Set point boundary control for a nonlinear distributed parameter system

2004 ◽  
Author(s):  
C.I. Bymes ◽  
D.S. Gilliam ◽  
A. Isidori ◽  
V.I. Shubov
Keyword(s):  
Boundary Control ◽  
Distributed Parameter ◽  
Distributed Parameter System ◽  
Point Boundary ◽  
Parameter System ◽  
Set Point ◽  
Nonlinear Distributed Parameter System

Switching Analysis for Constrained Bilinear Distributed Parameter System With Applications

1969 ◽  
Vol 91 (2) ◽  
pp. 277-283 ◽  
Author(s):  
D. L. Briggs ◽  
C. N. Shen
Keyword(s):  
Optimal Control ◽  
Boundary Control ◽  
Initial Conditions ◽  
Control Program ◽  
Necessary Condition ◽  
Stress Constraint ◽  
Distributed Parameter ◽  
Distributed Parameter System ◽  
Parameter System ◽  
State Equations

A distributed parameter thermal and stress model is developed for a nuclear rocket. The resultant equations for the optimal control problem are a pair of coupled, bilinear, partial differential equations. The thermal stress constraint forms an inequality which is a function of both the state and the control. The initial conditions are steady state, and the terminal condition is that the coolant flow obtain a fixed, higher level. The distributed parameter system is discretized in the space dimension to give an arbitrary order set of ordinary differential, state equations. It is shown how a result based on the Weierstrass necessary condition and derived by Berkovitz from the calculus of variations using a slack variable technique may be applied. This condition is shown to require the optimal control to be “boundary control” with no switching. The optimal control program must make the inequality constraint an equality at some location throughout the transient. Based on the result that boundary control is the optimal control, an algorithm is developed to compute the optimal control program. The algorithm was programmed on a digital computer and numerical results are given for the optimal flow program and the resultant stress distributions for various cases.

scholarly journals An existence theorem for an optimal control problem in banach spaces

1989 ◽  
Vol 39 (2) ◽  
pp. 239-247 ◽  
Author(s):  
Evgenios P. Avgerinos ◽  
Nikolaos S. Papageorgiou
Keyword(s):  
Optimal Control ◽  
Distributed Parameter ◽  
Control Constraints ◽  
Distributed Parameter System ◽  
State Control ◽  
Parameter System ◽  
Control Pair ◽  
Feedback Type ◽  
Cost Criterion ◽  
Nonlinear Distributed Parameter System

In this paper we prove the existence of an optimal admissible state-control pair for a nonlinear distributed parameter system, with control constraints of feedback type and with an integral cost criterion. An example is also worked in detail.

Optimal Control of Linear Distributed Parameter Systems by Shifted Legendre Polynomial Functions

1983 ◽  
Vol 105 (4) ◽  
pp. 222-226 ◽  
Author(s):  
Maw-Ling Wang ◽  
Rong-Yeu Chang
Keyword(s):  
Optimal Control ◽  
Boundary Value Problem ◽  
Legendre Polynomial ◽  
Boundary Value ◽  
Distributed Parameter ◽  
Polynomial Functions ◽  
Distributed Parameter System ◽  
Point Boundary ◽  
Parameter System ◽  
The Maximum Principle

The optimal control problem of a linear distributed parameter system is studied by employing the technique of shifted Legendre polynomial functions. A partial differential equation, which represents the linear distributed parameter system, is expanded into a set of ordinary differential equations for coefficients in the shifted Legendre polynomial expansion of the input and output signals. Expressing the performance index in terms of the expansion coefficients, we transformed an optimal control gain problem into a two point boundary value problem by applying the maximum principle. The two-point boundary value problem is reduced into an initial value problem, the solution of which can be easily obtained by the proposed computational algorithm. An illustrative example will be used to prove this point.

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