Adaptive control of nonlinear multivariable systems using neural networks

In this paper we examine the problem of control of multivariable systems using neural networks. The problem is discussed assuming different amounts of prior information concerning the plant and hence different levels of complexity. In the first stage it is assumed that the state equations describing the plant are known and that the state of the system is accessible. Following this the same problem is considered when the state equations are unknown. In the last stage the adaptive control of the multivariable system using only input-output data is discussed in detail. The objective of the paper is to demonstrate that results from nonlinear control theory and linear adaptive control theory can be used to design practically viable controllers for unknown nonlinear multivariable systems using neural networks. The different assumptions that have to be made, the choice of identifier and controller architectures and the generation of adaptive laws for the adjustment of the parameters of the neural networks form the core of the paper.<<ETX>>

[1]  P. Falb,et al.  Decoupling in the design and synthesis of multivariable control systems , 1967, IEEE Transactions on Automatic Control.

[2]  W. Wolovich.  On the stabilization of controllable systems , 1968 .

[3]  B. Anderson,et al.  Controllability, Observability and Stability of Linear Systems , 1968 .

[4]  L. Silverman.  Synthesis of Impulse Response Matrices by Internally Stable and Passive Realizations , 1968 .

[5]  L. Silverman.  Properties and application of inverse systems , 1968 .

[6]  J. Bongiorno,et al.  Observers for linear multivariable systems with applications , 1971 .

[7]  C. Desoer,et al.  The exact model matching of linear multivariable systems , 1972 .

[8]  L. Silverman,et al.  Model matching by state feedback and dynamic compensation , 1972 .

[9]  A. Morse,et al.  Structure of Index-Invariant Systems , 1973 .

[10]  W. Wolovich.  Linear multivariable systems , 1974 .

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

[12]  W. Wolovich,et al.  On the stability of solutions to minimal and nonminimal design problems , 1977 .

[13]  J. Glover.  Adaptive noise canceling applied to sinusoidal interferences , 1977 .

[14]  L. Khachiyan.  Polynomial algorithms in linear programming , 1980 .

[15]  George Kimura,et al.  Development of Interactor and a Solution of Block Decoupling Problem , 1981 .

[16]  V. Kučera.  Exact model matching, polynomial equation approach , 1981 .

[17]  Michael J. Todd,et al.  Feature Article - The Ellipsoid Method: A Survey , 1981, Oper. Res..

[18]  W. Wolovich,et al.  A parameter adaptive control structure for linear multivariable systems , 1982 .

[19]  A. Morse,et al.  Adaptive stabilization of linear systems with unknown high-frequency gains , 1984, The 23rd IEEE Conference on Decision and Control.

[20]  A. Ilchmann,et al.  Time-varying polynomial matrix systems , 1984 .

[21]  William A. Wolovich,et al.  Parameterization issues in multivariable adaptive control , 1984, Autom..

[22]  K. Narendra,et al.  Prior information in the design of multivariable adaptive controllers , 1984 .

[23]  K. Poolla,et al.  Robust control of linear time-invariant plants using periodic compensation , 1985 .

[24]  K. Kanai,et al.  Design of a Multivariable Discrete-Time Adaptive Control System with Unknown Deterministic Disturbances , 1985 .

[25]  D. Mayne,et al.  A continuous-time adaptive controller with integral action , 1985 .

[26]  Stephen J. Elliott,et al.  A multiple error LMS algorithm and its application to the active control of sound and vibration , 1987, IEEE Trans. Acoust. Speech Signal Process..

[27]  M. Vidyasagar,et al.  Direct globally convergent adaptive regulation of stable multivariable plants , 1987 .

[28]  B. Francis,et al.  Stability Theory for Linear Time-Invariant Plants with Periodic Digital Controllers , 1988, 1988 American Control Conference.

[29]  Petros A. Ioannou,et al.  Robust model reference adaptive control for multivariable plants , 1988 .

[30]  S. Sastry,et al.  Adaptive Control: Stability, Convergence and Robustness , 1989 .

[31]  P. Peres,et al.  a linear programming oriented procedure for quadratic stabilization of uncertain systems , 1989 .

[32]  John J. Shynk,et al.  Adaptive IIR filtering using parallel-form realizations , 1989, IEEE Trans. Acoust. Speech Signal Process..

[33]  Kumpati S. Narendra,et al.  Identification and control of dynamical systems using neural networks , 1990, IEEE Trans. Neural Networks.

[34]  J. Seo,et al.  Transfer matrices, realization, and control of continuous-time linear time-varying systems via polynomial fractional representations , 1990 .

[35]  Stephen P. Boyd,et al.  Identification of Systems with Parametric and Nonparametric Uncertainty , 1990, 1990 American Control Conference.

[36]  Sabine Mondié,et al.  Model reference robust adaptive control without a priori knowledge of the high frequency gain , 1990 .

[37]  P. Peres,et al.  On a convex parameter space method for linear control design of uncertain systems , 1991 .

[38]  P. Khosla,et al.  Harmonic generation in adaptive feedforward cancellation schemes , 1992, [1992] Proceedings of the 31st IEEE Conference on Decision and Control.

[39]  A. Morse,et al.  Applications of hysteresis switching in parameter adaptive control , 1992 .

[40]  G. Goodwin,et al.  Generalised sample hold functions: facts and fallacies , 1992, [1992] Proceedings of the 31st IEEE Conference on Decision and Control.

[41]  D. A. Lawrence,et al.  A geometric perspective on adaptive system performance , 1992, [1992] Proceedings of the 31st IEEE Conference on Decision and Control.

[42]  M. Hersh.  Adaptive algorithms for the simultaneous stabilization and decoupling of time-varying multivariable systems , 1992 .

[43]  P.J. Antsaklis,et al.  Learning to Coordinate Control Policies of Hybrid Systems , 1993, 1993 American Control Conference.

[44]  S. Masuda,et al.  A Unified Design Method for Model Reference Adaptive Control Systems Using the Coprime Factorization Approach , 1993 .

[45]  Kumpati S. Narendra,et al.  Control of nonlinear dynamical systems using neural networks: controllability and stabilization , 1993, IEEE Trans. Neural Networks.