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On PID control for synchronization of complex dynamical network with delayed nodes

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Science China(Technological Sciences) 2019年第8期62卷 1412-1422页

作者： GU HaiBo Lv JinHu lin zongli Key Laboratory of Systems and Control Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing 100190 China School of Mathematical Sciences University of Chinese Academy of Sciences Beijing 100049 China School of Automation Science and Electrical Engineering State Key Laboratory of Software Development Environment and Beijing Advanced Innovation Center for Big Data and Brain Machine Intelligence Beihang University Beijing 100083 China Charles L. Brown Department of Electrical and Computer Engineering University of Virginia Charlottesville VA 22904-4743 USA

Over the past two decades, synchronization, as an interesting collective behavior of complex dynamical networks, has been attracting much attention. To reveal and analyze the inherent mechanism of synchronization in complex dynamical networks with time delays in nodes, this paper attempts to use PD and PI control protocols to achieve synchronization. Based on a classical network model, we investigate the PD and PI control for synchronization of complex dynamical networks with delayed nodes and obtain some sufficient conditions. By using Lyapunov functions and appropriate state transformations, we prove that global synchronization can be achieved via the above control protocols. Finally, some simulation examples are illustrated to validate the effectiveness of the proposed theoretical results.

关键词： synchronization PID control complex dynamical network networked control system delayed node

Robust Semi-Global Leaderless Consensus and Containment Control of Identical linear Systems with Imperfect Actuators

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Journal of Systems Science & Complexity 2018年第1期31卷 69-86页

作者： SHI Liangren ZHAO Zhiyun lin zongli Department of Automation Shanghai Jiao Tong University and Key Laboratory of System Control and Information Processing of Ministry of Education Shanghai 200240 China Key Laboratory of Advanced Control and Optimization for Chemical Processes (East China University of Science and Technology) Ministry of Education Shanghai 200237 China Charles L. Brown Department of Electrical and Computer Engineering University of Virginia P.O. Box 400743 Charlottesville VA 22904-4743 USA

This paper investigates both the robust semi-global leaderless consensus problem and the robust semi-global containment control problem for a group of identical linear systems with imperfect actuators. The imperfect actuators are characterized by nonlinearities such as saturation and dead zone and there input output relationships are not precisely known. The dynamics of follower agents are also affected by the input additive disturbances. Low-and-high gain feedback consensus protocols are constructed to solve these problems. More specifically, it is shown that robust semi-global leaderless consensus can be achieved over a connected undirected graph and robust semi-global containment control can be achieved when each follower agent has access to the information of at least one leader agent. Numerical simulation illustrates the theoretical results.

关键词： Consensus containment control dead zone leaderless consensus multi-agent systems saturation

Control of a flexible rotor active magnetic bearing test rig: a characteristic model based all-coefficient adaptive control approach

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Control Theory and Technology 2014年第1期12卷 1-12页

作者： Long DI zongli lin Charles L. Brown Department of Electrical and Computer Engineering University of VirginiaP.O. Box 400743 Charlottesville VA 22904-4743 U.S.A.

Active magnetic bearings （AMBs） have found a wide range of applications in high-speed rotating machinery industry. The instability and nonlinearity of AMBs make controller designs difficult, and when AMBs are coupled with a flexible rotor, the resulting complex dynamics make the problems of stabilization and disturbance rejection, which are critical for a stable and smooth operation of the rotor AMB system, even more difficult. Proportional-integral-derivative （PID） control dominates the current AMB applications in the field. Even though PID controllers are easy to implement, there are critical performance limitations associated with them that prevent the more advanced applications of AMBs, which usually require stronger robustness and performance offered by modern control methods such as H-infinity control and if-synthesis. However, these advanced control designs rely heavily on the relatively accurate plant models and uncertainty characterizations, which are sometimes difficult to obtain. In this paper, we explore and report on the use of the characteristic model based all-coefficient adaptive control method to stabilize a flexible rotor AMB test rig. In spite of the simple structure of such a characteristic model based all-coefficient adaptive controller, both simulation and experimental results show its strong performance.

