Exact controllability of rational expectations model with multiplicative noise and input delay

This paper considers the rational expectations model with multiplicative noise and input delay,where the system dynamics rely on the conditional expectations of future states.The main contribution is to obtain a sufficient condition for the exact controllability of the rational expectations model.In particular,we derive a sufficient Gramian matrix condition and a rank condition for the delay-free case.The key is the solvability of the backward stochastic difference equations with input delay which is derived from the forward and backward stochastic system.

Pseudo-Predictor Feedback Control for Multiagent Systems with Both State and Input Delays

This paper is concerned with the consensus problem for high-order continuous-time multiagent systems with both state and input delays.A novel approach referred to as pseudopredictor feedback protocol is proposed.Unlike the predictorbased feedback protocol which utilizes the open-loop dynamics to predict the future states,the pseudo-predictor feedback protocol uses the closed-loop dynamics of the multiagent systems to predict the future agent states.Full-order/reduced-order observer-based pseudo-predictor feedback protocols are proposed,and it is shown that the consensus is achieved and the input delay is compensated by the proposed protocols.Necessary and sufficient conditions guaranteeing the stability of the integral delay systems are provided in terms of the stability of the series of retarded-type time-delay systems.Furthermore,compared with the existing predictor-based protocols,the proposed pseudo-predictor feedback protocol is independent of the input signals of the neighboring agents and is easier to implement.Finally,a numerical example is given to demonstrate the effectiveness of the proposed approaches.

Finite-time Stabilization of the Double Integrator Subject to Input Saturation and Input Delay

Abstract--The time-optimal control design of the double integrator is extended to the finite-time stabilization design that compensates both input saturation and input delay. With the aid of the Artstein＇s transformation, the problem is reduced to assigning a saturated finite-time stabilizer. Index Terms--Finite-time stabilization, input delay, saturated design.

Tracking Control of Uncertain Nonlinear Systems With Unknown Constant Input Delay

A robust delay compensator has been developed for a class of uncertain nonlinear systems with an unknown constant input delay.The control law consists of feedback terms based on the integral of past control values and a novel filtered tracking error,capable of compensating for input delays.Suitable Lyapunov-Krasovskii functionals are used to prove global uniformly ultimately bounded(GUUB)tracking,provided certain sufficient gain conditions,dependent on the bound of the delay,are satisfied.Simulation results illustrate the performance and robustness of the controller for different values of input delay.

Attitude stabilization of rigid spacecraft implemented in backstepping control with input delay

A backstepping method is used for nonlinear spacecraft attitude stabilization in the presence of external disturbances and time delay induced by the actuator. The kinematic model is established based on modified Rodrigues parameters (MRPs). Firstly, we get the desired angular velocity virtually drives the attitude parameters to origin, and then backstep it to the desired control torque required for stabilization. Considering the time delay induced by the actuator, the control torque functions only after the delayed time, therefore time compensation is needed in the controller. Stability analysis of the close-loop system is given afterwards. The infinite dimensional actuator state is modeled with a first-order hyperbolic partial differential equation (PDE), the L-2 norm of the system state is constructed and is proved to be exponentially stable. An inverse optimality theorem is also employed during controller design. Simulation results illustrate the efficiency of the proposed control law and it is robust to bounded external disturbances and time delay mismatch.

Robust H-infinity control for discrete-time T-S fuzzy systems with input delay

Delay-dependent robust H-infinity control for discrete-time Takagi-Sugeno (T-S) fuzzy systems with interval time-varying input delay is considered.By constructing a new Lyapunov-Krasovskii functional and using convex combination method,a delay-dependent condition is established,under which the resulted closed-loop systems via a fuzzy state feedback are robust asymptotically stable with given H-infinity norm bound.Then,an iterative algorithm based on the modified SLPMM algorithm is proposed to solve the fuzzy H-infinity controller.Finally,a numerical example is used to illustrate the effectiveness and feasibility of the approaches proposed.

A Fully Actuated System Approach for Stabilization of Discrete-Time Multiple-Input Nonlinear Systems with Distinct Input Delays

In this paper,the problem of stabilization is considered for discrete-time multiple-input nonlinear systems with distinct input delays law based on the fully actuated system approach.In order to compensate the input delays,a prediction scheme is presented to predict future states based on the closed-loop linear system.Then,a stabilizing law is constructed for nonlinear delayed systems by replacing the future states in the control law for the corresponding delay-free systems with their prediction.Finally,numerical examples are given to verify the effectiveness of the proposed approach.

