and Gentina criterion, new algebraic stability and feedback stabilization conditions under arbitrary switching are derived. The proposed results are explicit and obtained without searching a common Lyapunov function through the linear matrix inequalities approach, considered a difficult matter in this case. At last, two numerical simulation examples are shown to prove the practical utility of the suggested approach.

Fault estimation and synchronization control for complex dynamical networks with time‐varying coupling delay

AbstractThis article is devoted to simultaneously solve the problems of fault estimation and synchronization for a class of delayed coupling complex dynamical networks. First, an intermediate estimator is established for each node with the aid of the relative information from the neighboring nodes. Second, a distributed memory state feedback controller is designed with respect to the estimated state values and fault signals. Third, some error systems are formulated by introducing appropriate linear transformations. Then, a set of delay‐dependent criteria is obtained to ensure that the states of the resulting systems are uniformly bounded and subsequently, the explicit design method of the desired gain matrices is presented. At last, the feasibility of established theoretical results is validated by the support of two numerical examples in which one is an application example based on the aircraft model. Different from the existing fault estimation techniques, the proposed method does not require the observer matching condition and the upper bounds of the fault signals, which reduces the conservatism significantly.

Passive control for a class of T-S fuzzy systems with memory controller

Taking the advantage of fuzzy systems, a class of T-S fuzzy models used to describe nonlinear systems. Firstly, by designing a memory state feedback controller, we draw the conclude of robust stability and the conditions of passive control. Secondly, using Lyapunov stability and linear matrix inequality technology in MATLAB, we can utilize the gain matrix about the controller of the memory state feedback. Finally, a simulation example is given to illustrate the effectiveness of the proposed method.

Combined Constrained Robust Least Squares Approach and Block-Pulse Functions Technique for Tracking Control Synthesis of Uncertain Bilinear Systems with Multiple Time-Delayed States under Bounded Input Control

The present study tackles the tracking control problem for unstructured uncertain bilinear systems with multiple time-delayed states subject to control input constraints. First, a new method is introduced to design memory state feedback controllers with compensator gain based on the use of operational properties of block-pulse functions basis. The proposed technique permits transformation of the posed control problem into a constrained and robust optimization problem. The constrained robust least squares approach is then used for determination of the control gains. Second, new sufficient conditions are proposed for the practical stability analysis of the closed-loop system, where a domain of attraction is estimated. A real-world example, the headbox control of a paper machine, demonstrates the efficiency of the proposed method.

Finite-Time Stability of Fractional-Order Time-Varying Delays Gene Regulatory Networks with Structured Uncertainties and Controllers

In this paper, we investigate a class of fractional-order time-varying delays gene regulatory networks with structured uncertainties and controllers (DFGRNs). Our contributions lie in three aspects: first, a necessary and sufficient condition on the existence of the solution for the DFGRNs is given by using the properties of the Riemann–Liouville fractional derivative and Caputo’s fractional derivative; second, the unique solution of the DFGRNs is proved under given initial function and certain condition; third, some novel sufficient conditions on finite-time stability of the DFGRNs are established by using a generalized Gronwall inequality and norm technique, and some conclusions on the finite-time stability of the DFGRNs with memory state-feedback controllers are reached, and those conditions and conclusions depend on the fractional order of the DFGRNs. One of the most interesting findings is that the “estimated time” of the finite-time stability is indeed related to the structured uncertainties, state-feedback controllers, time delays, and the fractional order of the system.

Faulty actuator-based control synthesis for interval type-2 fuzzy systems via memory state feedback approach

This study focuses on the memory state feedback control problem for a family of time delayed interval type-2 Takagi-Sugeno fuzzy systems with external disturbance and actuator faulty input. Notably, an actuator fault model is implemented in the control design. In this study, the membership functions, the premise variables of the controller and the considered plant model are chosen freely. By employing the Lyapunov–Krasovskii functional method, the linear matrix inequality approach and the Abel lemma-based finite sum inequality, a set of sufficient conditions that guarantees the stability of the considered system is obtained via the extended passivity performance index. The developed theoretical results are validated with an artificial example and an application-oriented example.