Global adaptive observers for nonlinear systems via filtered transformations
TL;DR: In this article, the problem of determining global adaptive observers for a class of single-output nonlinear systems which are linear with respect to an unknown constant parameter vector is addressed, and sufficient conditions are given to observe asymptotically an equivalent state without persistency of excitation.
Abstract: The problem of determining global adaptive observers for a class of single-output nonlinear systems which are linear with respect to an unknown constant parameter vector is addressed. Sufficient conditions are given to observe asymptotically an equivalent state without persistency of excitation. Under additional geometric conditions the original state can be observed as well. The results obtained are based on a nonlinear change of coordinates driven by auxiliary filters (filtered transformations). >
Citations
More filters
TL;DR: A self-tuning version of the robust control capable of achieving set point regulation is developed in which the control gains are tuned by an output-feedback adaptive algorithm.
Abstract: For pt.I, see ibid., p.17-32 (1993). The problem of designing global output-feedback robust stabilizing controls for a class of single-input single-output minimum-phase uncertain nonlinear systems with known and constant relative degree is addressed. They are assumed to be linear with respect to the input and nonlinear with respect to an unknown constant parameter vector. The nonlinearities depend on the output only. The nonlinearities may be uncertain and are only required to be bounded by known smooth functions. The order of the robust compensator is equal to the relative degree minus one and is static when the relative degree is one. A self-tuning version of the robust control capable of achieving set point regulation is developed in which the control gains are tuned by an output-feedback adaptive algorithm. When the parameter vector enters linearly, the self-tuning regulator does not require the knowledge of parameter bounds and guarantees set point regulation for the same class of systems considered in Part I. >
607 citations
TL;DR: In this article, a unifying adaptive observer form is proposed, which emphasizes properties allowing some asymptotic state estimation in spite of unknown parameters, as well as additional properties which further allow parameter estimation.
303 citations
11 Dec 1991
TL;DR: In this article, the problem of designing global adaptive controls for a class of single-input-single-output nonlinear systems which are linear with respect to the input and to an unknown constant parameter vector is addressed.
Abstract: The authors address the problem of designing global adaptive controls for a class of single-input-single-output nonlinear systems which are linear with respect to the input and to an unknown constant parameter vector. They determine via geometric conditions a class of systems which can be globally controlled by a dynamic (adaptive), observer-based, output-feedback compensator. In suitable coordinates each system admits observers with linear error dynamics and has linear asymptotically stable zero dynamics: the feedback linearizability property is not required. When the parameters are shown, new sufficient conditions for global output-feedback control of nonlinear systems are obtained as a special case. The class of systems determined strictly contains the class of linear minimum phase ones with unknown poles and zeros, known sign of high frequency gain, and known relative degree. >
294 citations
TL;DR: The adaptive observers presented in this note guarantee arbitrarily fast exponential convergence both of parameter and state estimates to actual parameters and states, while previous adaptive observers guarantee only exponential (not arbitrarily fast) convergence.
Abstract: Concerns the same class of linearly parameterized single-output nonlinear systems that the authors previously identified in (1992) in terms of differential geometric conditions. When persistency of excitation conditions are satisfied, the adaptive observers presented in this note guarantee arbitrarily fast exponential convergence both of parameter and state estimates to actual parameters and states, while previous adaptive observers guarantee only exponential (not arbitrarily fast) convergence. This extends earlier results for linear systems. >
284 citations
TL;DR: In this paper, robust adaptive observers for nonlinear systems are presented which prevent parameter estimate drift and guarantee the input-to-state stability of the error dynamics with respect to disturbances and parameter time-derivatives.
Abstract: Since existing adaptive observers for nonlinear systems may generate unbounded parameter estimates in the presence of bounded disturbances, robust adaptive observers are presented which prevent parameter estimate drift. In addition the input-to-state stability of the error dynamics with respect to disturbances and parameter time-derivatives is guaranteed by generalizing a persistency of excitation result. Asymptotic convergence of state estimation errors is still achieved for systems in adaptive observer form when disturbances are not present, by a suitable extension of Barbalat's lemma.
235 citations
Cites background or methods or result from "Global adaptive observers for nonli..."
