Optimal Control in the Presence of Nondifferentiable State Constraints

1976 ◽  
Vol 98 (4) ◽  
pp. 432-439
Author(s):  
E. D. Eyman ◽  
D. P. Sudhakar
Keyword(s):  
Optimal Control ◽  
Integral Equation ◽  
Mathematical Programming ◽  
State Constraints ◽  
Necessary Conditions ◽  
Adjoint Equation ◽  
Phase Constraint ◽  
Maximal Condition ◽  
Phase Constraints ◽  
Differential Control

Necessary conditions are derived for optimality of differential control processes in the presence of nondifferentiable state (or phase) constraints. The techniques of general Mathematical Programming and the Dubovitskii-Milyutin Theorem are employed. The necessary conditions derived are in the form of an adjoint integral equation and a pointwise maximal condition. It is found that the gradient of the state (or phase) constraint can be replaced by the Gateaux differential of a certain form in the adjoint equation.

A Multiplier Rule for a Functional Subject to Certain Integrodifferential Constraints

1969 ◽  
Vol 91 (2) ◽  
pp. 185-189 ◽  
Author(s):  
M. Wittler ◽  
C. N. Shen
Keyword(s):  
Optimal Control ◽  
Integral Equation ◽  
Calculus Of Variations ◽  
Necessary Conditions ◽  
Inequality Constraint ◽  
Fundamental Lemma ◽  
First Order ◽  
Multiplier Rule ◽  
Nuclear Rocket ◽  
Equation Constraint

A problem in the optimal control of a nuclear rocket requires the minimization of a functional subject to an integral equation constraint and an integrodifferential inequality constraint. A theorem giving first-order necessary conditions is derived for this problem in the form of a multiplier rule. The existence of multipliers and the arbitrariness of certain variations is shown. The fundamental lemma of the calculus of variations is applied. A simple example demonstrates the applicability of the theorem.

scholarly journals Optimal control problems with elastic collisions

1989 ◽  
Vol 30 (4) ◽  
pp. 470-482
Author(s):  
J. M. Murray
Keyword(s):  
Optimal Control ◽  
State Vector ◽  
State Constraints ◽  
Optimal Control Problems ◽  
Necessary Conditions ◽  
The State ◽  
Control Problems ◽  
Elastic Collisions ◽  
Linear State

AbstractIn this paper consider we optimal control problems with linear state constraints where the states can be discontinuous at the boundary. In fact the state vector models the cause the position and velocity of a particle where the collisions with the boundary that cause the discontinuities are elastic. Necessary conditions are derived by looking at limits of approximate problems that are unconstrained.

scholarly journals The Derivation of Structural Properties of LM-g Splines by Necessary Condition of Optimal Control

2014 ◽  
Vol 2014 ◽  
pp. 1-5
Author(s):  
Xiongwei Liu ◽  
Xinjian Zhang ◽  
Lizhi Cheng
Keyword(s):  
Optimal Control ◽  
Control Theory ◽  
Structural Properties ◽  
Optimal Control Theory ◽  
State Constraints ◽  
Necessary Conditions ◽  
Necessary Condition ◽  
Interpolating Splines ◽  
The Relationship ◽  
Optimization And Optimal Control

The structural properties of LM-g splines are investigated by optimization and optimal control theory. The continuity and structure of LM-g splines are derived by using a class of necessary conditions with state constraints of optimal control and the relationship between LM-g interpolating splines and the corresponding L-g interpolating splines. This work provides a new method for further exploration of LM-g interpolating splines and its applications in the optimal control.

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