Optimal pointing control of robotic manipulators with state inequality constraints

1993 ◽  
Vol 16 (5) ◽  
pp. 966-969
Author(s):  
C.-H. Chuang
Keyword(s):  
Inequality Constraints ◽  
Robotic Manipulators ◽  
Pointing Control ◽  
State Inequality Constraints

Time-optimal motions of robotic manipulators

Robotica ◽  
2000 ◽  
Vol 18 (6) ◽  
pp. 659-667 ◽  
Author(s):  
Miroslaw Galicki ◽  
Dariusz Uciński
Keyword(s):  
Penalty Function ◽  
Function Method ◽  
Inequality Constraints ◽  
Admissible Solution ◽  
Robotic Manipulators ◽  
Penalty Function Method ◽  
Planning Time ◽  
Time Optimal ◽  
Joint Limits ◽  
State Inequality Constraints

An approach to planning time-optimal collision-free motions of robotic manipulators is presented. It is based on using a negative formulation of the Pontryagin Maximum Principle which handles efficiently various control and/or state constraints imposed on the manipulator motions, which arise naturally out of manipulator joint limits and obstacle avoidance. This approach becomes similar to that described by Weinreb and Bryson, as well as by Bryson and Ho if no state inequality constraints are imposed. In contrast to the penalty function method, the proposed algorithm does not require an initial admissible solution (i.e. an initial admissible trajectory) and finds manipulator trajectories with a smaller cost value than the penalty function approach. A computer example involving a planar redundant manipulator of three revolute kinematic pairs is included. The numerical results are compared with those obtained using an exterior penalty function method.

Optimal impulsive control for advertising strategy problems based on a gradient-based PSO algorithm

2018 ◽  
Vol 41 (8) ◽  
pp. 2280-2292 ◽  
Author(s):  
Xiang Wu ◽  
Jinxing Lin ◽  
Kanjian Zhang ◽  
Ming Cheng
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Inequality Constraints ◽  
Pso Algorithm ◽  
The State ◽  
Optimization Techniques ◽  
Advertising Strategy ◽  
Gradient Based ◽  
State Inequality Constraints

This paper considers an optimal advertising strategy problem. This is an important problem in marketing investment for new products in a free market. The main contributions of this paper are as follows. First, the problem is formulated as an optimal control problem of switched impulsive systems with the state inequality constraints, which is different from the existing nonlinear system models. As the complexity of such constraints and the switching instants are unknown, it is difficult to solve this problem by using conventional optimization techniques. To overcome this difficulty, by applying the penalty function, all the state inequality constraints are first written as non-differentiable penalty terms and imposed into the cost function. Then, the penalty terms are smoothed by using a novel smooth function, leading to a smooth optimal control problem with no state inequality constraints, and an improved gradient-based particle swarm optimization (PSO) algorithm is proposed for solving this problem. Error analysis results show that if the adjustable parameter is sufficiently small, the solution of the smooth optimal control problem is approximately equal to the original problem. Finally, a switched impulsive system for beer sales is established to illustrate the effectiveness of the developed algorithm.

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