DESIGNING REDUCED-ORDER CONTROLLERS OF MIXEDSENSITIVITY PROBLEM FOR FLIGHT CONTROL SYSTEMS

Based on linear matrix inequalities (LMI), the design method of reduced order controllers of mixed sensitivity problem is studied for flight control systems. It is shown that there exists a controller with order not greater than the difference between the generalized plant order and the number of independent control variables, if the mixed sensitivity problem is solvable for strict regular flight control plants. The proof is constructive, and an approach to design such a controller can be obtained in terms of a pair of feasible solution to the well known 3 LMI. Finally, an example of mixed sensitivity problem for a flight control system is given to demonstrate practice of the approach.

Static Output Feedback H_∞ Controllers Design for Descriptor Linear Systems Based on LMI

This paper considers the design problem of static output feedback H ∞ controllers for descriptor linear systems with linear matrix inequality (LMI) approach. Necessary and sufficient conditions for the existence of a static output feedback H ∞ controller are given in terms of LMIs. Furthermore, the design method of H ∞ controllers is provided using the solutions to the LMIs.

Reduced-Order GPIO Based Dynamic Event-Triggered Tracking Control of a Networked One-DOF Link Manipulator Without Velocity Measurement

In networked robot manipulators that deeply integrate control, communication and computation, the controller design needs to take into consideration the limited or costly system resources and the presence of disturbances/uncertainties. To cope with these requirements, this paper proposes a novel dynamic event-triggered robust tracking control method for a onedegree of freedom(DOF) link manipulator with external disturbance and system uncertainties via a reduced-order generalized proportional-integral observer(GPIO). By only using the sampled-data position signal, a new sampled-data robust output feedback tracking controller is proposed based on a reduced-order GPIO to attenuate the undesirable influence of the external disturbance and the system uncertainties. To save the communication resources, we propose a discrete-time dynamic event-triggering mechanism(DETM), where the estimates and the control signal are transmitted and computed only when the proposed discrete-time DETM is violated. It is shown that with the proposed control method, both tracking control properties and communication properties can be significantly improved. Finally, simulation results are shown to demonstrate the feasibility and efficacy of the proposed control approach.

A Family of Adaptive H_∞ Controllers with Full Information for Dissipative Hamiltonian Systems

This paper investigates a parameterization method of adaptive H∞ controllers for dissipative Hamiltonian systems with disturbances and unknown parameters.The family of adaptive H∞ controllers with full information is obtained by interconnecting an adaptive H∞ controller with a generalized zero-energy-gradient （ZEG） detectable,free generalized Hamiltonian system.The present parameterization method avoids solving Hamilton-Jacobi-Issacs equations and thus the controllers obtained are easier in operation as compared to some existing ones.Simulations show the effectiveness and feasibility of the adaptive control strategy proposed in this paper.

含时滞的不确定性交直流微电网直流母线电压H_∞控制

针对含通信网络延时的不确定性交直流微电网的直流母线电压稳定问题,提出了一种将状态空间法和阻抗分析法相融合的方法,构建具有时滞的范数有界不确定交直流微电网模型。基于系统鲁棒二次稳定的求解,获得了满足H_∞控制性能的时滞无关型状态反馈控制器的条件。然后应用S-procedure定理,提出一种降低时滞依赖型Lyapunov方法的泛函构造难度且无须再次求导的方法,引用Wirtinger积分不等式和自由矩阵的积分不等式,得到时滞依赖型的H_∞控制器。仿真分析验证了所提控制方法能在一定的通信延时约束下抑制不确定参数对直流母线电压的影响。

H_∞ Consensus Control of Discrete-Time Multi-Agent Systems Under Network Imperfections and External Disturbance

This paper presents a distributed control protocol for consensus control of multi-agent systems(MASs) under external disturbances and network imperfections, including communication delay and random packet dropout. To comply with the discrete nature of networked systems, in contrast to most of the existing work for MASs under network imperfections,the agents are modeled by discrete-time dynamics. The communication network is considered to be undirected, its delay is considered to be time-varying but bounded, and its packet dropout is modeled by a Bernoulli distributed white sequence.Sufficient conditions in terms of linear matrix inequalities(LMIs)for asymptotic mean-square consensus stability are derived under network imperfections without considering external disturbances.A desired disturbance attenuation level in the presence of both external disturbances and network imperfections is also provided.A simulation example is given to verify the effectiveness of the proposed approach in coping with network imperfection and disturbances.

Distributed H_∞ control of multi-agent systems with directed networks

This paper studies the distributed H∞control problem of identical linear time invariant multi-agent systems subject to external disturbances. A directed graph containing a spanning tree is used to model the communication topology. Based on the relative states of the neighbor agents and a subset of absolute states of the agents, distributed static H∞controllers are proposed. The concept of an H∞performance region is extended to the directed graph situation. Then the results are used to solve the leader–follower H∞consensus problem. Sufficient conditions are proposed based on bounded real lemma and algebraic graph theory. The effectiveness of the theoretical results is illustrated via numerical simulations.

