Multiple Input Delays Research Articles

Attack-free protocols design for leader-following consensus of discrete-time multi-agent systems with multiple input delays

The consensus problem for leader-following multi-agent systems (MASs) characterised by discrete-time multiple input delays linear systems with directed communication topologies is investigated. Under reasonable assumptions, full-order observer-based output feedback protocols are first established by using the relative outputs and inputs of neighbouring agents. In order to overcome the impact of potential network attacks, we truncate the relative inputs of the proposed protocols, namely the exchange of communication information between neighbouring agents is forbidden, so that the closed-loop leader-following MAS is inherently immune to being attacked and achieves consensus. Additionally, the improved attack-free protocols not only allow arbitrarily large yet bounded delays, but also only relative output measurement can be available, which reduces the communication burden and thus are easy to implement in practice. A numerical example is worked out to illustrate the effectiveness of the proposed approach.

Stabilization for Discrete-Time Stochastic Systems with Multiple Input Delays

Stabilization for Discrete-Time Stochastic Systems with Multiple Input Delays

Necessary and Sufficient Conditions for Stabilizing an Uncertain Stochastic Multidelay System

We focus on the problem of asymptotically mean-square stabilization in discrete-time stochastic systems that exhibit plant uncertainty, multiple input delays, and multiplicative noises. Our innovative contributions are described as follows. First, we employ a reduction method to transform the original model into a delay-free auxiliary system, and establish an equivalent proposition for stabilization based on this reformulation. On the basis of the reformulated model, we propose two stabilization criteria for the uncertainty-free case, including both Lyapunov-type and Riccati-type criteria. More generally, we extend the stabilization result to the uncertain model, and propose a necessary and sufficient stabilization criterion utilizing matrix homogeneous polynomials. Finally, we explore the existence and uniqueness of a delay margin under certain structural restrictions, and provide a closed-form representation of this margin.

Robust stabilization of uncertain nonlinear systems with infinite distributed input delays

This paper studies the robust stabilization problem of a class of uncertain Lipschitz nonlinear systems with infinite distributed input delays. A novel robust predictor feedback controller is developed and the controller gain can be obtained via solving a linear matrix inequality. It is shown that the proposed robust predictor feedback controller can globally exponentially stabilize the concerned uncertain nonlinear system with infinite distributed input delays. The key to the proposed approach is the development of several new quadratic Lyapunov functionals. The obtained results are extended to the case of systems with both multiple constant input delays and infinite distributed input delays. It is noted that the obtained results include some existing results on systems with constant input delays or bounded distributed input delays as special cases. Finally, two examples of Chua’s circuit and spacecraft rendezvous system are presented to illustrate the effectiveness of the proposed robust controllers.

Optimal control and non-zero-sum differential game for Hurwicz model considering uncertain dynamic systems with multiple input delays

ABSTRACT Uncertainty theory is a field in axiomatic mathematics committed to disposing of belief degrees. By dint of uncertain theory and Hurwicz criterion, this article mainly addresses optimal control and non-zero-sum differential game of uncertain delay dynamic systems, which are depicted as a sort of uncertain differential equation with multiple input delays. Employing the technology of dynamic programming, the optimality principle is put forward and the optimality equation is formulated simultaneously to deal with the optimal control problem. In addition, an equilibrium equation is derived to solve the Nash equilibrium for the multi-player non-zero-sum uncertain differential game on the strength of the proposed optimality equation. An example is devised to illustrate the availability of the results in the end.

Delay compensation of linear systems with multiple distributed input delays via memoryless feedback

Time-delay systems are widely used in industrial applications, such as chemical process and aerospace. The predictor-based feedback method is one of the effective ways to deal with such systems. This paper studies the delay compensation problem for linear systems with multiple distributed input delays. A novel state vector associated with the future state of the system is constructed, which reduces the original linear time-delay system to a linear delay-free system. Memory feedback controller is then designed, and necessary and sufficient conditions for the stability of the closed-loop system are acquired in accordance with the stability of an integral delay system. To avoid the difficult implementation problem of memory feedback controller, the memoryless feedback controller is proposed instead to compensate the multiple distributed input delays. Finally, the proposed controllers are applied to the design of the linearized liquid-level control resonant circuit system.

