Iterative identification for multiple-input systems with time-delays based on greedy pursuit and auxiliary model

This paper focuses on the identification of multiple-input single-output output-error systems with unknown time-delays. Since the time-delays are unknown, an identification model with a high dimensional and sparse parameter vector is derived based on overparameterization. Traditional identification methods cannot get sparse solutions and require a large number of observations unless the time-delays are predetermined. Inspired by the sparse optimization and the greedy algorithms, an auxiliary model based orthogonal matching pursuit iterative (AM-OMPI) algorithm is proposed by using the orthogonal matching pursuit, and then based on the gradient search, an auxiliary model based gradient pursuit iterative algorithm is proposed, which is computationally more efficient than the AM-OMPI algorithm. The proposed methods can simultaneously estimate the parameters and time-delays from a small number of sampled data. A simulation example is used to illustrate the effectiveness of the proposed algorithms.     

Stability analysis for systems with multiple/single time delays via a Cascade augmented L-K functional

This paper investigates stability of linear systems with multiple/single time-delays. Firstly, a three-level cascade augmented Lyapunov-Krasovskii (L-K) functional is introduced, in which interconnect information among delayed state vectors is fully taken into account. Based on a newly integral inequality and the cascade L-K functional, a novel stability criterion is derived for linear systems with multiple time-delays. Secondly, it is found that the proposed L-K functional is also suitable for linear systems with single time-delay if the delay-partitioning method is employed. This motivates us to obtain a less conservative stability condition for linear systems with single time-delay. Finally, Numerical examples are given to confirm the advantages of the proposed method.     

Composite anti-disturbance control for uncertain Markovian jump systems with actuator saturation based disturbance observer and adaptive neural network

This paper studies the problem of composite control for a class of uncertain Markovian jump systems (MJSs) with partial known transition rates, multiple disturbances and actuator saturation. Compared with the existing results, a novel robust composite control scheme is put forward by virtue of adaptive neural network technique. For MJSs, the partial unknown information on transition rates and the actuator saturation influence the design of disturbance observer and the robust H_∞ controller. Firstly, without taking account of external disturbances, the network reconstruction error and saturation, a novel robust adaptive control strategy is established to ensure that all the signals of the closed-loop system are asymptotically bounded in mean square. Secondly, the solvability condition for ensuring the robust H_∞ performance is given by using a modified adaptive law, where the saturation is treated as a disturbance-like signal. Finally, the simulations for a numerical example and an application example are performed to validate the effectiveness of the proposed results.     

Distributed formation control of double-integrator fractional-order multi-agent systems with relative damping and nonuniform time-delays

In this paper, distributed formation control problems are studied for double-integrator fractional-order multi-agent systems (DIFOMASs) with relative damping and nonuniform time-delays. The required state deviations of a group of multi-agent systems are achieved through a local state information interaction, which means that this group of multi-agent systems achieves formation control. In the context of this paper, the dynamic model is first established and the formation control protocol is designed for distributed formation control of DIFOMASs with relative damping under symmetric time-delays and asymmetric time-delays. Then, some sufficient conditions for achieving distributed formation control of DIFOMASs are acquired with the help of graph theory, matrix theory, stability theory and frequency-domain theory. In the end, two simulation examples are performed to verify the efficacy of our proposed method.     

RHONN identifier-control scheme for nonlinear discrete-time systems with unknown time-delays

This work presents a neural identifier-control scheme for uncertain nonlinear discrete-time systems with unknown time-delays. This scheme is based on a neural identifier to get a model of the system and a discrete-time block control technique based on sliding modes to generate the control law. The neural identifier is based on a Recurrent High Order Neural Network (RHONN) trained with an Extended Kalman Filter (EKF) based algorithm. Applicability is shown using real-time test results for linear induction motors. Also, a Lyapunov analysis is added in order to prove the semi-globally uniformly ultimately boundedness (SGUUB) of the proposed neural identifier-control scheme.     

Finite frequency range robust iterative learning control of linear discrete system with multiple time-delays

This paper uses repetitive process stability theory to design robust iterative learning control law for linear discrete systems with multiple time-delays and polytopic uncertainty. Both dynamic and static forms of the control law are considered and used when designing robust iterative learning control schemes. Also, based on the generalized Kalman-Yakubovich-Popov Lemma, the proposed design procedures a required frequency attenuation over a finite frequency range and the monotonic trial-to-trial error convergence. Moreover, linear matrix inequality techniques are applied to formulate the convergence conditions and to obtain formulas for the control law designs. Finally, an illustrative numerical simulation example is given and concludes the paper.     

