Adaptive Low-Gain Integral Control of Multivariable Well-Posed Linear Systems

The principle of low-gain integral control for finite-dimensional systems is well known. More recently, low-gain integral control results have been obtained for classes of infinite-dimensional systems. In this paper we show that integral control with a simple and natural adaptation of the integrator gain achieves tracking of constant reference signals for every exponentially stable, multivariable, well-posed, infinite-dimensional, linear system whose steady-state gain matrix has its spectrum in the open right-half plane. Our results considerably extend, improve, and simplify previous work by the authors [SIAM J. Control Optim. {35} (1997), pp. 78--116].

[1]  D. Salamon Infinite Dimensional Linear Systems with Unbounded Control and Observation: A Functional Analytic Approach. , 1987 .

[2]  Olof J. Staffans,et al.  J-energy preserving well-posed linear systems , 2001 .

[3]  E. Davison,et al.  Multivariable tuning regulators: The feedforward and robust control of a general servomechanism problem , 1975, 1975 IEEE Conference on Decision and Control including the 14th Symposium on Adaptive Processes.

[4]  W. Rudin Real and complex analysis , 1968 .

[5]  Olof J. Staffans,et al.  Transfer functions of regular linear systems. Part II: The system operator and the lax-phillips semigroup , 2002 .

[6]  乔花玲,et al.  关于Semigroups of Linear Operators and Applications to Partial Differential Equations的两个注解 , 2003 .

[7]  George Weiss,et al.  The representation of regular linear systems on Hilbert spaces , 1989 .

[8]  Jan Lunze Robust Multivariable Feedback Control , 1989 .

[9]  Edward J. Davison,et al.  An adaptive tracking problem with a control input constraint , 1993, Autom..

[10]  O. Staffans Well-Posed Linear Systems , 2005 .

[11]  Dietmar A. Salamon,et al.  Realization theory in Hilbert space , 1988, Mathematical systems theory.

[12]  George Weiss,et al.  Transfer Functions of Regular Linear Systems. Part I: Characterizations of Regularity , 1994 .

[13]  O. Staffans Quadratic optimal control of stable well-posed linear systems , 1997 .

[14]  E. Davison,et al.  The self-tuning robust servomechanism problem , 1987, 26th IEEE Conference on Decision and Control.

[15]  Ruth F. Curtain,et al.  Well posedness of triples of operators (in the sense of linear systems theory) , 1989 .

[16]  Stuart Townley,et al.  Low-Gain Control of Uncertain Regular Linear Systems , 1997 .

[17]  Manfred Morari Robust stability of systems with integral control , 1983 .

[18]  Stuart Townley,et al.  Integral control of linear systems with actuator nonlinearities: lower bounds for the maximal regulating gain , 1999, IEEE Trans. Autom. Control..

[19]  H. Logemann,et al.  High-gain adaptive stabilization of multivariable linear systems—revisited , 1992 .