...[ 5 ] A. Ferfera and A. Iggidr, “A remark on the stabilization of partially linear composite systems,” IEEE Trans....
[...]
...Hence, we generalize the results obtained in [ 5 ] to the case in which disturbances and time-varying parameters are present, since the desired adaptive observer is robust according to Definition 1. To this purpose, we need to extend the “Barbalat’s Lemma,” (see [9, p. 210]) to functions which are not uniformly continuous (see [10] for a similar result)....
[...]
...Following [2] and [ 5 ], we extend the filtered transformation...
[...]
...In [2] and [ 5 ], it is shown how to design adaptive observers for system (1) which provide, under persistency of excitation, asymptotically convergent estimates both of the state variables and of the parameter vector . The adaptive observer contains, in addition to state and parameter estimates dynamics, a dimensional auxiliary filter....
[...]
...Previous results on adaptive observers design were obtained (see [2], [ 5 ], and [7]) for nonlinear systems which are transformable by a global state space diffeomorphism into...
[...]
References
More filters
TL;DR: Observers can easily be constructed for those nonlinear systems which can be transformed into a linear system by change of state variables and output injection.
1,384 citations
TL;DR: In this article, an adaptive observer/identifier for single input/single output observable nonlinear systems that can be transformed to a certain observable canonical form is described, and sufficient conditions for stability of this observer are provided.
Abstract: An adaptive observer/identifier for single input/single output observable nonlinear systems that can be transformed to a certain observable canonical form is described. Sufficient conditions for stability of this observer are provided. These conditions are in terms of the structure of the system and canonical form, the boundedness of the parameter variations, and the sufficient richness of some signals. The scope of the canonical form and the use of the observer/identifier is motivated by the presentation of applications to time-invariant bilinear systems, nonlinear systems in phase-variable form a biotechnological process, and a robot manipulator. In each case, the specific stability conditions are presented. >
501 citations
TL;DR: In this paper, an adaptive version of the nonlinear observer obtained by A.J. Krener et al. is presented, which involves the cancellation of nonlinear terms by output injection, and necessary and sufficient conditions are given for transforming a nonlinear system by state-space change of coordinates into the special adaptive observer form.
Abstract: An adaptive version of the nonlinear observer obtained by A.J. Krener et al. (1983) is presented. This version involves the cancellation of nonlinear terms by output injection. As an intermediate step, necessary and sufficient conditions are given for transforming a nonlinear system by state-space change of coordinates into the special adaptive observer form that was used by Y. Bastin et al. (1988) to design adaptive observers. >
283 citations
TL;DR: In this paper, a new canonical form for an adaptive observer is presented which estimates the state and identifies the parameters of an unknown n th order linear time-invariant system.
Abstract: A new canonical form for an adaptive observer is presented which estimates the state and identifies the parameters of an unknown n th order linear time-invariant system. This is the simplest adaptive observer presented so far in the literature. The adaptive scheme is shown to be globally asymptotically stable, thus guaranteeing the convergence of the identification process.
100 citations
TL;DR: In this article, the problem of determining global adaptive observers for a class of single-output nonlinear systems which are linear with respect to an unknown constant parameter vector is addressed, and sufficient conditions are given for the construction of a global adaptive observer of an equivalent state, without persistency of excitation.
Abstract: We address the problem of determining global adaptive observers for a class of single-output nonlinear systems which are linear with respect to an unknown constant parameter vector. Sufficient conditions are given for the construction of a global adaptive observer of an equivalent state, without persistency of excitation. Under additional geometric conditions the original (physical) state can be asymptotically observed as well. The results obtained are based on nonlinear changes of coordinates driven by auxiliary filters (filtered transformations). When only a single in put is allowed and it is assumed to enter linearly in the state equations, we determine via geometric conditions a more restricted class of nonlinear single-input, single-output systems which can be globally stabilized by a dynamic (adaptive) observer-based output feedback control. Linear minimum-phase systems with unknown poles and zeroes, known sign of the high-frequency gain and known relative degree belong to such a class of systems. Systems which are not feedback linearizable may belong to such a class as well.
50 citations