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Delay-dependent stability and stabilization of a class of linear switched time-varying delay systems

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Journal of Systems Engineering and Electronics 2007年第2期18卷 320-326页

作者： zhang lixian Wang Changhong Gao Huijun Space Control and Inertial Technology Research Center Harbin Inst. of Technology Harbin 150001 P. R. China

The stability and stabilization of a class of linear switched time-varying delay systems are investigated. A piecewise quadratic Lyapunov function （PWQLF） is constructed and is used to obtain the stability conditions based on the linear matrix inequalities （LMIs）. The stabilizing controller for this class of system is then designed and the solution of the desired controller can be obtained by a cone complementary linearization algorithm. Numerical examples are provided to illustrate the less conservativeness of the new stability and the validity of the controller design procedures.

关键词： Linear switched systems Time-varying delay Delay-dependent stability Stabilization LMIs.

Stabilization of a class of fuzzy stochastic jump systems with partial information on jump and sojourn parameters

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Science China(Technological Sciences) 2021年第2期64卷 353-363页

作者： CAI Bo WENG Rui zhang RuiXian LIANG Ye zhang lixian School of Astronautics Harbin Institute of TechnologyHarbin 150001China Key Laboratory of System Control and Information Processing Ministry of EducationShanghai 200240China

This paper addresses the problem of the design of controller for fuzzy semi-Markov jump systems with hidden modes against the incomplete information on probability density functions of sojourn time. Two ubiquitous circumstances in practice are taken into account, which are often ignored in other related work:(1) the phenomenon that system modes cannot be accessed entirely is considered proactively;(2) finitely accessible information on probability density functions is studied in this paper. By virtue of hidden semi-Markov chain, the underlying systems are modeled as hidden semi-Markov jump systems, which are more general than semi-Markov jump systems. Sufficient conditions on the existence of desired accessible-mode-dependent fuzzy controller are derived such that the fuzzy hidden semi-Markov jump systems is mean square stable. Based on the emission probability matrix, the presented control policy overcomes the possible mode-mismatch between the system mode and the accessible ***, an example is provided to demonstrate the effectiveness of the proposed control method.

关键词： hidden modes probability density function stochastic switching systems time-varying controller Takagi-Sugeno(T-S)fuzzy system

Asynchronous Observer Design for Switched Linear Systems: A Tube-Based Approach

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IEEE/CAA Journal of Automatica Sinica 2020年第1期7卷 70-81页

作者： Minghao Han Ruixian zhang lixian zhang Ye Zhao Wei Pan School of Astronautics Harbin Institute of TechnologyHarbin 150080China School of Mechanical Engineering Georgia Institute of TechnologyAtlanta GA 30332 USA Department of Cognitive Robotics Delft University of TechnologyDelft 2628 CDNetherlands

This paper proposes a tube-based method for the asynchronous observation problem of discrete-time switched linear systems in the presence of amplitude-bounded *** stability conditions of the nominal observer error system under mode-dependent persistent dwell-time(MPDT)switching are first established. Taking the disturbances into account, a novel asynchronous MPDT robust positive invariant(RPI) set and an asynchronous MPDT generalized RPI(GRPI)set are determined for the difference system between the nominal and disturbed observer error systems. Further, the global uniform asymptotical stability of the observer error system is established in the sense of converging to the asynchronous MPDT GRPI set, i.e., the cross section of the tube of the observer error system. Finally, the proposed results are validated on a space robot manipulator example.

关键词： Asynchronous observer design generalized robust positive invariant(GRPI) set mode-dependent persistent dwell-time(MPDT) switched linear systems

Interpolated Bumpless Transfer Control for Asynchronously Switched Linear Systems

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IEEE/CAA Journal of Automatica Sinica 2024年第7期11卷 1579-1590页

作者： Shengao Lu Tong Wu lixian zhang Jianan Yang Ye Liang the School of Astronautics Harbin Institute of TechnologyHarbin 150080China the Department of Electrical and Computer Engineering National University of SingaporeSingapore 117583Singapore IEEE

This paper revisits the problem of bumpless transfer control(BTC) for discrete-time nondeterministic switched linear systems. The general case of asynchronous switching is considered for the first time in the field of BTC for switched systems. A new approach called interpolated bumpless transfer control(IBTC) is proposed, where the bumpless transfer controllers are formulated with the combination of the two adjacent modedependent controller gains, and are interpolated for finite steps once the switching is detected. In contrast with the existing approaches, IBTC does not necessarily run through the full interval of subsystems, as well as possesses the time-varying controller gains(with more flexibility and less conservatism) achieved from a control synthesis allowing for the stability and other performance of the whole switched system. Sufficient conditions ensuring stability and H_(∞) performance of the underlying system by IBTC are developed, and numerical examples verify the theoretical findings.

关键词： Asynchronous switching bumpless transfer H_∞control switched systems

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

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Journal of Systems Engineering and Electronics 2006年第3期17卷 576-585页

作者： Wu Ligang Wang Changhong Gao Huijun zhang lixian Space Control and Inertial Technology Research Center Harbin Inst. of Technology Harbin 150001 P. R. China

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.