Robust Adaptive Control for Robotic Systems With Input Time-Varying Delay Using Hamiltonian Method

This paper addresses the problem of robust adaptive control for robotic systems with model uncertainty and input time-varying delay. The Hamiltonian method is applied to develop the stabilization results of the robotic systems. Firstly, with the idea of shaping potential energy and the pre-feedback skill, the n degree-of-freedom(DOF) uncertain robotic systems are realized as an augmented dissipative Hamiltonian formulation with delay.Secondly, based on the obtained Hamiltonian system formulation and by using of the Lyapunov-Krasovskii(L-K) functional method, an adaptive controller is designed to show that the robotic systems can be asymptotically stabilized depending on the input delay. Meanwhile, some sufficient conditions are spelt out to guarantee the rationality and validity of the proposed control law. Finally, study of an illustrative example with simulations shows that the controller obtained in this paper works very well in handling uncertainties and input delay in the robotic systems.

Optimal Control and Stabilization for It?Systems with Input Delay

The paper considers the linear quadratic regulation(LQR)and stabilization problems for It?stochastic systems with two input channels of which one has input delay.The underlying problem actually falls into the field of asymmetric information control because of the nonidentical measurability induced by the input delay.In contrast with single-channel single-delay problems,the challenge of the problems under study lies in the interaction between the two channels which are measurable with respect to different filtrations.The key techniques conquering such difficulty are the stochastic maximum principle and the orthogonal decomposition and reorganization technique proposed in a companion paper.The authors provide a way to solve the delayed forward backward stochastic differential equation(D-FBSDE)arising from the maximum principle.The necessary and sufficient solvability condition and the optimal controller for the LQR problem are given in terms of a new Riccati differential equation established herein.Further,the necessary and sufficient stabilization condition in the mean square sense is provided and the optimal controller is given.The idea proposed in the paper can be extended to solve related control problems for stochastic systems with multiple input channels and multiple delays.

H∞ synchronization of the coronary artery system with input time-varying delay

This paper investigates the H_∞ synchronization of the coronary artery system with input delay and disturbance.We focus on reducing the conservatism of existing synchronization strategies.Base on the triple integral forms of the Lyapunov–Krasovskii functional（LKF）,we utilize single and double integral forms of Wirtinger-based inequality to guarantee that the synchronization feedback controller has good performance against time-varying delay and external disturbance.The effectiveness of our strategy can be exhibited by simulations under the different time-varying delays and different disturbances.

Observer-based control for fractional-order singular systems with orderα(0<α<1)and input delay

In this paper,observer-based control for fractional-order singular systems with orderα(0<α<1)and input delay is studied.On the basis of the Smith predictor and approximation error,the system with input delay is approximately equivalent to the system without input delay.Furthermore,based on the linear matrix inequality(LMI)technique,the necessary and sufficient condition of observer-based control is proposed.Since the condition is a nonstrict LMI,including the equality constraint,it will lead to some trouble when solving problems using toolbox.Thus,the strict LMI-based condition is improved in the paper.Finally,a numerical example and a direct current motor example are given to illustrate the effectiveness of the strict LMI-based condition.

Simultaneous Stabilization of Port-Hamiltonian Systems Subject to Actuation Saturation and Input Delay

This paper investigates the simultaneous stabilization of Port-Hamiltonian(PH) systems subject to actuation saturation(AS) and input delay. Firstly, two parallel connecting PH systems subject to the AS and input delay are proposed. Secondly, a simultaneous stabilization control law is designed by a difference between the two feedback control laws containing the input delay.Thirdly, computing a Lyapunov-Krasovskii function assures the simultaneous stabilization of the above systems. Finally, simulation is given to show the correctness of the proposed contents.

Robust Control for Interval Type-2 T-S Fuzzy Discrete Systems with Input Delays and Cyber Attacks

This paper focuses on the robust control issue for interval type-2 Takagi-Sugeno(IT2 T-S)fuzzy discrete systems with input delays and cyber attacks.The lower and upper membership functions are first utilized to IT2 fuzzy discrete systems to capture parameter uncertainties.By considering the influences of input delays and stochastic cyber attacks,a newly fuzzy robust controller is established.Afterward,the asymptotic stability sufficient conditions in form of LMIs for the IT2 closed-loop systems are given via establishing a Lyapunov-Krasovskii functional.Afterward,a solving algorithm for obtaining the controller gains is given.Finally,the effectiveness of the developed IT2 fuzzy method is verified by a numerical example.

