Obstacle Avoidance and Minimum Time Control of Cranes Using Flat Outputs and Nonlinear Programming

2004 ◽  
Author(s):  
Randhir Kumar ◽  
K. Kurien Issac
Keyword(s):  
Nonlinear Programming ◽  
Control Problem ◽  
Programming Problem ◽  
Obstacle Avoidance ◽  
Iterative Algorithm ◽  
Minimum Time ◽  
Nonlinear Programming Problem ◽  
Time Control

The problem addressed here is to determine controls for moving a load along specified trajectories which avoid obstacles. It is possible to use flat outputs to determine inputs when hoist motion is present. However, when hoist is locked, the system does not appear to be differentially flat, and hence the above approach could not be used. We propose an iterative algorithm for the problem of calculating trolley motions in this case. Results for load motions requiring (a) travel and traverse of the trolley and hoist, (b) travel and hoist, and (c) travel alone, are presented. We also use flat outputs to formulate the minimum time control problem as a nonlinear programming problem, with constraints arising from limits on trolley and hoist accelerations and velocities, and positive rope tension. Solutions obtained are also presented.

Trajectory Optimization for Spacecraft Proximity Rendezvous Using Direct Collocation Method

2012 ◽  
Vol 433-440 ◽  
pp. 6652-6656 ◽  
Author(s):  
Tao Liu ◽  
Yu Shan Zhao ◽  
Peng Shi ◽  
Bao Jun Li
Keyword(s):  
Nonlinear Programming ◽  
Control Problem ◽  
Programming Problem ◽  
Collocation Method ◽  
Trajectory Optimization ◽  
Collocation Methods ◽  
Nonlinear Programming Problem ◽  
Reference Orbit ◽  
Direct Collocation ◽  
Direct Collocation Method

Trajectory optimization problem for spacecraft proximity rendezvous with path constraints was discussed using direct collocation method. Firstly, the model of spacecraft proximity rendezvous in elliptic orbit optimization control problem was presented, with the dynamic equations established in the target local orbital frame, and the performance index was minimizing the total fuel consumption. After that the optimal control problem was transcribed into a large scale problem of Nonlinear Programming Problem (NLP) by means of Hermite-Simpson discretization, which was one of the direct collocation methods. Then the nonlinear programming problem was solved using MATLAB software package SNOPT. Finally, to verify this method, the fuel-optimal trajectory for finite thrust was planned for proximity rendezvous with elliptic reference orbit. Numerical simulation results demonstrate that the proposed method was feasible, and was not sensitive to the initial condition, having good robustness.

scholarly journals Best Proximity Points for Some Classes of Proximal Contractions

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Maryam A. Alghamdi ◽  
Naseer Shahzad ◽  
Francesca Vetro
Keyword(s):  
Approximate Solution ◽  
Nonlinear Programming ◽  
Programming Problem ◽  
Iterative Algorithm ◽  
Best Proximity Point ◽  
Sufficient Conditions ◽  
Nonlinear Programming Problem ◽  
Optimal Approximate Solution ◽  
Unique Point ◽  
Banach’S Contraction Principle

Given a self-mapping and a non-self-mapping , the aim of this work is to provide sufficient conditions for the existence of a unique point , calledg-best proximity point, which satisfies . In so doing, we provide a useful answer for the resolution of the nonlinear programming problem of globally minimizing the real valued function , thereby getting an optimal approximate solution to the equation . An iterative algorithm is also presented to compute a solution of such problems. Our results generalize a result due to Rhoades (2001) and hence such results provide an extension of Banach's contraction principle to the case of non-self-mappings.

scholarly journals Comparative Study of AMPL, Pyomo and JuMP Optimization Modeling Languages on a Flood Control Problem Example

