Necessary and sufficient conditions for optimal control of quasilinear partial differential systems

1984 ◽  
Vol 43 (1) ◽  
pp. 89-101 ◽  
Author(s):  
N. A. Derzko ◽  
S. P. Sethi ◽  
G. L. Thompson
Keyword(s):  
Optimal Control ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Partial Differential ◽  
Differential Systems ◽  
Necessary And Sufficient

Symmetry-based algorithms to relate partial differential equations: I. Local symmetries

1990 ◽  
Vol 1 (3) ◽  
pp. 189-216 ◽  
Author(s):  
G. W. Bluman ◽  
S. Kumei
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Sufficient Conditions ◽  
Linear Partial Differential Equation ◽  
Variable Coefficients ◽  
Necessary And Sufficient Conditions ◽  
Partial Differential ◽  
Flow Equations ◽  
Local Symmetries ◽  
Necessary And Sufficient

Simple and systematic algorithms for relating differential equations are given. They are based on comparing the local symmetries admitted by the equations. Comparisons of the infinitesimal generators and their Lie algebras of given and target equations lead to necessary conditions for the existence of mappings which relate them. Necessary and sufficient conditions are presented for the existence of invertible mappings from a given nonlinear system of partial differential equations to some linear system of equations with examples including the hodograph and Legendre transformations, and the linearizations of a nonlinear telegraph equation, a nonlinear diffusion equation, and nonlinear fluid flow equations. Necessary and sufficient conditions are also given for the existence of an invertible point transformation which maps a linear partial differential equation with variable coefficients to a linear equation with constant coefficients. Other types of mappings are also considered including the Miura transformation and the invertible mapping which relates the cylindrical KdV and the KdV equations.

scholarly journals Linear-quadratic optimization and some general hypotheses on optimal control

1999 ◽  
Vol 5 (4) ◽  
pp. 275-289 ◽  
Author(s):  
L. I. Rozonoer
Keyword(s):  
Optimal Control ◽  
Initial Data ◽  
Optimization Problem ◽  
Sufficient Conditions ◽  
Quadratic Optimization ◽  
Necessary And Sufficient Conditions ◽  
Maximum Condition ◽  
Linear Quadratic ◽  
Existence Of Optimal Control ◽  
Necessary And Sufficient

Necessary and sufficient conditions for existence of optimal control for all initial data are proved forLQ-optimization problem. If these conditions are fulfilled, necessary and sufficient conditions of optimality are formulated. Basing on the results, some general hypotheses on optimal control in terms of Pontryagin's maximum condition and Bellman's equation are proposed.

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