A perspective on convergence of adaptive control algorithms

This paper presents an overview of the current status of convergence theory for adaptive control algorithms. Rather than giving a comprehensive survey, the paper aims to emphasize the conceptual common ground between different approaches. Possible areas for future research are also discussed.

[1]  P. Kokotovic,et al.  Singular perturbations and robust redesign of adaptive control , 1982, 1982 21st IEEE Conference on Decision and Control.

[2]  H. Chen,et al.  Recursive system identification and adaptive control by use of the modified least squares algorithm , 1983, The 22nd IEEE Conference on Decision and Control.

[3]  Bruce A. Francis,et al.  The internal model principle of control theory , 1976, Autom..

[4]  T. R. Fortescue,et al.  Implementation of self-tuning regulators with variable forgetting factors , 1981, Autom..

[5]  P. Gawthrop.  On the stability and convergence of a self-tuning controller , 1980 .

[6]  Peter E. Caines,et al.  The strong consistency of the stochastic gradient algorithm of adaptive control , 1984 .

[7]  P. Kumar,et al.  Adaptive control with the stochastic approximation algorithm: Geometry and convergence , 1985 .

[8]  P. Ramadge,et al.  Discrete-time multivariable adaptive control , 1979 .

[9]  L. Valavani,et al.  Robustness of adaptive control algorithms in the presence of unmodeled dynamics , 1982, 1982 21st IEEE Conference on Decision and Control.

[10]  B. Anderson,et al.  Optimal Filtering , 1979, IEEE Transactions on Systems, Man, and Cybernetics.

[11]  G. Goodwin,et al.  Adaptive control of nonminimum phase systems , 1981 .

[12]  Anuradha M. Annaswamy,et al.  Error Models for Stable Hybrid Adaptive Systems , 1983 .

[13]  G. Stein,et al.  Multivariable feedback design: Concepts for a classical/modern synthesis , 1981 .

[14]  J. Cruz,et al.  RELATIONSHIP BETWEEN SENSITIVITY AND STABILITY OF MULTIVARIABLE FEEDBACK SYSTEMS. , 1981 .

[15]  James Thomas Harris,et al.  Theory and Application of Self-Tuning Regulators , 1977 .

[16]  Robert Kosut,et al.  Performance robustness properties of adaptive control systems , 1982, 1982 21st IEEE Conference on Decision and Control.

[17]  A. Morse.  Global stability of parameter-adaptive control systems , 1979 .

[18]  G. Goodwin,et al.  Persistency of excitation in the presence of possibly unbounded signals , 1985 .

[19]  P. Ramadge,et al.  Discrete Time Stochastic Adaptive Control , 1981 .

[20]  L. Praly.  Towards a globally stable direct adaptive control scheme for not necessarily minimum phase systems , 1983, The 22nd IEEE Conference on Decision and Control.

[21]  Bo Egardt,et al.  Stability of Adaptive Controllers , 1979 .

[22]  A. Morse,et al.  Adaptive control of single-input, single-output linear systems , 1977, 1977 IEEE Conference on Decision and Control including the 16th Symposium on Adaptive Processes and A Special Symposium on Fuzzy Set Theory and Applications.

[23]  V. Borkar,et al.  Adaptive control of Markov chains, I: Finite parameter set , 1979 .

[24]  C. Richard Johnson,et al.  Exponential convergence of adaptive identification and control algorithms , 1981, Autom..

[25]  G. Goodwin,et al.  Model reference adaptive control of system having purely deterministic disturbances , 1983 .

[26]  David Q. Mayne,et al.  Deterministic convergence of a self-tuning regulator with variable forgetting factor , 1981 .

[27]  Stephen A. Billings,et al.  Self-tuning and adaptive control: theory and applications , 1981 .

[28]  G. P. Szegö,et al.  Stability theory of dynamical systems , 1970 .

[29]  Austin Blaquière,et al.  Nonlinear System Analysis , 1966 .

[30]  K. Narendra,et al.  Bounded error adaptive control , 1980, 1980 19th IEEE Conference on Decision and Control including the Symposium on Adaptive Processes.

[31]  K. Narendra,et al.  Stable discrete adaptive control , 1980 .

[32]  Richard Bellman,et al.  Adaptive Control Processes: A Guided Tour , 1961, The Mathematical Gazette.

