The unfalsified control concept: A direct path from experiment to controller

The philosophical issues pertaining to the problem of going from experiment to controller design are discussed. The “unfalsified control” concept is introduced as a framework for determining control laws whose ability to meet given performance specifications is at least not invalidated (i.e., not falsified) by the available data. The approach is “model-free” in the sense that no plant model is required — only plant input-output data. When implemented in real time, the result is an adaptive robust controller which modifies itself whenever a new piece of data invalidates the present controller. A simple design example based on fixed-order LTI controllers and an L2-inequality performance criterion is presented.

[1]  G. Zames.  Functional Analysis Applied to Nonlinear Feedback Systems , 1963 .

[2]  Michael G. Safonov,et al.  A robust ellipsoidal-bound approach to direct adaptive control , 1994 .

[3]  Bart Kosko,et al.  Function approximation with additive fuzzy systems , 1995 .

[4]  Michael G. Safonov,et al.  CACSD using the state-space L/sup infinity / theory-a design example , 1988 .

[5]  Michael G. Safonov,et al.  Thoughts on identification for control , 1994 .

[6]  I. W. Sandberg,et al.  On the L 2 -boundedness of solutions of nonlinear functional equations , 1964 .

[7]  Qiang Liu,et al.  Robust H∞ control design for benchmark problem #2 , 1992, 1992 American Control Conference.

[8]  Robert L. Kosut.  Adaptive Uncertainty Modeling: On-Line Robust Control Design , 1987, 1987 American Control Conference.

[9]  C. F. Long,et al.  Influence of the manufacturing process on the scheduling problem , 1976 .

[10]  Roy S. Smith,et al.  Model Invalidation: A Connection between Robust Control and Identification , 1989 .

[11]  Stephen P. Boyd,et al.  Set-membership identification of systems with parametric and nonparametric uncertainty , 1992 .

[12]  Michael G. Safonov,et al.  Convex set theoretic adaptor control systems , 1993, Proceedings of 32nd IEEE Conference on Decision and Control.

[13]  Pramod Khargonekar,et al.  A Time-Domain Approach to Model Validation , 1992, 1992 American Control Conference.

[14]  Richard Y. Chiang,et al.  Robust control toolbox , 1996 .

[15]  Pramod P. Khargonekar,et al.  Sufficient conditions for robust performance of adaptive controllers with general uncertainty structure , 1992, Autom..

[16]  G. Zames.  On the input-output stability of time-varying nonlinear feedback systems Part one: Conditions derived using concepts of loop gain, conicity, and positivity , 1966 .

[17]  Dennis S. Bernstein,et al.  Benchmark Problems for Robust Control Design , 1991, 1991 American Control Conference.

[18]  G. Zames.  On the input-output stability of time-varying nonlinear feedback systems--Part II: Conditions involving circles in the frequency plane and sector nonlinearities , 1966 .

[19]  John Doyle,et al.  Model validation: a connection between robust control and identification , 1992 .

[20]  Michael G. Safonov,et al.  Stability and Robustness of Multivariable Feedback Systems , 1980 .

[21]  Roy S. Smith,et al.  An informal review of model validation , 1994 .

[22]  J. Willems.  Paradigms and puzzles in the theory of dynamical systems , 1991 .

[23]  Hung T. Nguyen,et al.  Theoretical aspects of fuzzy control , 1995 .

[24]  Michael Athans,et al.  On stability theory , 1978, 1978 IEEE Conference on Decision and Control including the 17th Symposium on Adaptive Processes.

[25]  Michael G. Safonov,et al.  Set Theoretic Adaptor Control Systems , 1993, 1993 American Control Conference.

[26]  I. Sandberg.  A frequency-domain condition for the stability of feedback systems containing a single time-varying nonlinear element , 1964 .

[27]  Michael G. Safonov,et al.  Data, consistency and feedback: a new approach to robust direct adaptive control , 1994, Proceedings of 1994 American Control Conference - ACC '94.

[28]  F. Schweppe.  Recursive state estimation: Unknown but bounded errors and system inputs , 1967 .