Adaptive Compensation of Unmatched Disturbances in Unstable MIMO LTI Plants with Distinct Input Delays

The paper concerns the problem of adaptive compensation of unmatched disturbances in linear time-invariant (LTI) multi-input multi-output (MIMO) unstable plants with multiple distinct input delays. The external disturbances affect both the input and the output of the plant and are represented by multi-harmonic signals with unknown parameters (frequencies, phases, and amplitudes). The paper extends results of the paper Nikiforov et al. (2021) on adaptive compensation of unmatched disturbances to the case of distinct input delays. To overcome the problem of multiple distinct input delays, a special scheme of the disturbance prediction is proposed and used for design of the adaptive control law.

Fault‐tolerant controller design for nonlinear systems with multiple input and state delays based on sliding mode algorithm

AbstractIn this article, a novel sliding mode control (SMC) strategy for nonlinear Lipschitz systems with multiple and dissimilar time delays in the states and inputs is proposed. Using linear matrix inequality, a modified integral sliding surface scientifically based on which the innovative SMC approach is developed. Lyapunov–Krasovskii's theory is employed to guarantee asymptotic stability of the closed‐loop system, such that states starting from any arbitrary initial conditions reach the sliding surface in a finite time and stay on it for all subsequent time. It is also proved that the practical effects of the actuator's faults are simultaneously attenuated. An online adaptive tuning law is used to estimate and isolate actuators' possible faults reliably. From the implementation point of view, the controller structure is more straightforward than the most existing recent fault‐tolerant control methods. Simulation results performed on practical nonlinear systems (quadruple tank and industrial continuous stirred tank reactor) verified the outstanding merits of the proposed approach. The operational capabilities of the proposed scheme in the presence of actuators' faults and multiple delays in the states and inputs were also demonstrated.

Controllability on a class of switched time-varying systems with impulses and multiple time delays

The problem of complete controllability is addressed for a class of switched time-varying impulsive systems under multiple input delays. Several controllability criteria are obtained with the aid of algebraic and geometric tools. Firstly, the explicit expression of solution on every impulsive interval for such systems is derived by mathematical induction and variation of parameters. Then, complete controllability is investigated for the underlying system based on the solution established. Specifically, the new necessary or/and sufficient algebraic controllability conditions are obtained without assuming that all impulse-dependent matrices are non-singular. In addition, the geometric criteria with regard to the constant matrices are further discussed when the considered system reduces to a time-invariant case. Finally, numerical examples are worked out to demonstrate the controllability tests derived in this paper. It is shown that the existence of the delayed term will potentially affect the controllability of the studied system. In contrast to the existing literatures, the criteria derived in this paper removing some constrained assumptions have less conservatism and can be used to verify the controllability of a more general linear hybrid system.

On pole assignment of high-order discrete-time linear systems with multiple state and input delays

<p style='text-indent:20px;'>This paper studies the problem of pole assignment for high-order discrete-time linear systems with multiple state and input delays. When the number of state delays is larger than or equal to that of input delays, an effective predictor feedback controller is proposed based on the augmented technique, and the design process for the feedback gain is also presented. In addition, it is proved that the pole assignment problem is solvable if and only if the solutions to a linear matrix equation are such that a matrix is nonsingular. When the number of state delays is smaller than that of input delays, the original system is first transformed into a delay-free system with keeping the system controllability invariant, and then, the corresponding controller with designable feedback gain is established. To characterize all of the feedback gains, a factorization approach is introduced which can provide full degree of freedom. Numerical examples are employed to illustrate the effectiveness of the proposed approaches.</p>

