DETERMINISTIC CONTROL OF UNCERTAIN SYSTEMS1

Mathematical models embodied in dynamical systems contain uncertain elements due to modelling imperfections (parameter uncertainties) and external disturbances (input uncertainties). Taking a deterministic point of view, controllers are proposed which assure stable behavior. When the bounds of the uncertain elements are known, the proposed controllers are of the feedback type, utilizing only information about uncertainty bounds. When these bounds are themselves uncertain, adaptive controllers are put forward; these utilize dynamic adaption of the control parameters. The use of these controls is illustrated by examples.

[1]  L. Grujic,et al.  Continuous-time tracking systems incorporating Lur'e plants with multiple non-linearities , 1980 .

[2]  G. Leitmann.  On the Efficacy of Nonlinear Control in Uncertain Linear Systems , 1981 .

[3]  M. Corless,et al.  Adaptive control of systems containing uncertain functions and unknown functions with uncertain bounds , 1983 .

[4]  M. Corless,et al.  Continuous state feedback guaranteeing uniform ultimate boundedness for uncertain dynamic systems , 1981 .

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

[6]  M. A. Aizerman,et al.  Theory of dynamic systems which incorporate elements with incomplete information and its relation to the theory of discontinuous systems , 1978 .

[7]  R. Carroll,et al.  Survey of adaptive control using Liapunov design , 1973 .

[8]  B. Barmish,et al.  On guaranteed stability of uncertain linear systems via linear control , 1981 .

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

[10]  S. Gutman,et al.  Properties of Min-Max Controllers in Uncertain Dynamical Systems , 1982 .

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

[12]  R. V. Monopoli,et al.  Model following control of gas turbine engines , 1981 .

[13]  R. E. Kalman,et al.  Control System Analysis and Design Via the “Second Method” of Lyapunov: I—Continuous-Time Systems , 1960 .

[14]  George Leitmann,et al.  DETERMINISTIC CONTROL OF UNCERTAIN SYSTEMS , 1980 .

[15]  G. Leitmann.  Guaranteed Asymptotic Stability for Some Linear Systems With Bounded Uncertainties , 1979 .

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

[17]  C. Johnson.  Optimal control of the linear regulator with constant disturbances , 1968 .

[18]  M. Corless,et al.  A new class of stabilizing controllers for uncertain dynamical systems , 1982, 1982 21st IEEE Conference on Decision and Control.

[19]  R. V. Monopoli,et al.  Engineering aspects of control system design via the ''direct method'' of Liapunov , 1966 .

[20]  H. Kushner.  On the status of optimal control and stability for stochastic systems. , 1966 .

[21]  G. Leitmann,et al.  Stabilizing feedback control for dynamical systems with bounded uncertainty , 1976, 1976 IEEE Conference on Decision and Control including the 15th Symposium on Adaptive Processes.

[22]  Ian R. Petersen,et al.  Structural Stabilization of Uncertain Systems: Necessity of the Matching Condition , 1985 .

[23]  S. Gutman.  Uncertain dynamical systems--A Lyapunov min-max approach , 1979 .