Direct Shooting Method for Optimal Control of the Highly Nonlinear Differential-Algebraic Systems

2015 ◽  
pp. 75-90
Author(s):  
Paweł Dra̧g ◽  
Krystyn Styczeń
Keyword(s):  
Optimal Control ◽  
Shooting Method ◽  
Algebraic Systems ◽  
Highly Nonlinear ◽  
Direct Shooting

Optimization in the Design and Control of Robotic Manipulators: A Survey

1989 ◽  
Vol 42 (4) ◽  
pp. 117-128 ◽  
Author(s):  
S. S. Rao ◽  
P. K. Bhatti
Keyword(s):  
Optimal Control ◽  
Robot Manipulator ◽  
Research Effort ◽  
Industrial Robot ◽  
Load Capacity ◽  
Robotic Manipulators ◽  
Optimization Techniques ◽  
Highly Nonlinear ◽  
Manipulator Design ◽  
And Control

Robotics is a relatively new and evolving technology being applied to manufacturing automation and is fast replacing the special-purpose machines or hard automation as it is often called. Demands for higher productivity, better and uniform quality products, and better working environments are primary reasons for its development. An industrial robot is a multifunctional and computer-controlled mechanical manipulator exhibiting a complex and highly nonlinear behavior. Even though most current robots have anthropomorphic configurations, they have far inferior manipulating abilities compared to humans. A great deal of research effort is presently being directed toward improving their overall performance by using optimal mechanical structures and control strategies. The optimal design of robot manipulators can include kinematic performance characteristics such as workspace, accuracy, repeatability, and redundancy. The static load capacity as well as dynamic criteria such as generalized inertia ellipsoid, dynamic manipulability, and vibratory response have also been considered in the design stages. The optimal control problems typically involve trajectory planning, time-optimal control, energy-optimal control, and mixed-optimal control. The constraints in a robot manipulator design problem usually involve link stresses, actuator torques, elastic deformation of links, and collision avoidance. This paper presents a review of the literature on the issues of optimum design and control of robotic manipulators and also the various optimization techniques currently available for application to robotics.

Sufficiency and sensitivity for nonlinear optimal control problems on time scales via coercivity

2018 ◽  
Vol 24 (4) ◽  
pp. 1705-1734 ◽  
Author(s):  
Roman Šimon Hilscher ◽  
Vera Zeidan
Keyword(s):  
Optimal Control ◽  
Time Scales ◽  
Shooting Method ◽  
Optimal Control Problems ◽  
Sufficient Conditions ◽  
Nonlinear Optimal Control ◽  
Control Problems ◽  
Local Minimality ◽  
The Second Variation ◽  
Accessory Problem

The main focus of this paper is to develop a sufficiency criterion for optimality in nonlinear optimal control problems defined on time scales. In particular, it is shown that the coercivity of the second variation together with the controllability of the linearized dynamic system are sufficient for the weak local minimality. The method employed is based on a direct approach using the structure of this optimal control problem. The second aim pertains to the sensitivity analysis for parametric control problems defined on time scales with separately varying state endpoints. Assuming a slight strengthening of the sufficiency criterion at a base value of the parameter, the perturbed problem is shown to have a weak local minimum and the corresponding multipliers are shown to be continuously differentiable with respect to the parameter. A link is established between (i) a modification of the shooting method for solving the associated boundary value problem, and (ii) the sufficient conditions involving the coercivity of the accessory problem, as opposed to the Riccati equation, which is also used for this task. This link is new even for the continuous time setting.

scholarly journals Comparison of a Triple Inverted Pendulum Stabilization Using Optimal Control Technique

2020 ◽  
Author(s):  
Mustefa Jibril ◽  
Messay Tadese ◽  
Eliyas Alemayehu Tadese
Keyword(s):  
Optimal Control ◽  
Impulse Response ◽  
Inverted Pendulum ◽  
Control Method ◽  
Pole Placement ◽  
Control Technique ◽  
Comparison Results ◽  
Highly Nonlinear ◽  
Pole Placement Controller ◽  
Triple Inverted Pendulum

In this paper, modelling design and analysis of a triple inverted pendulum have been done using Matlab/Script toolbox. Since a triple inverted pendulum is highly nonlinear, strongly unstable without using feedback control system. In this paper an optimal control method means a linear quadratic regulator and pole placement controllers are used to stabilize the triple inverted pendulum upside. The impulse response simulation of the open loop system shows us that the pendulum is unstable. The comparison of the closed loop impulse response simulation of the pendulum with LQR and pole placement controllers results that both controllers have stabilized the system but the pendulum with LQR controllers have a high overshoot with long settling time than the pendulum with pole placement controller. Finally the comparison results prove that the pendulum with pole placement controller improve the stability of the system.

scholarly journals Optimal control of COVID-19

2021 ◽  
Vol 11 (1) ◽  
pp. 114-122
Author(s):  
Nacima Moussouni ◽  
Mohamed Aliane
Keyword(s):  
Infectious Disease ◽  
Optimal Control ◽  
Maximum Principle ◽  
Indirect Method ◽  
Shooting Method ◽  
Discretization Method ◽  
Seir Model ◽  
The World ◽  
Respiratory Droplets ◽  
The Pontryagin Maximum Principle

Coronavirus disease of 2019 or COVID-19 (acronym for coronavirus disease 2019) is an emerging infectious disease caused by a strain of coronavirus called SARS-CoV-22, contagious with human-to-human transmission via respiratory droplets or by touching contaminated surfaces then touching them face. Faced with what the world lives, to define this problem, we have modeled it as an optimal control problem based on the models of William Ogilvy Kermack et Anderson Gray McKendrick, called SEIR model, modified by adding compartments suitable for our study. Our objective in this work is to maximize the number of recovered people while minimizing the number of infected. We solved the problem theoretically using the Pontryagin maximum principle, numerically we used and compared results of two methods namely the indirect method (shooting method) and the Euler discretization method, implemented in MATLAB.

Sign in / Sign up

Export Citation Format

Share Document