[33]  Richard M. Johnstone,et al.  Adaptive systems and time varying plants , 1983 .

[34]  Graham C. Goodwin,et al.  Adaptive filtering prediction and control , 1984 .

[35]  Claude Samson,et al.  Stability analysis of adaptively controlled systems subject to bounded disturbances , 1983, Autom..

[36]  V. Solo.  The convergence of AML , 1979 .

[37]  J. Martín-Sánchez,et al.  A globally stable APCS in the presence of bounded noises and disturbances , 1984 .

[38]  G. Goodwin,et al.  Stochastic adaptive control for exponentially convergent time-varying systems , 1984 .

[39]  K. Narendra,et al.  Stable adaptive controller design, part II: Proof of stability , 1980 .

[40]  Peter E. Caines,et al.  On the adaptive control of a class of systems with random parameters and disturbances , 1985, Autom..

[41]  Rolf Johansson.  Multivariable Adaptive Control , 1983 .

[42]  B. Egardt.  Unification of some discrete-time adaptive control schemes , 1980 .

[43]  P. Hall,et al.  Martingale Limit Theory and Its Application , 1980 .

[44]  Luc Dugard,et al.  Prior knowledge in model reference adaptive control of multi-input multi-output systems , 1983, The 22nd IEEE Conference on Decision and Control.

[45]  G. Goodwin,et al.  Deterministic convergence of a self-tuning regulator with covariance resetting , 1983 .

[46]  Lennart Ljung,et al.  On positive real transfer functions and the convergence of some recursive schemes , 1977 .

[47]  Hybrid adaptive control of continuous time systems , 1982 .

[48]  K. Narendra,et al.  Stable model reference adaptive control in the presence of bounded disturbances , 1982 .

[49]  Lennart Ljung,et al.  Theory and Practice of Recursive Identification , 1983 .

[50]  J. Fuchs.  On the good use of the spectral radius of a matrix , 1982 .

[51]  G. Goodwin,et al.  Adaptive Control of a Class of Linear Time Varying Systems , 1983 .

[52]  L. Praly,et al.  Towards a direct adaptive control scheme for general disturbed mimo systems , 1982 .

[53]  B. Egardt.  Stability analysis of discrete-time adaptive control schemes , 1980 .

[54]  Y. Bar-Shalom,et al.  Dual effect, certainty equivalence, and separation in stochastic control , 1974 .

[55]  D. Naidu,et al.  Optimal Control Systems , 2018 .

[56]  Kumpati S. Narendra,et al.  Adaptation and learning in automatic systems , 1974 .

[57]  Lennart Ljung,et al.  Theory and applications of self-tuning regulators , 1977, Autom..

[58]  P. Moylan,et al.  Dissipative Dynamical Systems: Basic Input-Output and State Properties , 1980 .

[59]  L. Ljung,et al.  Adaptive control based on explicit criterion minimization , 1981, Autom..

[60]  P. Kumar.  Simultaneous identification and adaptive control of unknown systems over finite parameter sets , 1983 .

[61]  K. Narendra,et al.  Stable adaptive controller design--Direct control , 1978 .

[62]  John B. Moore,et al.  Persistence of excitation in extended least squares , 1983 .

[63]  Björn Wittenmark,et al.  On Self Tuning Regulators , 1973 .

[64]  Thomas Kailath,et al.  Linear Systems , 1980 .

[65]  Petros A. Ioannou,et al.  Adaptive Systems with Reduced Models , 1983 .

[66]  Kumpati S. Narendra,et al.  Applications of Adaptive Control , 1980 .

[67]  A. Laub,et al.  Feedback properties of multivariable systems: The role and use of the return difference matrix , 1981 .

[68]  P. Falb,et al.  Invariants and Canonical Forms under Dynamic Compensation , 1976 .

[69]  G. Goodwin,et al.  A globally convergent adaptive pole placement algorithm without a persistency of excitation requirement , 1984 .

[70]  Richard M. Johnstone,et al.  Global adaptive pole positioning , 1985, IEEE Transactions on Automatic Control.

[71]  Y. D. Landau,et al.  Adaptive control: The model reference approach , 1979, IEEE Transactions on Systems, Man, and Cybernetics.

[72]  Graham C. Goodwin,et al.  Stochastic adaptive control using a modified least squares algorithm , 1982, Autom..