A new definition of the minimum-phase property for nonlinear systems, with an application to adaptive control

2002 ◽  
Author(s):  
D. Liberzon ◽  
A.S. Morse ◽  
E.D. Sontag
Keyword(s):  
Adaptive Control ◽  
Nonlinear Systems ◽  
Minimum Phase ◽  
Phase Property ◽  
Definition Of

Output-Input Stability: A New Variant of the Minimum-Phase Property for Nonlinear Systems

2001 ◽  
Vol 34 (6) ◽  
pp. 711-716
Author(s):  
Daniel Liberzon ◽  
A. Stephen Morse ◽  
Eduardo D. Sontag
Keyword(s):  
Nonlinear Systems ◽  
Minimum Phase ◽  
New Variant ◽  
Phase Property

Adaptive control based on Barrier Lyapunov function for a class of full-state constrained stochastic nonlinear systems with dead-zone and unmodeled dynamics

2021 ◽  
pp. 014233122098563
Author(s):  
Fei Shen ◽  
Xinjun Wang ◽  
Xinghui Yin
Keyword(s):  
Adaptive Control ◽  
Nonlinear Systems ◽  
Lyapunov Function ◽  
Dead Zone ◽  
Small Neighborhood ◽  
Unmodeled Dynamics ◽  
Stochastic Nonlinear Systems ◽  
Dynamic Surface ◽  
Barrier Lyapunov Function ◽  
Full State

This paper investigates the problem of adaptive control based on Barrier Lyapunov function for a class of full-state constrained stochastic nonlinear systems with dead-zone and unmodeled dynamics. To stabilize such a system, a dynamic signal is introduced to dominate unmodeled dynamics and an assistant signal is constructed to compensate for the effect of the dead zone. Dynamic surface control is used to solve the “complexity explosion” problem in traditional backstepping design. Two cases of symmetric and asymmetric Barrier Lyapunov functions are discussed respectively in this paper. The proposed Barrier Lyapunov function based on backstepping method can ensure that the output tracking error converges in the small neighborhood of the origin. This control scheme can ensure that semi-globally uniformly ultimately boundedness of all signals in the closed-loop system. Two simulation cases are proposed to verify the effectiveness of the theoretical method.

scholarly journals Local modal participation analysis of nonlinear systems using Poincaré linearization

2019 ◽  
Vol 99 (1) ◽  
pp. 803-811 ◽  
Author(s):  
Boumediene Hamzi ◽  
Eyad H. Abed
Keyword(s):  
Nonlinear Systems ◽  
Autonomous Systems ◽  
Analytical Formula ◽  
Linear Case ◽  
Local Mode ◽  
Initial Condition ◽  
Initial State ◽  
State Participation ◽  
Symmetry Assumption ◽  
Definition Of

AbstractThe paper studies an extension to nonlinear systems of a recently proposed approach to the definition of modal participation factors. A definition is given for local mode-in-state participation factors for smooth nonlinear autonomous systems. While the definition is general, the resulting measures depend on the assumed uncertainty law governing the system initial condition, as in the linear case. The work follows Hashlamoun et al. (IEEE Trans Autom Control 54(7):1439–1449 2009) in taking a mathematical expectation (or set-theoretic average) of a modal contribution measure over an uncertain set of system initial state. Poincaré linearization is used to replace the nonlinear system with a locally equivalent linear system. It is found that under a symmetry assumption on the distribution of the initial state, the tractable calculation and analytical formula for mode-in-state participation factors found for the linear case persists to the nonlinear setting. This paper is dedicated to the memory of Professor Ali H. Nayfeh.

Real-Time Modular Deep Neural Network-Based Adaptive Control of Nonlinear Systems

2021 ◽  
pp. 1-1
Author(s):  
Duc M. Le ◽  
Max L. Greene ◽  
Wanjiku A. Makumi ◽  
Warren E. Dixon
Keyword(s):  
Neural Network ◽  
Adaptive Control ◽  
Nonlinear Systems ◽  
Real Time ◽  
Deep Neural Network
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