Global adaptive stabilization in the absence of information on the sign of the high frequency gain

Willems, Jan C.; Byrnes, Greg

doi:10.1007/bfb0004944

Cited by 175 publications

(64 citation statements)

References 1 publication

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This idea arose in several seminal papers almost at the same time: [34], [42], [4], [31]. Subsequently, it was generalized, preserving its simplicity, to different system classes: multivariable systems [16], unknown sign of the high-frequency gain [35], nonlinear systems [38], discontinuous feedback strategies within the framework of differential inclusions [36,37], infinite-dimensional systems [29], transient behaviour [33], tracking including an internal model [8,28], to name but a few.…”

Section: High-gain Adaptive Controlmentioning

confidence: 99%

High‐gain control without identification: a survey

Ilchmann¹,

Ryan

2008

GAMM-Mitteilungen

107

View full text Add to dashboard Cite

Three related but distinct scenarios for tracking control of uncertain systems are reviewed: asymptotic tracking, approximate tracking with prescribed asymptotic error bound, tracking with prescribed transient behaviour. A variety of system classes are considered, ranging from finite-dimensional linear minimum-phase systems to nonlinear, infinite-dimensional systems described by functional differential equations. These classes are determined only by structural assumptions, such as stable zero dynamics and known relative degree. The objective is a single (and simple) control structure which is effective for every member of the underlying system class: no attempt is made to identify the particular system being controlled.

show abstract

Section: High-gain Adaptive Controlmentioning

confidence: 99%

High‐gain control without identification: a survey

Ilchmann¹,

Ryan

2008

GAMM-Mitteilungen

107

View full text Add to dashboard Cite

show abstract

“…However, it is not known in advance how many switchings are necessary or in which time the correct sign will be found out. See Morse (1983), Nussbaum (1983) and Willems and Byrnes (1984). For systems of the form (5.1) only two iterations are necessary to find out the correct sign S e {1, -1} of the control law u,: Sk,y,.…”

Section: Qi3)mentioning

confidence: 99%

“…in Willems and Byrnes (1984). Furthermore, the controller is capable of tolerating time-varying nonlinear additive state, input and output perturbations.…”

Section: Qi3)mentioning

confidence: 99%

“…If the sign of the feedback gain bc is not known, then the discrete-time case is much easier to handle than the continuous-time case. There is no need to implement a Nussbaum-type controller [see Willems and Byrnes (1984)]. However, as the simulations show, the output becomes very large before settling to zero even when the initial condition is very small.…”

Section: Qi3)mentioning

confidence: 99%

See 1 more Smart Citation

Robust adaptive stabilization of discrete-time first-order systems

Ilchmann

1991

Automatica

View full text Add to dashboard Cite

“…By way of motivation, consider the well-studied (see, for example, [4,6,9]) class of finite-dimensional, real, linear, minimum-phase, M-input (u(t)), M-output (y(t)) systems of relative degree one having high-frequency gain B ∈ R M×M with B + B T > 0. Systems of this class can, in suitable coordinates, be expressed in the form of two …”

Section: Introductionmentioning

confidence: 99%

Tracking control: Performance funnels and prescribed transient behaviour

Ilchmann

Ryan

Trenn

2005

Systems & Control Letters

104

View full text Add to dashboard Cite

Tracking of a reference signal (assumed bounded with essentially bounded derivative) is considered in the context of a class of nonlinear systems, with output y, described by functional differential equations (a generalization of the class of linear minimum-phase systems of relative degree one with positive high-frequency gain). The primary control objective is tracking with prescribed accuracy: given > 0 (arbitrarily small), determine a feedback strategy which ensures that for every admissible system and reference signal, the tracking error e = y − r is ultimately smaller than (that is, e(t) < for all t sufficiently large). The second objective is guaranteed transient performance: the evolution of the tracking error should be contained in a prescribed performance funnel F. Adopting the simple non-adaptive feedback control structure u(t) = −k(t)e(t), it is shown that the above objectives can be attained if the gain is generated by the nonlinear, memoryless feedback k(t) = K F (t, e(t)), where K F is any continuous function exhibiting two specific properties, the first of which ensures that if (t, e(t)) approaches the funnel boundary, then the gain attains values sufficiently large to preclude boundary contact, and the second of which obviates the need for large gain values away from the funnel boundary.

show abstract

Global adaptive stabilization in the absence of information on the sign of the high frequency gain

Cited by 175 publications

References 1 publication

High‐gain control without identification: a survey

High‐gain control without identification: a survey

Robust adaptive stabilization of discrete-time first-order systems

Tracking control: Performance funnels and prescribed transient behaviour

Contact Info

Product

Resources

About