关键词： Active magnetic bearings Adaptive control Characteristic modeling Flexible rotor Robustness

New coordination scheme for multi-robot systems based on state space models

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Journal of Systems Engineering and Electronics 2008年第4期19卷 722-734页

作者： Xie Wenlong Su Jianbo lin zongli Dept. of Automation Shanghai Jiaotong Univ. Shanghai 200240 P. R. China Charles L. Brown Dept. of Electrical and Computer Engineering Univ of Virginia Charlottesville VA 22904-4743 USA

A new coordination scheme for multi-robot systems is proposed. A state space model of the multi- robot system is defined and constructed in which the system＇s initial and goal states are included along with the task definition and the system＇s internal and external constraints. Task accomplishment is considered a transition of the system state in its state space （SS） under the system＇s constraints. Therefore, if there exists a connectable path within reachable area of the SS from the initial state to the goal state, the task is realizable. The optimal strategy for the task realization under constraints is investigated and reached by searching for the optimal state transition trajectory of the robot system in the SS. Moreover, if there is no connectable path, which means the task cannot be performed Successfully, the task could be transformed to be realizable by making the initial state and the goal state connectable and finding a path connecting them in the system＇s SS. This might be done via adjusting the system＇s configuration and/or task constraints. Experiments of multi-robot formation control with obstacles in the environment are conducted and simulation results show the validity of the proposed method.

关键词： multi-robot system coordination state space formation maneuver subgoal

Distributed Cooperative Control of Battery Energy Storage Systems in DC Microgrids

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IEEE/CAA Journal of Automatica Sinica 2021年第3期8卷 606-616页

作者： Tingyang Meng zongli lin Yacov A.Shamash Charles L.Brown Department of Electrical and Computer Engineering University of VirginiaCharlottesvilleVA 22904-4743 USA Department of Electrical and Computer Engineering Stony Brook UniversityStony BrookNY 11794-2350 USA

The control of battery energy storage systems(BESSs)plays an important role in the management of *** this paper,the problem of balancing the state-ofcharge(SoC)of the networked battery units in a BESS while meeting the total charging/discharging power requirement is formulated and solved as a distributed control *** on the communication topology among the battery units are established under which a control law is designed for each battery unit to solve the control problem based on distributed average reference power estimators and distributed average unit state *** types of estimators are *** achieves asymptotic estimation and the other achieves finite time *** show that,under the proposed control laws,SoC balancing of all battery units is achieved and the total charging/discharging power of the BESS tracks the desired power.A simulation example is shown to verify the theoretical results.

关键词： Cooperative control energy storage systems microgrids multi-agent systems

Semi-global weighted output average tracking of discrete-time heterogeneous multi-agent systems subject to input saturation and external disturbances

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Control Theory and Technology 2023年第3期21卷 315-333页

作者： Qilin Song Yuanlong Li Yijing Xie zongli lin Department of Automation Shanghai Jiao Tong UniversityShanghai 200240China Department of Electrical Engineering University of Texas at ArlingtonArlington 76019TXUSA Charles L.Brown Department of Electrical and Computer Engineering University of VirginiaCharlottesville 22904-4743VAUSA

In this paper,we revisit the semi-global weighted output average tracking problem for a discrete-time multi-agent system subject to input saturation and external *** multi-agent system consists of multiple heterogeneous linear systems as leader agents and multiple heterogeneous linear systems as follower *** design both the state feedback and output feedback control protocols for each follower *** particular,a distributed state observer is designed for each follower agent that estimates the state of each leader *** the output feedback case,state observer is also designed for each follower agent to estimate its own *** these estimates,we design low gain-based distributed control protocols,parameterized in a scalar low gain *** is shown that,for any bounded set of the initial conditions,these control protocols cause the follower agents to track the weighted average of the outputs of the leader agents as long as the value of the low gain parameter is tuned sufficiently *** results illustrate the validity of the theoretical results.