Consensus stability of a class of second-order multi-agent systems with nonuniform time-delays

This paper is concerned with a consensus problem of a class of second-order multi-agent systems with nonuniform time-delays. A distributed consensus algorithm is adopted to drive all agents to reach consensus and move together with a constant velocity. By a frequency domain approach, an upper bound on the maximum of the time-delays that can be tolerated is given for the consensus of the system.     

State space model identification of multirate processes with time-delay using the expectation maximization

This paper presents the problems of state space model identification of multirate processes with unknown time delay. The aim is to identify a multirate state space model to approximate the parameter-varying time-delay system. The identification problems are formulated under the framework of the expectation maximization algorithm. Through introducing two hidden variables, a new expectation maximization algorithm is derived to estimate the unknown model parameters and the time-delays simultaneously. The effectiveness of the proposed algorithm is validated by a simulation example.     

Distributed fusion receding horizon filtering for uncertain linear stochastic systems with time-delay sensors

A new distributed fusion receding horizon filtering problem is investigated for uncertain linear stochastic systems with time-delay sensors. First, we construct a local receding horizon Kalman filter having time delays (LRHKFTDs) in both the system and measurement models. The key technique is the derivation of recursive error cross-covariance equations between LRHKFTDs in order to compute the optimal matrix fusion weights. It is the first time to present distributed fusion receding horizon filter for linear discrete-time systems with delayed sensors. It has a parallel structure that enables processing of multisensory time-delay measurements, so the calculation burden can be reduced and it is more reliable than the centralized version if some sensors turn faulty. Simulations for a multiple time-delays system show the effectiveness of the proposed filter in comparison with centralized receding horizon filter and non-receding versions.     

Functional observer based controller for stabilizing Takagi–Sugeno fuzzy systems with time-delays

This paper investigates the construction of a fuzzy functional observer for nonlinear systems with time-delays, and the application of the observer to estimate the state functions of the parallel distributed compensation controller for stabilizing the system. Two types of time-delays are considered: constant and time-varying delays with bounded time derivative. Stability conditions are obtained using Lyapunov–Krasovskii functional approach; and the conditions are transformed into linear matrix inequalities with equality constraints so that observer parameters can be calculated using the solution of these inequalities. Functional observer construction procedures are presented considering both constant and time-varying time-delays. Two examples, including one for obtaining a power system stabilizer for a single machine infinite bus system, are presented to illustrate effectiveness of the proposed design procedures.     

Global stabilization of linear systems subject to input saturation and time delays

This note is concerned with global stabilization of linear systems subject to input saturation and time delays. Based on the Luenberger canonical form, two new decoupling methods are proposed. For the decoupled system, according to some special canonical forms, we propose two control laws for systems with input time-delays and systems with input saturation and time-delays, and give explicit conditions to ensure the global stability of the closed-loop system. Two special canonical forms contain time delays in input and state vectors, which is essential in recursive design. In addition, for the system subject to input saturation and time-delay, we introduce some free parameters when designing the controller, which can improve the instantaneous performance of the closed-loop system. Finally, the proposed approach is applied on the multi-agent system to design global stabilizing controllers and the effectiveness of the proposed controllers are illustrated by numerical simulations.     

Distributed rotating formation control of second-order leader-following multi-agent systems with nonuniform delays

In this paper, the leader-following rotating formation control problem is investigated for second-order multi-agent systems with nonuniform time-delays. We propose a distributed algorithm to drive all agents to achieve a desired formation and orbit around a common point. By a frequency domain analysis method, the upper bound of the maximum time-delay is obtained. Finally, a numerical simulation is given to illustrate the obtained results.     

