scholarly journals Multiphase Return Trajectory Optimization Based on Hybrid Algorithm

2016 ◽  
Vol 2016 ◽  
pp. 1-8 ◽  
Author(s):  
Yi Yang ◽  
Ying Nan
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Trajectory Optimization ◽  
Pseudospectral Method ◽  
Optimization Method ◽  
Natural Computation ◽  
Improve Calculation ◽  
Computation Algorithm ◽  
The Right

A hybrid trajectory optimization method consisting of Gauss pseudospectral method (GPM) and natural computation algorithm has been developed and utilized to solve multiphase return trajectory optimization problem, where a phase is defined as a subinterval in which the right-hand side of the differential equation is continuous. GPM converts the optimal control problem to a nonlinear programming problem (NLP), which helps to improve calculation accuracy and speed of natural computation algorithm. Through numerical simulations, it is found that the multiphase optimal control problem could be solved perfectly.

scholarly journals An Optimal Control Problem by a Hybrid System of Hyperbolic and Ordinary Differential Equations

Games ◽  
2021 ◽  
Vol 12 (1) ◽  
pp. 23
Author(s):  
Alexander Arguchintsev ◽  
Vasilisa Poplevko
Keyword(s):  
Optimal Control ◽  
Differential Equations ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Ordinary Differential Equations ◽  
Hyperbolic Equations ◽  
Control Methods ◽  
The Right ◽  
The Cost ◽  
Optimal Control Methods

This paper deals with an optimal control problem for a linear system of first-order hyperbolic equations with a function on the right-hand side determined from controlled bilinear ordinary differential equations. These ordinary differential equations are linear with respect to state functions with controlled coefficients. Such problems arise in the simulation of some processes of chemical technology and population dynamics. Normally, general optimal control methods are used for these problems because of bilinear ordinary differential equations. In this paper, the problem is reduced to an optimal control problem for a system of ordinary differential equations. The reduction is based on non-classic exact increment formulas for the cost-functional. This treatment allows to use a number of efficient optimal control methods for the problem. An example illustrates the approach.

Energy efficiency path planning for a quadrotor aerial vehicle

2021 ◽  
pp. 014233122110585
Author(s):  
Fouad Yacef ◽  
Nassim Rizoug ◽  
Laid Degaa ◽  
Omar Bouhali ◽  
Mustapha Hamerlain
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Weather Conditions ◽  
Optimization Method ◽  
Control Approach ◽  
Mission Success ◽  
Aerial Vehicle ◽  
Vehicle Trajectory ◽  
Point To Point

Unmanned aerial vehicles are used today in many real-world applications. In all these applications, the vehicle endurance (flight time) is an important constraint that affects mission success. This study investigates the limitations of embedded energy for a quadrotor aerial vehicle. We consider a quadrotor simple tasked to travel from an initial hover configuration to a final hover configuration. In order to have a precise approximation of the consumed energy, we propose a power consumption model with battery dynamic, motor dynamic, and rotor efficiency function. We then introduce an optimization algorithm to minimize the energy consumption during quadrotor aerial vehicle mission. The proposed algorithm is based on an optimal control problem formulated for the quadrotor model and solved using nonlinear programming. In the optimal control problem, we seek to find control inputs (rotor velocity) and vehicle trajectory between initial and final configurations that minimize the consumed energy during a point-to-point mission. We extensively test in simulation experiments the proposed algorithm under normal and windy weather conditions. We compare the proposed optimization method with a nonlinear adaptive control approach to highlight the saved amount of energy.

Trajectory Optimization for DDE Models of Supercavitating Underwater Vehicles

2008 ◽  
Vol 131 (1) ◽  
Author(s):  
Carlo L. Bottasso ◽  
Francesco Scorcelletti ◽  
Massimo Ruzzene ◽  
Seong S. Ahn
Keyword(s):  
Optimal Control ◽  
Differential Equations ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Trajectory Optimization ◽  
Past History ◽  
Flight Mechanics ◽  
Multiple Shooting ◽  
Supercavitating Vehicles ◽  
Delay Differential

In this study we first develop a flight mechanics model for supercavitating vehicles, which is formulated to account for the dependence of the cavity shape from the past history of the system. This mathematical model is governed by a particular class of delay differential equations, featuring time delays on the states of the system. Next, flight trajectories and maneuvering strategies for supercavitating vehicles are obtained by solving an optimal control problem, whose solution, given a cost function and general constraints and bounds on states and controls, yields the control time histories that maneuver the vehicle according to a desired strategy, together with the associated flight path. The optimal control problem is solved using a novel direct multiple shooting approach, which is formulated to properly handle conditions dictated by the delay differential equation formulation governing the dynamic behavior of the vehicle. Specifically, the new formulation enforces the state continuity line conditions in a least-squares sense using local interpolations, which supports local time stepping and drastically reduces the number of optimization unknowns. Examples of maneuvers and resulting trajectories demonstrate the effectiveness of the proposed methodology and the generality of the formulation. The results are also compared with those obtained from a previously developed model governed by ordinary differential equations to highlight the differences and demonstrate the need for the current formulation.

A pseudospectral method for solving optimal control problem of a hybrid tracked vehicle

2017 ◽  
Vol 194 ◽  
pp. 588-595 ◽  
Author(s):  
Shouyang Wei ◽  
Yuan Zou ◽  
Fengchun Sun ◽  
Onder Christopher
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Pseudospectral Method ◽  
Tracked Vehicle

Optimal motion planning of juggling by 3-DOF manipulators using adaptive PSO algorithm

Robotica ◽  
2013 ◽  
Vol 32 (6) ◽  
pp. 967-984 ◽  
Author(s):  
Adel Akbarimajd
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Minimum Energy ◽  
Pso Algorithm ◽  
Optimization Method ◽  
Horizontal Distance ◽  
Optimal Motion Planning ◽  
Adaptive Pso ◽  
Joint Motions

SUMMARYThree-DOF manipulators were employed for juggling of polygonal objects in order to have full control over object's configuration. Dynamic grasp condition is obtained for the instances that the manipulators carry the object on their palms. Manipulation problem is modeled as a nonlinear optimal control problem. In this optimal control problem, time of free flight is used as a free parameter to determine throw and catch times. Cost function is selected to get maximum covered horizontal distance using minimum energy. By selecting third-order polynomials for joint motions, the problem is changed to a constrained parameter selection problem. Adaptive particle swarm optimization method is consequently employed to solve the optimization problem. Effectiveness of the optimization algorithm is verified by a set of simulations in MSC. ADAMS.

Convergence for the optimal control problems using collocation at Legendre-Gauss points

2021 ◽  
pp. 014233122110433
Author(s):  
Heng Mai
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Shooting Method ◽  
Pseudospectral Method ◽  
Single Step ◽  
The Novel ◽  
Step Method ◽  
Gauss Method ◽  
Gauss Points

The convergence of the novel Legendre-Gauss method is established for solving a continuous optimal control problem using collocation at Legendre-Gauss points. The method allows for changes in the number of Legendre-Gauss points to meet the error tolerance. The continuous optimal control problem is first discretized into a nonlinear programming problem at Gauss collocations by the Legendre-Gauss method. Subsequently, we prove the convergence of the Legendre-Gauss algorithm under the assumption that the continuous optimal control problem has a smooth solution. Compared with those of the shooting method, the single step method, and the general pseudospectral method, the numerical example shows that the Legendre-Gauss method has higher computational efficiency and accuracy in solving the optimal control problem.

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