Predictor-based safety control for systems with multiple time-varying delays

Control barrier functions (CBFs) have been recently considered for ensuring safety of nonlinear input-affine systems by means of appropriately designed controllers rendering a desired superlevel set of the CBF function forward invariant. In this work, we consider the safety control problem for nonlinear input-affine systems with multiple time-varying input delays. In order to ensure safety, we first design a set of predictors that estimate the state of the system at different future times by utilizing the control laws designed to ensure safety of the delay-free system. Under the assumption of perfect estimation of the future states, we show that under the designed controller, the closed-loop performance of the systems with and without the input delays is the same by the time the input with the largest delay acts on the system with delays for the first time.

Model Predictive Control for Automatic Carrier Landing with Time Delay

This paper focuses on the problem of automatic carrier landing control with time delay, and an antidelay model predictive control (AD-MPC) scheme for carrier landing based on the symplectic pseudospectral (SP) method and a prediction error method with particle swarm optimization (PE-PSO) is designed. Firstly, the mathematical model for carrier landing control with time delay is given, and based on the Padé approximation (PA) principle, the model with time delay is transformed into an equivalent nondelay one. Furthermore, a guidance trajectory based on the predicted trajectory shape and position deviation is designed in the MPC framework to eliminate the influence of carrier deck motion and real-time error. At the same time, a rolling optimal control block is designed based on the SP algorithm, in which the steady-state carrier air wake compensation is introduced to suppress the interference of the air wake. On this basis, the PE-PSO delay estimation algorithm is proposed to estimate the unknown delay parameter in the equivalent control model. The simulation results show that the delay estimation error of the PE-PSO algorithm is smaller than 2 ms, and the AD-MPC algorithm proposed in this paper can limit the landing height error within ±0.14 m under the condition of multiple disturbances and system input delay. The control accuracy of AD-MPC is much higher than that of the traditional pole assignment algorithm, and its computational efficiency meets the requirement of real-time online tracking.

Stabilization and optimal control of discrete-time systems with multiplicative noise and multiple input delays

This paper is concerned with the stabilization and optimal control of discrete-time systems with multiplicative noise and multiple input delays. First, it is shown that the systems are stabilizable if and only if some algebraic Riccati-type equations have a solution which satisfies a given condition. To the best of our knowledge, this is the first time to propose a necessary and sufficient stabilizing condition for general multiple-input delay systems with multiplicative noise. The method constructs a Lyapunov–Krasovskii function based on the optimal cost of a finite-horizon LQR problem. Next, under the assumption that the system is stabilizable, an infinite-horizon LQR problem is investigated. The optimal control and the optimal cost are given by the above algebraic Riccati-type equations. Finally, based on the above stabilizing condition, an exact delay range for the stabilization of the system is derived in a special case.

Perimeter Control of Multiregion Urban Traffic Networks With Time-Varying Delays

In this paper, an adaptive perimeter control problem is studied for urban traffic networks with multiple regions, time-varying state, and input delays. After defining state variables by partition the accumulation variable of each region, a system model is formulated as nonlinear ordinary differential equations based on the concept of macroscopic fundamental diagram. Both the travel times of vehicles as well as evacuation process of traffic jams are first introduced into the system dynamics, and they are modeled as input and state delays, respectively. The control objective is to stabilize the number of vehicles in each region to desired values. By employing the model reference adaptive control scheme and asymptotical sliding mode technique, two filters and adaptive laws for control parameters are designed by using only the information of the reference model. With properly constructed Lyapunov functions, the stability of tracking error with regard to the reference signals is analyzed. Lastly, a simulation example is given to demonstrate the effectiveness of the proposed methods.