Robust H∞ control for a class of uncertain nonlinear systems with mixed time-delays

This paper is concerned with the robust H_∞ control problem for a general class of uncertain nonlinear systems with mixed time-delays. The mixed time-delays consist of both discrete and distributed delays. We aim to design a memoryless state feedback controller such that the closed-loop system is robustly stable for all admissible uncertainties with guaranteed H_∞ disturbance rejection attenuation level. By introducing a new Lyapunov–Krasovskii functional that reflects the mixed delays, sufficient conditions are established for the closed-loop system ensuring the robust stability as well as the H_∞ performance requirement. The controller design is facilitated in terms of the solvability of a Hamilton–Jacobi inequality. Two numerical examples are utilized to demonstrate the effectiveness of the proposed methods.     

State and unknown input estimation for discrete time multiple model

This paper deals with the state estimation of nonlinear discrete systems described by a multiple model with unknown inputs. The main goal concerns the simultaneous estimation of the system's state and the unknown inputs. This goal is achieved through the design of a multiple observer based on the elimination of the unknown inputs. It is shown that the observer gains are solutions of a set of linear matrix inequalities. After that, an unknown input estimation method is proposed. An academic example and an application dealing with message decoding illustrate the effectiveness of the proposed multiple observer.     

Analysis of distributed consensus protocols with multi-equilibria under time-delays

In this paper, we propose a novel method for addressing the multi-equilibria consensus problem for a network of n agents with dynamics evolving in discrete-time. In this method, we introduce, for the first time in the literature, two concepts called primary and secondary layer subgraphs. Then, we present our main results on directed graphs such that multiple consensus equilibria states are achieved, thereby extending the existing single-state consensus convergence results in the literature. Furthermore, we propose an algorithm to determine the number of equilibria for any given directed graph automatically by a computer program. We also analyze the convergence properties of multi-equilibria consensus in directed networks with time-delays under the assumption that all delays are bounded. We show that introducing communication time-delays does not affect the number of equilibria of the given network. Finally, we verify our theoretical results via numerical examples.     

Robust fuzzy stabilization of hybrid discrete delay T–S systems

Novel results on robust fuzzy stabilization are developed hereafter for discrete hybrid systems in the (T–S) fuzzy framework. The systems are subject to fractional parametric uncertainties and bounded time-delays. Linear matrix inequalities-based conditions are derived for stability analysis. By optimizing an appropriate performance measure, both stabilizing gains and the switching signal are generated. The analytical findings are validated on a typical water-quality system application to demonstrate the efficacy of the developed techniques.     

Finite-time stochastic boundedness for Markovian jumping systems via the sliding mode control

The finite-time stochastic boundedness (FTSB) via the sliding mode control (SMC) approach is analyzed for Markovian jumping systems (MJSs) with time-delays. First, an integral switching surface is constructed. And to make sure the reachability of the sliding mode surface in a finite-time, an SMC law is designed. In addition, the delay-dependent criteria for FTSB are obtained over the reaching phase and the sliding motion phase. Furthermore, in line with linear matrix inequalities (LMIs), sufficient conditions are provided to guarantee the FTSB of systems over the whole finite-time interval. Lastly, an example is given to indicate the validity of the proposed approach.     

Consensus of discrete-time second-order agents with time-varying topology and time-varying delays

This paper studies the consensus problem of multiple agents with discrete-time second-order dynamics. It is assumed that the information obtained by each agent is with time-varying delays and the interaction topology is time-varying, where the associated direct graphs may not have spanning trees. Under the condition that the union graph is strongly connected and balanced, it is shown that there exist controller gains such that consensus can be reached for any bounded time-delays. Moreover, a method is provided to design controller gains. Simulations are performed to validate the theoretical results.     

Decentralized fault tolerant model predictive control of discrete-time interconnected nonlinear systems

This paper presents a novel approach to address the decentralized fault tolerant model predictive control of discrete-time interconnected nonlinear systems. The overall system is composed of a number of discrete-time interconnected nonlinear subsystems at the presence of multiple faults occurring at unknown time-instants. In order to deal with the unknown interconnection effects and changes in model dynamics due to multiple faults, both passive and active fault tolerant control design are considered. In the Active fault tolerant case an online approximation algorithm is applied to estimate the unknown interconnection effects and changes in model dynamics due to multiple faults. Besides, the decentralized control strategy is implemented for each subsystem with the model predictive control algorithm subject to some constraints. It is showed that the proposed method guarantees input-to-state stability characterization for both local subsystems and the global system under some predetermined assumptions. The simulation results are exploited to illustrate the applicability of the proposed method.