Robust Attainability of a Closed Set for Nonlinear Systems with Imperfect Initial State Information

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.

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Iterative learning control algorithm for sensor fault nonlinear systems

Journal of Intelligent & Fuzzy Systems ◽

10.3233/jifs-189432 ◽

2020 ◽

pp. 1-8

Author(s):

Zimian Lan

Keyword(s):

Nonlinear Systems ◽

Iterative Learning Control ◽

Control Algorithm ◽

Tracking Error ◽

Learning Control ◽

Open Loop ◽

Iterative Learning ◽

Sensor Fault ◽

Initial State ◽

Control Gain

In this paper, we propose a new iterative learning control algorithm for sensor faults in nonlinear systems. The algorithm does not depend on the initial value of the system and is combined with the open-loop D-type iterative learning law. We design a period that shortens as the number of iterations increases. During this period, the controller corrects the state deviation, so that the system tracking error converges to the boundary unrelated to the initial state error, which is determined only by the system’s uncertainty and interference. Furthermore, based on the λ norm theory, the appropriate control gain is selected to suppress the tracking error caused by the sensor fault, and the uniform convergence of the control algorithm and the boundedness of the error are proved. The simulation results of the speed control of the injection molding machine system verify the effectiveness of the algorithm.

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A Maxmin Distance Problem

Journal of Dynamic Systems Measurement and Control ◽

10.1115/1.3426562 ◽

1972 ◽

Vol 94 (2) ◽

pp. 155-158 ◽

Cited By ~ 7

Author(s):

R. Aggarwal ◽

G. Leitmann

Keyword(s):

Minimum Distance ◽

Terminal State ◽

Initial State ◽

Closed Set ◽

Distance Problem

The problem of maximizing the minimum distance of a dynamical system’s state from a given closed set, while transferring the system from a given initial state to a given terminal state, is considered. Two different methods of solution of this problem are given.

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