A transformation technique for optimal control problems with partially linear state inequality constraints

1979 ◽  
Vol 28 (2) ◽  
pp. 185-212 ◽  
Author(s):  
A. Miele ◽  
A. K. Wu ◽  
C. T. Liu
Keyword(s):  
Optimal Control ◽  
Optimal Control Problems ◽  
Inequality Constraints ◽  
Control Problems ◽  
Transformation Technique ◽  
Partially Linear ◽  
Linear State ◽  
State Inequality Constraints

scholarly journals AN EFFICIENT COMPUTATIONAL APPROACH TO A CLASS OF MINMAX OPTIMAL CONTROL PROBLEMS WITH APPLICATIONS

2009 ◽  
Vol 51 (2) ◽  
pp. 162-177 ◽  
Author(s):  
B. LI ◽  
K. L. TEO ◽  
G. H. ZHAO ◽  
G. R. DUAN
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Optimal Control Problems ◽  
Inequality Constraints ◽  
Necessary Condition ◽  
Computation Method ◽  
Control Problems ◽  
Continuous State ◽  
State Inequality Constraints

AbstractIn this paper, an efficient computation method is developed for solving a general class of minmax optimal control problems, where the minimum deviation from the violation of the continuous state inequality constraints is maximized. The constraint transcription method is used to construct a smooth approximate function for each of the continuous state inequality constraints. We then obtain an approximate optimal control problem with the integral of the summation of these smooth approximate functions as its cost function. A necessary condition and a sufficient condition are derived showing the relationship between the original problem and the smooth approximate problem. We then construct a violation function from the solution of the smooth approximate optimal control problem and the original continuous state inequality constraints in such a way that the optimal control of the minmax problem is equivalent to the largest root of the violation function, and hence can be solved by the bisection search method. The control parametrization and a time scaling transform are applied to these optimal control problems. We then consider two practical problems: the obstacle avoidance optimal control problem and the abort landing of an aircraft in a windshear downburst.

A weak maximum principle for optimal control problems with mixed constraints under a constant rank condition

2020 ◽  
Vol 37 (3) ◽  
pp. 1021-1047
Author(s):  
Roberto Andreani ◽  
Valeriano Antunes de Oliveira ◽  
Jamielli Tomaz Pereira ◽  
Geraldo Nunes Silva
Keyword(s):  
Optimal Control ◽  
Maximum Principle ◽  
Optimal Control Problems ◽  
Necessary Optimality Conditions ◽  
Inequality Constraints ◽  
Equality Constraints ◽  
Control Problems ◽  
Constant Rank ◽  
Rank Condition ◽  
Weak Maximum Principle

Abstract Necessary optimality conditions for optimal control problems with mixed state-control equality constraints are obtained. The necessary conditions are given in the form of a weak maximum principle and are obtained under (i) a new regularity condition for problems with mixed linear equality constraints and (ii) a constant rank type condition for the general non-linear case. Some instances of problems with equality and inequality constraints are also covered. Illustrative examples are presented.

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