2021 ◽  
Vol 25 (4) ◽  
pp. 19-24
Author(s):  
Andrzej Karbowski ◽  
Krzysztof Wyskiel
Keyword(s):  
Nonlinear Programming ◽  
Comparative Study ◽  
Control Problem ◽  
Programming Problem ◽  
Discrete Time ◽  
Flood Control ◽  
Modeling Languages ◽  
Nonlinear Programming Problem ◽  
Optimization Modeling

The purpose of this work is a comparative study of three languages (environments) of optimization modeling: AMPL, Pyomo and JuMP. The comparison will be based on three implementations of an optimal discrete-time flood control problem formulated as a nonlinear programming problem. The codes for individual models and differences between them will be presented and discussed. Various aspects will be taken into account, e.g. simplicity and intuitiveness of implementation.

scholarly journals Best Proximity Point Results for MK-Proximal Contractions

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
Mohamed Jleli ◽  
Erdal Karapınar ◽  
Bessem Samet
Keyword(s):  
Nonlinear Programming ◽  
Programming Problem ◽  
Iterative Algorithm ◽  
Distance Function ◽  
Metric Space ◽  
Optimization Problems ◽  
Best Proximity Point ◽  
Nonlinear Programming Problem ◽  
New Class ◽  
Contractive Mappings

LetAandBbe nonempty subsets of a metric space with the distance function d, andT:A→Bis a given non-self-mapping. The purpose of this paper is to solve the nonlinear programming problem that consists in minimizing the real-valued functionx↦d(x,Tx), whereTbelongs to a new class of contractive mappings. We provide also an iterative algorithm to find a solution of such optimization problems.

scholarly journals Trust-Region Based Penalty Barrier Algorithm for Constrained Nonlinear Programming Problems: An Application of Design of Minimum Cost Canal Sections

Mathematics ◽  
2021 ◽  
Vol 9 (13) ◽  
pp. 1551
Author(s):  
Bothina El-Sobky ◽  
Yousria Abo-Elnaga ◽  
Abd Allah A. Mousa ◽  
Mohamed A. El-Shorbagy
Keyword(s):  
Nonlinear Programming ◽  
Global Convergence ◽  
Programming Problem ◽  
Trust Region ◽  
Convergence Theory ◽  
Benchmark Problems ◽  
Nonlinear Programming Problem ◽  
Barrier Method ◽  
Starting Point ◽  
Constrained Nonlinear Programming

In this paper, a penalty method is used together with a barrier method to transform a constrained nonlinear programming problem into an unconstrained nonlinear programming problem. In the proposed approach, Newton’s method is applied to the barrier Karush–Kuhn–Tucker conditions. To ensure global convergence from any starting point, a trust-region globalization strategy is used. A global convergence theory of the penalty–barrier trust-region (PBTR) algorithm is studied under four standard assumptions. The PBTR has new features; it is simpler, has rapid convergerce, and is easy to implement. Numerical simulation was performed on some benchmark problems. The proposed algorithm was implemented to find the optimal design of a canal section for minimum water loss for a triangle cross-section application. The results are promising when compared with well-known algorithms.

Minimax Input Shaper Design Using Linear Programming

2008 ◽  
Vol 130 (5) ◽  
Author(s):  
Tarunraj Singh
Keyword(s):  
Linear Programming ◽  
Nonlinear Programming ◽  
Programming Problem ◽  
Linear Programming Problem ◽  
Barycentric Coordinates ◽  
Nonlinear Programming Problem ◽  
Dome A ◽  
Input Shaper ◽  
Maximum Value ◽  
The Cost

The focus of this paper is on the design of robust input shapers where the maximum value of the cost function over the domain of uncertainty is minimized. This nonlinear programming problem is reformulated as a linear programming problem by approximating a n-dimensional hypersphere with multiple hyperplanes (as in a geodesic dome). A recursive technique to approximate a hypersphere to any level of accuracy is developed using barycentric coordinates. The proposed technique is illustrated on the spring-mass-dashpot and the benchmark floating oscillator problem undergoing a rest-to-rest maneuver. It is shown that the results of the linear programming problem are nearly identical to that of the nonlinear programming problem.

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