String stability of interconnected systems

Introduces the notion of string stability of a countably infinite interconnection of a class of nonlinear systems. Intuitively, string stability implies uniform boundedness of all the states of the interconnected system for all time if the initial states of the interconnected system are uniformly bounded. It is well known that the input output gain of all the subsystems less than unity guarantees that the interconnected system is input-output stable. The authors derive sufficient ("weak coupling") conditions which guarantee the asymptotic string stability of a class of interconnected systems. Under the same "weak coupling" conditions, string-stable interconnected systems remain string stable in the presence of small structural/singular perturbations. In the presence of parameter mismatch, these "weak coupling" conditions ensure that the states of all the subsystems are all uniformly bounded when a gradient-based parameter adaptation law is used and that the states of all the systems go to zero asymptotically.

[1]  W. Rudin Principles of mathematical analysis , 1964 .

[2]  M. Athans,et al.  On the optimal error regulation of a string of moving vehicles , 1966 .

[3]  R. E. Fenton,et al.  A study of automatic car following , 1969 .

[4]  W. Thompson Exponential stability of interconnected systems , 1970 .

[5]  S. Melzer,et al.  Optimal regulation of systems described by a countably infinite number of objects , 1971 .

[6]  Dragoslav D. Siljak,et al.  Stability of Large-Scale Systems under Structural Perturbations , 1972, IEEE Trans. Syst. Man Cybern..

[7]  Dragoslav D. Šiljak,et al.  On stability of large-scale systems under structural perturbations. , 1973 .

[8]  A. Michel Stability Analysis of Interconnected Systems , 1974 .

[9]  K. Chu Decentralized Control of High-Speed Vehicular Strings , 1974 .

[10]  K. Chu Optimal dencentralized regulation for a string of coupled systems , 1974 .

[11]  L. Peppard,et al.  String stability of relative-motion PID vehicle control systems , 1974 .

[12]  C. Desoer,et al.  Feedback Systems: Input-Output Properties , 1975 .

[13]  E. Davison,et al.  The optimal decentralized control of a large power system: Load and frequency control , 1976, 1976 IEEE Conference on Decision and Control including the 15th Symposium on Adaptive Processes.

[14]  Reggie J. Caudill,et al.  Vehicle-Follower Longitudinal Control for Automated Transit Vehicles , 1977 .

[15]  P. Krishnaprasad,et al.  Homogeneous interconnected systems: An example , 1980, 1980 19th IEEE Conference on Decision and Control including the Symposium on Adaptive Processes.

[16]  C. A. Desoer,et al.  Nonlinear Systems Analysis , 1978 .

[17]  Temporal stability of N-dimensional linear processors and its applications , 1980 .

[18]  Mathukumalli Vidyasagar,et al.  Input-Output Analysis of Large-Scale Interconnected Systems , 1981 .

[19]  M. Vidyasagar,et al.  New relationships between input-output and Lyapunov stability , 1982 .

[20]  L. Hunt,et al.  Global transformations of nonlinear systems , 1983 .

[21]  Enrique Barbieri,et al.  Decentralized control of a class of distributed systems , 1985, 1985 24th IEEE Conference on Decision and Control.

[22]  A. Isidori Nonlinear Control Systems , 1985 .

[23]  Hassan K. Khalil,et al.  Singular perturbation methods in control : analysis and design , 1986 .

[24]  Anuradha M. Annaswamy,et al.  Stable Adaptive Systems , 1989 .

[25]  A. Isidori,et al.  Adaptive control of linearizable systems , 1989 .

[26]  Charles A. Desoer,et al.  INDIRECT ADAPTIVE CONTROL OF A CLASS OF INTERCONNECTED NONLINEAR DYNAMICAL SYSTEMS , 1991 .

[27]  Weiping Li,et al.  Applied Nonlinear Control , 1991 .

[28]  J.K. Hedrick,et al.  Longitudinal Vehicle Controller Design for IVHS Systems , 1991, 1991 American Control Conference.

[29]  Charles A. Desoer,et al.  Control of interconnected nonlinear dynamical systems: the platoon problem , 1992 .

[30]  E. Barbieri Stability Analysis of a Class of Interconnected Systems , 1993 .

[31]  J.K. Hedrick,et al.  Direct adaptive longitudinal control of vehicle platoons , 1994, Proceedings of 1994 33rd IEEE Conference on Decision and Control.