Adaptive nonlinear regulation: estimation from the Lyapunov equation

  title={Adaptive nonlinear regulation: estimation from the Lyapunov equation},
  author={Jean-Baptiste Pomet and L. Praly},
  journal={IEEE Transactions on Automatic Control},
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. > 
Direct adaptive control for nonlinear uncertain system based on control Lyapunov function method
Abstract The problem of adaptive stabilization of a class of multi-input nonlinear systems with unknown parameters both in the state vector-field and the input vector-field has been considered. ByExpand
Adaptive Control for Time-varying Nonlinear System
An adaptive control scheme is proposed for a kind of time-varying nonlinear systems. In the scheme the nonlinear systems are divided into a finite number of subsystems, which are in strict feedbackExpand
ℒ1 adaptive controller for nonlinear reference systems
In this paper, we consider nonlinear affine-in-control systems and present the L1 adaptive controller for the case when the performance specifications are defined via a nonlinear system of similarExpand
Adaptive control of a class of nonlinearly parameterized plants
  • J. Boskovic
  • Computer Science, Mathematics
  • IEEE Trans. Autom. Control.
  • 1998
A stable adaptive control method is developed for a class of first-order nonlinearly parameterized plants that yield a stable system in which the output errors are guaranteed to converge to zero. Expand
Adaptive Control of a Class of Nonlinearly Parameterized Plants
A stable adaptive control method is developed for a class of first-order nonlinearly parameterized plants. The method is based on modified adaptive algorithms that yield a stable system in which theExpand
Robust control design of nonlinear adaptive control systems with unmodelled dynamics
A new design scheme for the construction of control for the nonlinear adaptive control problem is devised by using the backstepping and variable structure techniques to suppress the unmodeled dynamics while regulate the corresponding closed loop system to a small neighborhood of the origin globally. Expand
Design and performance analysis of a direct adaptive controller for nonlinear systems
A direct adaptive controller is developed based on multilayer neural networks (MNNs) for a class of nonlinear systems, which avoids the possible singularity problem of the controller usually met in adaptive control design. Expand
Robust adaptive control of strict-feedback nonlinear systems with nonlinear parameterization
  • J. Wang, Z. Qu
  • Mathematics
  • Proceedings of the 2003 American Control Conference, 2003.
  • 2003
This paper presents a new robust adaptive control approach for a class of uncertain strict feedback nonlinear systems with nonlinear parameterization by employing Nussbaum gain and a smooth parameterExpand
Adaptive dynamic surface control for disturbance attenuation of nonlinear systems
This paper proposes an adaptive dynamic surface control (DSC) approach for disturbance attenuation of uncertain nonlinear systems in the parametric strict-feedback form. In the proposed controlExpand
Output controller for uncertain nonlinear systems with structural, parametric, and signal disturbances
The problem of exponential stability for disturbed systems which can be represented as a feedback connection of a linear dynamical system with unknown parameters and a uncertain nonlinearity satisfying a sector constraint is considered. Expand


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
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