关键词： sliding mode control H∞ control nonlinearity state-delayed system linear matrix inequality (LMIs)

Benefits of redundant channels in observer-based H∞ control for discrete-time switched linear systems

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Science China(Technological Sciences) 2016年第1期59卷 55-62页

作者： ZHU YanZheng zhang lixian LIN WeiYang LI Zhan YU ShuYou State Key Laboratory of Automotive Simulation and Control Jilin University School of Astronautics Harbin Institute of Technology Department of Control Science and Engineering Jilin University

In this paper, the H∞ control problem is investigated for a class of discrete-time switched linear systems with modal persistent dwell-time(MPDT) switching. The redundant channels are considered to use in the data transmission to benefit the capability of overcoming the fragility of networks commonly configured by a single channel in the communication networks subject to random packet losses. In light of a new class of Lyapunov functions, the desired observer-based quasi-time-dependent controllers, which have less conservatism than the time-independent ones, are designed such that the resulting closed-loop system is exponentially mean-square stable with a guaranteed H_∞ disturbance attenuation performance. The MPDT can be minimized while ensuring the existence of such a class of observer-based controllers for a given period of persistence. An example of DC-DC boost converter is provided to verify the effectiveness of theoretical findings.

关键词： modal persistent dwell-time observer-based control packet losses redundant channels switched systems

An abnormal displacement change during holding period in nanoindentation tests on zirconia dental ceramic

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Journal of Advanced Ceramics 2016年第2期5卷 153-158页

作者： lixian zhang Longquan SHAO Lei LI Danyu JIANG Department of Prosthodontics the First Hospital of Yunnan Province Kunming 650000 China Department of Stomatology Nanfang Hospital Southern Medical University Guangzhou 510515 China Analysis and Testing Center for Inorganic Materials the State Key Laboratory of High Performance Ceramics and Superfine Microstructure Shanghai Institute of Ceramics Shanghai 200050 China

An abnormal displacement change observed during the holding period in nanoindentation tests on a zirconia dental ceramic was reported in this paper. It was found that, at the initial stage of the holding period, the measured displacement versus time curves were similar in shape with the typical indentation creep curve reported in previous studies. As the holding lasted for long time, however, an evident reduction in displacement was observed for tests with high loading rate, implying that another unknown process, which might result in a decrease in displacement, would co-exist with creep during holding period. Elastic recovery was suggested to be one of the possible sources for such a displacement reduction. An empirical method was also proposed to eliminate the effect of this displacement reduction on the determination of hardness and Young's modulus.

关键词： zirconia nanoindentation displacement elastic recovery

High speed interpolation for micro-line trajectory and adaptive real-time look-ahead scheme in CNC machining

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Science China(Technological Sciences) 2011年第6期54卷 1481-1495页

作者： zhang lixian SUN RuiYong GAO XiaoShan LI HongBo Key Laboratory of Mathematics Mechanization AMSS Chinese Academy of Sciences Beijing 100190 China Graduate University of Chinese Academy of Sciences Beijing 100049 China

CNC machining plays an important role in mechanical manufacturing.A key issue is to improve the machining feedrate while keeping the machining precision and satisfying the acceleration constraints of the CNC *** the consecutive micro-line segments interpolation,the velocities at the junction of two segments are the bottlenecks for the machining *** paper proposes a multi-period turning method to improve the feedrate at the junctions using the linear acceleration and deceleration mode,which utilizes the maximal acceleration capabilities of the NC machine while satisfying the machining precision.A new and more efficient look-ahead method and a feedrate override method are also proposed to boast the global machining *** proposed algorithm has been implemented on Blue Sky NC System,and experimented in real material *** with several existing algorithms,the current algorithm can improve the manufacturing time ranging from 50% to 180%,depending on the machining parameters,and also results in better machining *** addition,the algorithm also satisfies the need of real-time interpolation.

关键词： CNC micro-line segment multi-period turning look-ahead scheme real-time interpolation feedrate override

Robust reinforcement learning with UUB guarantee for safe motion control of autonomous robots

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Science China(Technological Sciences) 2024年第1期67卷 172-182页

作者： zhang RuiXian HAN YiNing SU Man LIN ZeFeng LI HaoWei zhang lixian School of Astronautics Harbin Institute of TechnologyHarbin 150001China School of Management Harbin Institute of TechnologyHarbin 150001China Beijing Institute of Tracking and Telecommunication Technology Beijing 100094China

This paper addresses the issue of safety in reinforcement learning(RL)with disturbances and its application in the safety-constrained motion control of autonomous *** tackle this problem,a robust Lyapunov value function(rLVF)is *** rLVF is obtained by introducing a data-based LVF under the worst-case disturbance of the observed *** the rLVF,a uniformly ultimate boundedness criterion is *** criterion is desired to ensure that the cost function,which serves as a safety criterion,ultimately converges to a range via the policy to be ***,to mitigate the drastic variation of the rLVF caused by differences in states,a smoothing regularization of the rLVF is *** train policies with safety guarantees under the worst disturbances of the observed states,an off-policy robust RL algorithm is *** proposed algorithm is applied to motion control tasks of an autonomous vehicle and a cartpole,which involve external disturbances and variations of the model parameters,*** experimental results demonstrate the effectiveness of the theoretical findings and the advantages of the proposed algorithm in terms of robustness and safety.

关键词： motion control reinforcement learning robustness stability

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