Sliding mode H_∞ control for a class of uncertain nonlinear state-delayed systems

A new proportional-integral （PI） sliding surface is designed for a class of uncertain nonlinear state-delayed systems. Based on this, an adaptive sliding mode controller （ASMC） is synthesized, which guarantees the occurrence of sliding mode even when the system is undergoing parameter uncertainties and external disturbance. The resulting sliding mode has the same order as the original system, so that it becomes easy to solve the H∞ control problem by designing a memoryless H∞ state feedback controller. A delay-dependent sufficient condition is proposed in terms of linear matrix inequalities （LMIs）, which guarantees the sliding mode robust asymptotically stable and has a noise attenuation level γ in an H∞ sense. The admissible state feedback controller can be found by solving a sequential minimization problem subject to LMI constraints by applying the cone complementary linearization method. This design scheme combines the strong robustness of the sliding mode control with the H∞ norm performance. A numerical example is given to illustrate the effectiveness of the proposed scheme.

Disturbance rejection and H_∞ pinning control of linear complex dynamical networks

This paper concerns the disturbance rejection problem of a linear complex dynamical network subject to external disturbances. A dynamical network is said to be robust to disturbance, if the H∞ norm of its transfer function matrix from the disturbance to the performance variable is satisfactorily small. It is shown that the disturbance rejection problem of a dynamical network can be solved by analysing the H∞ control problem of a set of independent systems whose dimensions are equal to that of a single node. A counter-intuitive result is that the disturbance rejection level of the whole network with a diffusive coupling will never be better than that of an isolated node. To improve this, local feedback injections are applied to a small fraction of the nodes in the network. Some criteria for possible performance improvement are derived in terms of linear matrix inequalities. It is further demonstrated via a simulation example that one can indeed improve the disturbance rejection level of the network by pinning the nodes with higher degrees than pinning those with lower degrees.

Robust H_∞ Controller Design for Uncertain Neutral Systems via Dynamic Observer Based Output Feedback

In this paper, the dynamic observer-based controller design for a class of neutral systems with H∞ control is considered. An observer-based output feedback is derived for systems with polytopic parameter uncertainties. This controller assures delay-dependent stabilization and H∞ norm bound attenuation from the disturbance input to the controlled output. Numerical examples are provided for illustration and comparison of the proposed conditions.

Linearization of T-S fuzzy systems and robust H_∞ control

Takagi-Sugeno(T-S) fuzzy model is difficult to be linearized because of membership functions included.So,novel T-S fuzzy state transformation and T-S fuzzy feedback are proposed for the linearization of T-S fuzzy system.The novel T-S fuzzy state transformation is the fuzzy combination of local linear transformation which transforms local linear models in the T-S fuzzy model into the local linear controllable canonical models.The fuzzy combination of local linear controllable canonical model gives controllable canonical T-S fuzzy model and then nonlinear feedback is obtained easily.After the linearization of T-S fuzzy model,a robust H∞ controller with the robustness of sliding model control(SMC) is designed.As a result,controlled T-S fuzzy system shows the performance of H∞ control and the robustness of SMC.

Robust H_∞ control for uncertain descriptor systems with state and control delay

The problem of robust stabilization for uncertain continuous descriptor system with state and control delay is considered. The time-varying parametric uncertainty is assumed to be norm-bounded. The purpose of the robust stabilization is to design a memoryless state feedback law such that the resulting closed-loop system is robustly stable A sufficient condition that uncertain continuous descriptor system is robustly stabilizabled by state feedback law is derived in terms of linear matrix inequality （LMI）. Finally, a numerical example is provided to demonstrate the application of the proposed method.

Robust H_∞ control for aseismic structures with uncertainties in model parameters

This paper presents a robust H∞ output feedback control approach for structural systems with uncertainties in model parameters by using available acceleration measurements and proposes conditions for the existence of such a robust output feedback controller. The uncertainties of structural stiffness, damping and mass parameters are assumed to be norm-bounded. The proposed control approach is formulated within the framework of linear matrix inequalities, for which existing convex optimization techniques, such as the LM1 toolbox in MATLAB, can be used effectively and conveniently. To illustrate the effectiveness of the proposed robust H∞ strategy, a six-story building was subjected both to the 1940 E1 Centro earthquake record and to a suddenly applied Kanai-Tajimi filtered white noise random excitation. The results show that the proposed robust H∞ controller provides satisfactory results with or without variation of the structural stiffness, damping and mass parameters.

