Convex–Concave Decomposition of Nonlinear Equality Constraints in Optimal Control

2021 ◽  
Vol 44 (1) ◽  
pp. 4-14
Author(s):  
Ping Lu
Keyword(s):  
Optimal Control ◽  
Equality Constraints ◽  
Nonlinear Equality

A Modification of Feasible Direction Optimization Method for Handling Equality Constraints

1988 ◽  
Author(s):  
Yong Chen ◽  
Bailin Li
Keyword(s):  
Nonlinear Programming ◽  
Efficient Algorithm ◽  
Optimization Method ◽  
Equality Constraints ◽  
Feasible Region ◽  
Feasible Direction ◽  
Feasible Direction Method ◽  
Traditional Algorithm ◽  
Inequality Type ◽  
Nonlinear Equality

Abstract The Feasible Direction Method of Zoutendijk has proven to be one of the efficient algorithm currently available for solving nonlinear programming problems with only inequality type constraints. Since in the case of having equality type constraints, there does not exist nonzero direction close to the feasible region, the traditional algorithm can not work properly. In this paper, a modified feasible direction finding technique has been proposed in order to handle nonlinear equality constraints for the Feasible Direction Method. The algorithm is based on searching along directions intersecting the tangent of the equality constraints at some angle which makes the move toward the interior of the feasible region.

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.

A Modification of Feasible Direction Optimization Method for Handling Equality Constraints

1989 ◽  
Vol 111 (3) ◽  
pp. 442-445
Author(s):  
Yong Chen ◽  
Bailin Li
Keyword(s):  
Nonlinear Programming ◽  
Optimization Method ◽  
Direction Finding ◽  
Equality Constraints ◽  
Feasible Region ◽  
Feasible Direction ◽  
Feasible Direction Method ◽  
Traditional Algorithm ◽  
Inequality Type ◽  
Nonlinear Equality

The Feasible Direction Method of Zoutendijk has proven to be one of the most efficient algorithms currently available for solving nonlinear programming problems with only inequality type constraints. Since in the case of equality type constraints, there exists no nonzero direction close to the feasible region, the traditional algorithm cannot work properly. In this paper, a modified feasible direction finding technique has been proposed in order to handle nonlinear equality constraints for the Feasible Direction Method. The algorithm is based on searching along directions intersecting the tangent of the equality constraints at some angle which makes the move toward the interior of the feasible region.

Optimal Control for a Pitcher’s Motion Modeled as Constrained Mechanical System

2009 ◽  
Author(s):  
Sina Ober-Blo¨baum ◽  
Julia Timmermann
Keyword(s):  
Optimal Control ◽  
Muscle Force ◽  
Control Method ◽  
Control Effort ◽  
Constrained Mechanical Systems ◽  
Time Stepping ◽  
D’Alembert Principle ◽  
Optimal Control Method ◽  
Multi Body ◽  
Nonlinear Equality

In this contribution, a recently developed optimal control method for constrained mechanical systems is applied to determine optimal motions and muscle force evolutions for a pitcher’s arm. The method is based on a discrete constrained version of the Lagrange-d’Alembert principle leading to structure preserving time-stepping equations. A reduction technique is used to derive the nonlinear equality constraints for the minimization of a given objective function. Different multi-body models for the pitcher’s arm are investigated and compared with respect to the motion itself, the control effort, the pitch velocity, and the pitch duration time. In particular, the use of a muscle model allows for an identification of limits on the maximal forces that ensure more realistic optimal pitch motions.

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