Adaptive nonlinear regulation: estimation from the Lyapunov equation

@article{Pomet1992AdaptiveNR,
  title={Adaptive nonlinear regulation: estimation from the Lyapunov equation},
  author={Jean-Baptiste Pomet and L. Praly},
  journal={IEEE Transactions on Automatic Control},
  year={1992},
  volume={37},
  pages={729-740}
}
A stabilizing adaptive controller for a nonlinear system depending affinely on some unknown parameters is presented. It is assumed that this system is feedback stabilizable. A key feature of the method is the use of the Lyapunov equation to design the adaptive law. A result on local stability, two different conditions for global stability, and a local result where the initial conditions of the state of the system only are restricted are given. > 
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References

SHOWING 1-10 OF 19 REFERENCES
Lyapunov design of stabilizing controllers
A state feedback law for an affine nonlinear system that makes a compact set containing the equilibrium of interest globally attractive is designed. The problem is solved by designing a so-calledExpand
Adaptive Regulation of Nonlinear Systems with Unmodeled Dynamics
Conditions are given for global stability of an adaptive control law designed for the reduced order model of a class of higher order nonlinear plants. In the presence of unmodeled dynamics. whichExpand
Adaptive Stabilization for Nonlinear Systems in the Plane
Abstract We propose an adaptive controller to globally stabilize a compact set for a planar system depending linearly on unknown parameters. Global rec tifiabili ty of the cont rol vector field isExpand
A model reference adaptive control scheme for pure-feedback nonlinear systems
A model reference adaptive control (MRAC) scheme is presented for nonlinear systems in a pure-feedback canonical form with unknown parameters. The present of parameter uncertainty in the systemExpand
Adaptive control of linearizable systems
The authors give some initial results on the adaptive control of minimum-phase nonlinear systems which are exactly input-output linearizable by state feedback. Parameter adaptation is used as aExpand
ROBUSTNESS OF ADAPTIVE NONLINEAR CONTROL UNDER AN EXTENDED MATCHING CONDITION1
TLDR
A new direct adaptive regulation scheme is proposed for nonlinear systems satisfying an extended matching condition and is shown that the new scheme is robust with respect to unmodeled dynamics. Expand
Robustness of Adaptive Nonlinear Control Under an Extended Matching Condition
Abstract A new direct adaptive regulation scheme is proposed for nonlinear systems satisfying an extended matching condition. For this class of systems, the usual overparametrization in parameterExpand
Nonlinear Process Control: An Adaptive Approach which Uses Physical Models
Abstract In this paper we develop a simple stabilizing control system for the Continuous Stirred Tank Reactor (CSTR). A physically based argument is used to develop a Lyapunov function which isExpand
Systematic Design of Adaptive Controllers for Feedback Linearizable Systems
A systematic procedure is developed for the design of new adaptive regulation and trackdng schemes for a class of feedback linearizable nonlinear systems. The coordinate-free geometric conditions,Expand
On the Adaptive Control of Robot Manipulators
A new adaptive robot control algorithm is derived, which consists of a PD feedback part and a full dynamics feedfor ward compensation part, with the unknown manipulator and payload parameters beingExpand
...
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