Improved H_∞ control for networked control systems with network-induced delay and packet dropout

The H_∞ performance analysis and controller design for linear networked control systems(NCSs) are presented.The NCSs are considered a linear continuous system with time-varying interval input delay by assuming that the sensor is time-driven and the logic Zero-order-holder(ZOH) and controller are event-driven.Based on this model,the delay interval is divided into two equal subintervals for H_∞ performance analysis.An improved H_∞ stabilization condition is obtained in linear matrix inequalities(LMIs) framework by adequately considering the information about the bounds of the input delay to construct novel Lyapunov–Krasovskii functionals(LKFs).For the purpose of reducing the conservatism of the proposed results,the bounds of the LKFs differential cross terms are properly estimated without introducing any slack matrix variables.Moreover,the H_∞ controller is reasonably designed to guarantee the robust asymptotic stability for the linear NCSs with an H_∞ performance level γ.Numerical simulation examples are included to validate the reduced conservatism and effectiveness of our proposed method.

H_∞ Synchronization of Chaotic Systems via Delayed Feedback Control

The H∞ synchronization problem for a class of delayed chaotic systems with external disturbance is investigated. A novel delayed feedback controller is established under which the chaotic master and slave systems are synchronized with a guaranteed H∞ performance. Based on the Lyapunov stability theory, a delay-dependent condition is derived and formulated in the form of linear matrix inequality （LMI）. A numerical simulation is also presented to validate the effectiveness of the developed theoretical results.

H_∞ Robust Fault-Tolerant Controller Design for an Autonomous Underwater Vehicle’s Navigation Control System

In order to improve the security and reliability for autonomous underwater vehicle （AUV） navigation, an H∞ robust fault-tolerant controller was designed after analyzing variations in state-feedback gain Operating conditions and the design method were then analyzed so that the control problem could be expressed as a mathematical optimization problem. This permitted the use of linear matrix inequalities （LMI） to solve for the Hv controller for the system. When considering different actuator failures, these conditions were then also mathematically expressed, allowing the H∞ robust controller to solve for these events and thus be fault-tolerant. Finally, simulation results showed that the H∞ robust fault-tolerant controller could provide precise AUV navigation control with strong robustness.

Design and Comparison of H∞/H2 Controllers for Frigate Rudder Roll Stabilization

Roll motion of ships can be distinguished in two parts:an unavoidable part due to their natural movement while turning and an unwanted and avoidable part that is due to encounter with waves and rough seas in general.For the attenuation of the unwanted part of roll motion,ways have been developed such as addition of controllable fins and changes in shape.This paper investigates the effectiveness of augmenting the rudder used for rejecting part of the unwanted roll,while maintaining steering and course changing ability.For this purpose,a controller is designed,which acts through intentional superposition of fast,compared with course change,movements of rudder,in order to attenuate the high-frequency roll effects from encountering rough seas.The results obtained by simulation to exogenous disturbance support the conclusion that the roll stabilization for displacement can be effective at least when displacement hull vessels are considered.Moreover,robust stability and performance is verified for the proposed control scheme over the entire operating range of interest.

Mixed H_2/H_∞ State Feedback Attitude Control of Microsatellite Based on Extended LMI Method

For the appearance of the additive perturbation of controller gain when the controller parameter has minute adjustment at the initial running stage of system,to avoid the adverse effects,this paper investigates the mixed H_2/H_∞ state feedback attitude control problem of microsatellite based on extended LMI method.Firstly,the microsatellite attitude control system is established and transformed into corresponding state space form.Then,without the equivalence restriction of the two Lyapunov variables of H_2 and H∞performance,this paper introduces additional variables to design the mixed H_2/H_∞ control method based on LMI which can also reduce the conservatives.Finally,numerical simulations are analyzed to show that the proposed method can make the satellite stable within 20 s whether there is additive perturbation of the controller gain or not.The comparative analysis of the simulation results between extended LMI method and traditional LMI method also demonstrates the effectiveness and feasibility of the proposed method in this paper.

Robust reliable H_∞ control for discrete-time Markov jump linear systems with actuator failures

The robust reliable H∞ control problem for discrete-time Markovian jump systems with actuator failures is studied. A more practical model of actuator failures than outage is considered. Based on the state feedback method, the resulting closed-loop systems are reliable in that they remain robust stochastically stable and satisfy a certain level of H∞ disturbance attenuation not only when all actuators are operational, but also in case of some actuator failures, The solvability condition of controllers can be equivalent to a feasibility problem of coupled linear matrix inequalities （LMIs）. A numerical example is also given to illustrate the design procedures and their effectiveness.

Robust H_∞ control for discrete-time polytopic uncertain systems with linear fractional vertices

The robust H∞ control problem for discrete-time uncertain systems is investigated in this paper. The uncertain systems are modelled as a polytopic type with linear fractional uncertainty in the vertices. A new linear matrix inequality (LMI) characterization of the H∞ performance for discrete systems is given by introducing a matrix slack variable which decouples the matrix of a Lyapunov function candidate and the parametric matrices of the system. This feature enables one to derive sufficient conditions for discrete uncertain systems by using parameter-dependent Lyapunov functions with less conservativeness. Based on the result, H∞ performance analysis and controller design are carried out. A numerical example is included to demonstrate the effectiveness of the proposed results.