Infinite horizon LQR for systems with multiple delays in a single input channel

This paper is concerned with the linear quadratic regulation （LQR） problem for both linear discrete-time systems and linear continuous-time systems with multiple delays in a single input channel. Our solution is given in terms of the solution to a two-dimensional Riccati difference equation for the discrete-time case and a Riccati partial differential equation for the continuous-time case. The conditions for convergence and stability are provided.

Robust H∞ compensator with constraints for attitude manoeuvres of a quadrotor subject to unknown stochastic input delays

This paper addresses the robust compensator design problem for theattitude tracking of an indoor micro quadrotor subject to unknownstochastic input delays and input constraints. The attitude dynamicsof the micro quadrotor is modelled as a nonlinear system with linear parametric uncertainties, unknown stochastic input delays, inputconstraints and disturbances. Based on the uncertain model and theHanlanay’s inequality, both robust H∞ attitude tracking controllerand suboptimal robust H∞ controller with constraints are developed by constructing an appropriate Lyapunov–Krasvokii functionand presenting standard linear matrix inequalities. The suggestedcontrollers not only achieve the exponential stabilisation of attitudeof the quadrotor but also guarantee the given H∞ performance.Finally, both numerical simulation and experimental results are provided to illustrate the effectiveness and merits of the proposedmethods.

TSM control of the delayed input system

The paper proposed a terminal sliding mode control method for the delayed input system with uncertainties. Firstly, through the state transformation, the original system was transformed into the non-delayed controllabte canonical form system. Then the paper designed a terminal sliding mode and terminal sliding control law with Lyapunov method for the transformed system. Through the method, the reaching time of the any initial state and the convergencing time to the equilibrium points are constrained in finite time. The simulation results show the validation of the method.

Guaranteed cost sampled-data control for uncertain nonlinear time-varying delay system

The robust guaranteed cost sampled-data control was studied for a class of uncertain nonlinear systems with time-varying delay. The parameter uncertainties are time-varying norm-bounded and appear in both the state and the input control matrices. By applying an input delay approach, the system was transformed into a continuous time-delay system. Attention was focused on the design of a robust guaranteed cost sampled-data control law which guarantees that the closed-loop system is asymptotically stable and the quadratic performance index is less than a certain bound for all admissible uncertainties. By applying Lyapunov stability theory, the theorems were derived to provide sufficient conditions for the existence of robust guaranteed cost sampled-data control law in the form of linear matrix inequalities (LMIs), especially an optimal state-feedback guaranteed cost sampled-data control law which ensures the minimization of the guaranteed cost was given. The effectiveness of the proposed method was illustrated by a simulation example with the asymptotically stable curves of system state under the initial condition of x(0)=[0.679 6 0].

Decentralized state observer scheme for uncertain time-delay T-S fuzzy interconnected systems

This paper focuses on a class of T-S fuzzy interconnected systems with time delays and time-varying parameter uncertainties. Observer-based output feedback decentralized controller is designed such that the closed-loop interconnected system is asymptotically stable in the Lyapunov sense in probability for all admissible uncertainties and time delays. Sufficient conditions for robustly asymptotically stability of the systems are given in terms of a set of linear matrix inequalities （LMIs）.

Stabilization with Arbitrary Convergence Rate for the Schr?dinger Equation Subjected to an Input Time Delay

The stabilization problem for the Schr?dinger equation with an input time delay is considered from the view of system equivalence.First,a linear transform from the original system into an exponentially stable system with arbitrary decay rate,also called"target system",is introduced.The linear transform is constructed via a kind of Volterra-type integration with singular kernels functions.As a result,a feedback control law for the original system is obtained.Secondly,a linear transform from the target system into the original closed-loop system is derived.Finally,the exponential stability with arbitrary decay rate of the closed-loop system is obtained through the established equivalence between the original closed-loop system and the target one.The authors conclude this work with some numerical simulations giving support to the results obtained in this paper.

Adaptive control for a class of nonlinear systems with time-varying delays in state and input

This paper is concerned with the adaptive stabilization problem of uncertain input delayed systems.A solution to this problem is given for a class of uncertain nonlinear systems with time-varying delays in both state and input.An adaptive asymptotically stabilizing controller,which can guarantee the stability of the closed-loop system and the convergence of the original system state,is designed by means of the Lyapunov-Krasovskii functional stability theory combined with linear matrix inequalities (LMIs) and nonlinear adaptive techniques.Some numerical examples are presented to demonstrate the effectiveness of the derived controller.