Input-output linearization of retarded nonlinear systems by an extended Lie derivative

Oguchi, Toshiki; Watanabe, Atsushi; Nakamizo, Takayoshi

doi:10.1109/cdc.1998.758475

Cited by 14 publications

(10 citation statements)

References 11 publications

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“…If k(φ) ∈ U for all φ ∈ C (i.e., the saturation constraints are fulfilled by the continuous time control law), and (4.1) holds (globally), then global stabilization in the sampleand-hold sense is achieved, according to Theorem 5.3. The following corollary shows how Theorem 5.5 can be applied to the particular class of nonlinear retarded systems which are input-output feedback linearizable and stabilizable by (continuous time) state feedback (see [57,Theorem 3.3], [15], [16], [44]). …”

Section: Stabilization In the Sample-and-hold Sensementioning

confidence: 97%

“…The map Ψ describes the change of coordinates by which the control law (6.12) is found and, by the control law (6.12), the following ODE dψ(x(t)) dt = Hψ(x(t)), t ≥ 0, holds (see [16], [44], [15]). The functional V is a CLKF, in C S , for the system described by (6.11), according to Definition 4.1.…”

Section: Example 2 (Seementioning

confidence: 99%

“…By the tools of differential geometry for retarded systems (see [16], [44]), the following state feedback control law, which, if applied in continuous time, globally stabilizes the Downloaded 11/18/14 to 69.166.47.144. Redistribution subject to SIAM license or copyright; see http://www.siam.org/journals/ojsa.php system described by (6.11), can be found (see [15]):…”

Section: Example 2 (Seementioning

confidence: 99%

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Stabilization in the Sample-and-Hold Sense of Nonlinear Retarded Systems

Pepe¹

2014

SIAM J. Control Optim.

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In this paper, the problem of the stabilization in the sample-and-hold sense for fully nonlinear systems with an arbitrary number of arbitrary discrete as well as of distributed time delays is studied. It is shown that steepest descent feedbacks, continuous or not, induced by Lyapunov-Krasovskii functionals in a suitable (large) class, are stabilizers in the sample-and-hold sense. The fact that discontinuities are overcome by the sampling and holding process enlarges greatly the possibility of finding successful controllers for retarded nonlinear systems, by means of control Lyapunov-Krasovskii functionals. Introduction.The notion of stabilization in the sample-and-hold sense has been introduced in 1997 by Clarke et al. in [9], and widely studied for systems described by ordinary differential equations. The following result holds for nonlinear systems described by ordinary differential equations (see [9], [7]): any steepest descent feedback, induced by a control Lyapunov function, is a stabilizer in the sample-andhold sense. The main advantage of this result is the possibility of using discontinuous steepest descent feedbacks. In this paper we prove an analogous result for nonlinear retarded systems.The stabilization problem for nonlinear systems with delays in the state and/or in the input has involved many researchers, at least in the last ten years (see, for instance, [2], [3], [4], [16], [19], [34], [38], [40], [42], [43], [44], [56], [60]). Though many methods are available in the literature, the problem of global stabilization for fully nonlinear systems with an arbitrary number of discrete delays, of any size, and of distributed delays, is far from being completely solved. This paper concerns the study of a stabilization method for retarded systems, in the path proposed by Artstein in [1] for systems described by ordinary differential equations, that is, by control Lyapunov functions (see [1], [55]). A known problem when dealing with control Lyapunov functions is that in some cases the candidate feedback control law is discontinuous (see [7]). For instance, when control Lyapunov-Razumikhin functions for retarded systems (see [22]) are used, the problem of the feedback discontinuity can arise if one makes use of universal formulas such as Sontag's one (see [55]). By suitable control Lyapunov-Krasovskii functionals, continuous feedback control laws can be provided by universal formulas (see [23]), when the small control property is satisfied (see [55] and references therein). In [26], [27], the authors prove the equivalence of the existence of a completely locally Lipschitz control Lyapunov-Krasovskii functional satisfying the small control property, and the stabilizability property by means of

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Section: Stabilization In the Sample-and-hold Sensementioning

confidence: 97%

Section: Example 2 (Seementioning

confidence: 99%

Section: Example 2 (Seementioning

confidence: 99%

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Stabilization in the Sample-and-Hold Sense of Nonlinear Retarded Systems

Pepe¹

2014

SIAM J. Control Optim.

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“…We stress that the boundedness problem of u, in the case of constant delays and non-delayed inputs, is extensively investigated in the literature (see, e.g., [15], see also [8, Lemma A1]).…”

Section: Input-output Linearizationmentioning

confidence: 99%

“…This is based on the possibility of defining, locally (around a convenient state) and starting from a sufficiently smooth output, a suitable coordinate transformation permitting an equivalent linear representation of a subsystem (and maybe the overall system) in the new coordinates. This approach is widely studied in the case of delay-free (see, e.g., [4,12,17], and references therein) and constant-delay control systems (see, e.g., [2,5,8,9,11,14,15,21], see also the more recent paper [1], where, motivated by some observability problems of nonlinear constant-delay systems, necessary and sufficient conditions allowing an equivalent linear weakly observable time-delay system representation have been presented.…”

Section: Introductionmentioning

confidence: 99%

Further remarks on input-output linearization of SISO time-varying delay systems

Haidar¹,

Nicolau²,

Barbot³

et al. 2017

2017 Proceedings of the Conference on Control and Its Applications

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Recent Results on Glucose–Insulin Predictions by Means of a State Observer for Time Delay Systems

Palumbo¹,

Pepe

Panunzi³

et al. 2015

Lecture Notes in Bioengineering

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To achieve accurate and affordable predictions of glucose and insulin plasma concentrations is of paramount importance, especially in the field of the artificial pancreas, where real-time measurements could be properly exploited in model-based glucose control algorithms. This note focuses on a recently developed research line that makes use of a state observer to estimate insulin in real-time from glucose measurements, since it is known that insulin measurements are slower and more cumbersome to obtain, more expensive and also less accurate. Based on these predictions, glucose control algorithms can be designed, and can be exploited for both intra-venous and subcutaneous insulin infusions. The safety, robustness and efficacy of the observer-based control algorithms have been validated on a population of rather heterogenous virtual patients, modeled by a different, comprehensive model of the glucose-insulin system, recently accepted by the Food and Drug Administration as a substitute of animal trials.

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Input-output linearization of retarded nonlinear systems by an extended Lie derivative

Cited by 14 publications

References 11 publications

Stabilization in the Sample-and-Hold Sense of Nonlinear Retarded Systems

Stabilization in the Sample-and-Hold Sense of Nonlinear Retarded Systems

Further remarks on input-output linearization of SISO time-varying delay systems

Recent Results on Glucose–Insulin Predictions by Means of a State Observer for Time Delay Systems

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