Universal λ-tracking for nonlinearly-perturbed systems in the presence of noise

Ilchmann, Achim; Ryan, E. P.

doi:10.1016/0005-1098(94)90035-3

Cited by 152 publications

(69 citation statements)

References 10 publications

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“…The concept of λ-tracking is implicit in [33], albeit is a somewhat different context to that considered here. The concept as described above was introduced for the linear class (1) in [18], for infinitedimensional linear systems in [15], for the nonlinear class (1) in [1,13], for the nonlinear class (7) in [19], and, for systems modelled by differential inclusions in [38]. Discussion on contributions to systems of higher relative degree are postponed until Section 6.…”

Section: High-gain Adaptive λ-Controlmentioning

confidence: 99%

High‐gain control without identification: a survey

Ilchmann¹,

Ryan

2008

GAMM-Mitteilungen

110

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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.

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Section: High-gain Adaptive λ-Controlmentioning

confidence: 99%

High‐gain control without identification: a survey

Ilchmann¹,

Ryan

2008

GAMM-Mitteilungen

110

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“…As is well known (see, for example, [7]), the following output feedback strategy (a variant of the seminal results in [23,15,13,14]) is an (R, L)-universal λ-servomechanism in the sense that, for each system of class L and reference signal r ∈ R, the strategy ensures (i) boundedness of the state, (ii) convergence of the controller gain, and (iii) output tracking with prescribed accuracy λ (in the sense that d λ ( e(t) ) → 0 as t → ∞, where e(t) := y(t) − r(t) is the tracking error):…”

Section: Mq Hmentioning

confidence: 75%

Systems of Controlled Functional Differential Equations and Adaptive Tracking

Ilchmann¹,

Ryan²,

Sangwin³

2002

SIAM J. Control Optim.

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Abstract. An adaptive servomechanism is developed in the context of the problem of approximate or practical tracking (with prescribed asymptotic accuracy), by the system output, of any admissible reference signal (absolutely continuous and bounded with essentially bounded derivative) for every member of a class of controlled dynamical systems modelled by functional differential equations.Key words. adaptive control, nonlinear systems, functional differential equations, practical tracking, universal servomechanism AMS subject classifications. 93C23, 93C10, 93C40, 34K20PII. S03630129003797041. Introduction. A servomechanism problem is addressed in the context of a class of controlled dynamical systems having the interconnected structure shown in the dashed box in Figure 1. In particular, the aim is the development of an adaptive servomechanism which, for every system of the underlying class, ensures practical tracking (in the sense that prespecified asymptotic tracking accuracy, quantified by λ > 0, is assured), by the system output, of an arbitrary reference signal assumed to be locally absolutely continuous and bounded with essentially bounded derivative. (We denote by R the class of such functions and remark that bounded globally Lipschitz functions form an easily recognized subclass.) The system consists of the interconnection of two blocks: The dynamic block Σ 1 , which can be influenced directly by the system input/control u (an R M -valued function), is also driven by the output w from the dynamic block Σ 2 . Viewed abstractly, the block Σ 2 can be considered as a causal operator which maps the system output y (an R M -valued function) to w (an internal quantity, unavailable for feedback purposes).In essence, the underlying system class S consists of infinite-dimensional nonlinear M -input u, M -output y systems (p, f, g, T ), given by a controlled nonlinear functional differential equation of the form (1.1)ẏ (t) = f (p(t), (T y)(t))+g(p(t), (T y)(t), u(t)), y| [−h,0]

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“…The {tracking concept is adopted from Ilchmann and Ryan (1994 with t 0 = 0 , k 0 > 1 , applied to any system given by (2.1) with cb > 0, yields a closed{loop system which admits a unique solution x() dened on the whole half{axis [0; 1) and satises On the other hand, sampling the x{dynamics on a sampling interval of length h j gives x(t j ) determined approximately by an Euler discretization with step length h j .…”

Section: Introductionmentioning

confidence: 99%

“…This dead-zone idea has been used, in conjuction with suitable output feedback control laws, to extend applicability of the high-gain adaptive controllers to rejection of measurement noise and tracking of large classes of reference signals with guaranteed robustness in the presence of nonlinear disturbances, see Ilchmann and Ryan (1994), and for nonlinear systems in Allg ower et al (1995). The analogue for sampling stabilization of scalar systems is given as follows.…”

Section: Introductionmentioning

confidence: 99%