关键词： Distributed average tracking Input saturation Low gain feedback Heterogeneous multi-agent systems Output regulation

Design of switched linear systems in the presence of actuator saturation and L-infinity disturbances

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控制理论与应用（英文版） 2010年第3期8卷 333-343页

作者： Liang LU zongli lin Haijun FANG Department of Automation Shanghai/iao Tong University Shanghai 200030 China Department of Electrical and Computer Engineering University of Virginia P.O. Box 400743 Charlottesville VA 22904-4743 USA MKS Instrument 100 Highpower Road Rochester NY 14623 USA

This paper considers the problem of disturbance tolerance/rejection of a switched system resulting from a family of linear systems subject to actuator saturation and E-infinity disturbances. For a given set of linear feedback gains, a given switching scheme and a given bound on the E-infinity norm of the disturbances, conditions are established, in terms of linear or bilinear matrix inequalities, under which a set of a certain form is invariant for a given switched linear system in the presence of actuator saturation and E-infinity disturbances, and the closed-loop system possesses a certain level of disturbance rejection capability. With these conditions, the design of feedback gains and switching scheme can be formulated and solved as constrained optimization problems. Disturbance tolerance is measured by the largest bound on the disturbances for which the trajectories starting from a given set remain bounded. Disturbance rejection is measured either by the E-infinity norm of the system output or by the system＇s ability to steer its state into and/or keep it within a small neighborhood of the origin. In the event that all systems in the family are identical, the switched system reduces to a single system under a switching feedback law. Simulation results show that such a single system under a switching feedback law could have stronger disturbance tolerance/rejection capability than a single linear feedback law can.

关键词： Actuator saturation Disturbance rejection Disturbance tolerance L-infinity performance Set invariance Switched systems

Development of a Bias Compensating Q-Learning Controller for a Multi-Zone HVAC Facility

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IEEE/CAA Journal of Automatica Sinica 2023年第8期10卷 1704-1715页

作者： Syed Ali Asad Rizvi Amanda J.Pertzborn zongli lin IEEE the Department of Electrical and Computer Engineering Tennessee Technological UniversityCookevilleTN 38505 USA the Mechanical Systems and Controls Group in the Building Energy and Environment Division at the National Institute of Standards and Technology(NIST) GaithersburgMD 20899 USA the Charles L.Brown Department of Electrical and Computer Engineering University of VirginiaCharlottesvilleVA 22904-4743 USA

We present the development of a bias compensating reinforcement learning(RL)algorithm that optimizes thermal comfort(by minimizing tracking error)and control utilization(by penalizing setpoint deviations)in a multi-zone heating,ventilation,and air-conditioning(HVAC)lab facility subject to unmeasurable disturbances and unknown *** is shown that the presence of unmeasurable disturbance results in an inconsistent learning equation in traditional RL controllers leading to parameter estimation bias(even with integral action support),and in the extreme case,the divergence of the learning *** demonstrate this issue by applying the popular Q-learning algorithm to linear quadratic regulation(LQR)of a multi-zone HVAC environment and showing that,even with integral support,the algorithm exhibits bias issue during the learning phase when the HVAC disturbance is unmeasurable due to unknown heat gains,occupancy variations,light sources,and outside weather *** address this difficulty,we present a bias compensating learning equation that learns a lumped bias term as a result of disturbances(and possibly other sources)in conjunction with the optimal control *** results show that the proposed scheme not only recovers the bias-free optimal control parameters but it does so without explicitly learning the dynamic model or estimating the disturbances,demonstrating the effectiveness of the algorithm in addressing the above challenges.

关键词： HVAC control optimal tracking Q-learning reinforcement learning(RL)

On semi-global stabilization of minimum phase nonlinear systems without vector relative degrees

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Science in China(Series F) 2009年第11期52卷 2153-2162页

作者： LIU XinMin lin zongli Charles L. Brown Department of Electrical and Computer Engineering University of Virginia P.O. Box 400473 Charlottesville VA 22904-4743 USA

Recently, we developed a structural decomposition for multiple input multiple output nonlinear systems that are affine in control but otherwise general. This structural decomposition simplifies the conventional backstepping design and allows a new backstepping design procedure that is able to stabilize some systems on which the conventional backstepping is not applicable. In this paper we further exploit the properties of such a decomposition for the purpose of solving the semi-global stabilization problem for minimum phase nonlinear systems without vector relative degrees. By taking advantage of special structure of the decomposed system, we first apply the low gain design to the part of system that possesses a linear dynamics. The low gain design results in an augmented zero dynamics that is locally stable at the origin with a domain of attraction that can be made arbitrarily large by lowering the gain. With this augmented zero dynamics, backstepping design is then applied to achieve semi-global stabilization of the overall system.

关键词： nonlinear systems structural decomposition semi-global stabilization low gain feedback