Optimal control for networked control systems with multiple delays and packet dropouts

This article focuses on the problem of optimal linear quadratic Gaussian control for networked control systems with multiple delays and packet dropouts. The main contributions are twofold. Firstly, based on the introduced maximum principle for linear quadratic Gaussian system with multiple input delays and packet dropouts, a nonhomogeneous relationship between the state and costate is obtained, which is the key technical tool to solve the problem. Secondly, a necessary and sufficient condition for the optimal networked control problem is given in virtue of the coupled Riccati equations, and the explicit expression of the optimal controller is presented. Numerical examples are shown to illustrate the proposed algorithm.

Robust Receding Horizon Control with Free Control Moves for Polytopic Parametric Uncertainty Systems Subject to Multiple Input Delays

A robust receding horizon control (RHC) with free control moves is applied to polytopic parametric uncertainty systems with multiple input delays and unstable system matrices. A difficulty in the previous robust RHC work is that the free control moves are unsuitable for the system with input time delay, which is overcome in this paper by the design based on the augmented state. As a result, the synthesis of local control based on augmented feedback is given offline to alleviate the online computation burden. The free control moves before the augmented feedback are the online decision variables, which are solved by minimizing a sequence of nonnegative scalars online. The recursive feasibility is guaranteed by adopting the augmented state space equation. By adjusting the robust positively invariant set, the stability of the closed-loop system is guaranteed. Simulation results demonstrate that the proposed algorithm improves the control performance effectively.

An adaptive controller for uncertain nonlinear systems with multiple time delays

This paper leverages the predictor-based model reference adaptive control (PMRAC) architecture to develop an adaptive compensation scheme for uncertain nonlinear systems with multiple input and state delays. The controller is composed of a state predictor, an auxiliary system, and adaptive laws. The adaptive laws are designed through a Lyapunov function in such a way that the predictor state and the auxiliary state asymptotically converge to the system state given that a stability condition holds. Satisfying this delay-dependent stability condition, formulated in the form of a linear matrix inequality (LMI), also ensures the input-to-state stability of the closed-loop control system. Numerical case studies with a standard F-16 aircraft model are discussed to illustrate the efficacy of the proposed control framework.

Consensus control of multi-agent systems with input and communication delay: A frequency domain perspective

This paper describes consensus control of multi-agent systems (MAS) with input and communication delay in the frequency domain. Each agent of MAS is a linear continuous-time system. The considered linear dynamic model of each agent involves multiple input delays. An H2 controller is proposed for optimal performance and robustness of the MAS. The internal stability approach is employed to compute the H2 controller and the performance index of the overall MAS. A sufficient criterion is derived for gain and delay margin to reach convergence. The simulation paradigm shows the effectiveness of the proposed control scheme.

An Output Feedback Predictive Control for Stochastic Stabilization of a System With Multiple Fixed State Delays and Multiple Markov Input Delays

This paper studies the stochastic stabilization with an output feedback predictive control for a linear system with multiple fixed state delays and multiple Markov input delays. The two equivalent systems are developed through two steps. The original system is transformed to a system with augmented states in a state delay free form. Then, it is further transformed into a system with a predictive state in an input delay free form. The stochastic stability condition of the equivalent system is shown to be a sufficient condition for the stochastic stability of the original system. The stability condition is given as a set of linear matrix inequalities of which matrix size depends only on the maximum state delay, not on the maximum input delay. Simulation results show that the proposed methods provide similar or better performance than the conventional method while their complexities are much smaller in most cases.

A Class of Second-Order Consensus Protocol in Multi-Agent Systems with Multiple Input Delays

This paper is concerned with the consensus problems for second-order multi-agent systems with multiple input delays. Different from all standard consensus algorithms with uniform delays, the authors aim to find the largest input-delay margin which can guarantee the consensus for the case when delays are nonuniform. Based on frequency domain analysis and matrix theory, an upper bound for maximum tolerable input-delay is given in terms of the relationship with scaling strengths and largest eigenvalue of the Lapalician matrix. Simulation results are provided to illustrate the obtained results.