scholarly journals Control of Nonlinear Distributed Parameter Systems Based on Global Approximation

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Chunyan Du ◽  
Guansheng Xing
Keyword(s):  
Nonlinear Systems ◽  
Sliding Mode ◽  
Linear Time ◽  
Distributed Parameter Systems ◽  
Distributed Parameter ◽  
Global Approximation ◽  
Iterative Approximation ◽  
Control Techniques ◽  
Time Varying Systems ◽  
Iterative Approximation Method

We extend an iterative approximation method to nonlinear, distributed parameter systems given by partial differential and functional equations. The nonlinear system is approached by a sequence of linear time-varying systems, which globally converges in the limit to the original nonlinear systems considered. This allows many linear control techniques to be applied to nonlinear systems. Here we design a sliding mode controller for a nonlinear wave equation to demonstrate the effectiveness of this method.

Existence of Solutions of Riccati Differential Equations

2012 ◽  
Vol 134 (3) ◽  
Author(s):  
Sinan Kilicaslan ◽  
Stephen P. Banks
Keyword(s):  
Differential Equation ◽  
Nonlinear Systems ◽  
Existence Of Solutions ◽  
Linear Time ◽  
Sufficient Conditions ◽  
Necessary Condition ◽  
Time Varying ◽  
Riccati Differential Equation ◽  
Riccati Differential Equations ◽  
Time Varying Systems

A necessary condition for the existence of the solution of the Riccati differential equation for both linear, time varying systems and nonlinear systems is introduced. First, a necessary condition for the existence of the solution of the Riccati differential equation for linear, time varying systems is proposed. Then, the sufficient conditions to satisfy the necessary condition are given. After that, the existence of the solution of the Riccati differential equation is generalized for nonlinear systems.

Control-Oriented Modeling of Distributed Parameter Systems

1992 ◽  
Vol 114 (3) ◽  
pp. 339-346 ◽  
Author(s):  
A. J. Helmicki ◽  
C. A. Jacobson ◽  
C. N. Nett
Keyword(s):  
Linear Time ◽  
Distributed Parameter Systems ◽  
Distributed Parameter ◽  
Physical Processes ◽  
Linear Time Invariant ◽  
Time Invariant ◽  
Theoretical Results

In this paper the use of linear, time-invariant, distributed parameter systems (LTI-DPS) as models of physical processes is considered from a control viewpoint. Specifically, recent theoretical results obtained by the authors for the control-oriented modeling of LTI-DPS are concisely reviewed and then a series of applications is given in order to illustrate the practical ramifications of these results.

Frequency Domain Stability Criteria for Distributed Parameter Systems

1970 ◽  
Vol 92 (2) ◽  
pp. 377-384 ◽  
Author(s):  
H. C. Khatri
Keyword(s):  
Frequency Domain ◽  
Stability Criterion ◽  
Closed Loop ◽  
Linear Time ◽  
Distributed Parameter Systems ◽  
Open Loop ◽  
Distributed Parameter ◽  
Stability Criteria ◽  
Domain Stability ◽  
Loop Stability

For distributed parameter systems, open-loop stability in the sense of bounded outputs for bounded inputs, and closed-loop asymptotic stability are considered. Frequency domain stability criteria for open and closed-loop distributed parameter systems are given. The closed-loop stability criterion is similar to V. M. Popov’s stability criterion for lumped systems. The criteria are limited to those linear, time-invariant systems whose dynamics can be described by a transfer function which is the ratio of the multiple transform of the output to the multiple transform of the input. The input may or may not be distributed. An example is given to illustrate the applications of the stability criteria.

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