Optimal Control Strategies for Wheeled Mobile Robot With Bounded Inputs

2010 ◽  
Author(s):  
Ilan Zohar ◽  
Amit Ailon
Keyword(s):  
Optimal Control ◽  
Mobile Robot ◽  
Control Strategies ◽  
Equations Of Motion ◽  
Wheeled Mobile Robots ◽  
Optimal Control Strategy ◽  
Input Signals ◽  
Control Objective ◽  
Quadratic Index ◽  
Algebraic Constraints

This paper presents a simple approach for solving optimal control problems in wheeled mobile robots with bounded inputs. The control objective is to minimize a quadratic index of performance subject to differential constraints (the mobile robot equations of motion). The solution to the problem is obtained by utilizing an explicit trajectory parametrization method, which allows us to establish a sub-optimal control strategy by minimizing a multivariable function subject to a set of algebraic constraints. The approach is based on the flatness property, which allows us to represent the flat output by a polynomial. The bounds on the input signals are taken into consideration in the current analysis.

Optimal Control Strategy for Ice-Storage System Based on Hourly Dynamic Load Simulation

2013 ◽  
Vol 671-674 ◽  
pp. 2515-2519
Author(s):  
Xue Mei Wang ◽  
Zhen Hai Wang ◽  
Xing Long Wu
Keyword(s):  
Optimal Control ◽  
Air Conditioning ◽  
Control Strategies ◽  
Storage System ◽  
Simulation Software ◽  
Ice Storage ◽  
Optimal Control Strategy ◽  
Air Conditioning System ◽  
Energy Plus ◽  
Load Simulation

This project aims to study the optimal control model of the ice-storage system which is theoretically close to the optimal control and also applicable to actual engineering. Using Energy Plus, the energy consumption simulation software, and the simple solution method of optimal control, researchers can analyze and compare the annual operation costs of the ice-storage air-conditioning system of a project in Beijing under different control strategies. Researchers obtained the power rates of the air-conditioning system in the office building under the conditions of chiller-priority and optimal contro1 throughout the cooling season. Through analysis and comparison, they find that after the implementation of optimal control, the annually saved power bills mainly result from non-design conditions, especially in the transitional seasons.

scholarly journals Optimal Control Strategy Design Based on Dynamic Programming for a Dual-Motor Coupling-Propulsion System

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Shuo Zhang ◽  
Chengning Zhang ◽  
Guangwei Han ◽  
Qinghui Wang
Keyword(s):  
Optimal Control ◽  
Dynamic Programming ◽  
Energy Loss ◽  
Control Strategy ◽  
Control Strategies ◽  
Propulsion System ◽  
Dynamic Features ◽  
Optimal Control Strategy ◽  
Control Rules ◽  
Electric Bus

A dual-motor coupling-propulsion electric bus (DMCPEB) is modeled, and its optimal control strategy is studied in this paper. The necessary dynamic features of energy loss for subsystems is modeled. Dynamic programming (DP) technique is applied to find the optimal control strategy including upshift threshold, downshift threshold, and power split ratio between the main motor and auxiliary motor. Improved control rules are extracted from the DP-based control solution, forming near-optimal control strategies. Simulation results demonstrate that a significant improvement in reducing energy loss due to the dual-motor coupling-propulsion system (DMCPS) running is realized without increasing the frequency of the mode switch.

scholarly journals The value of monitoring to control evolving populations

2015 ◽  
Vol 112 (4) ◽  
pp. 1007-1012 ◽  
Author(s):  
Andrej Fischer ◽  
Ignacio Vázquez-García ◽  
Ville Mustonen
Keyword(s):  
Optimal Control ◽  
Stochastic Optimal Control ◽  
Finite Population ◽  
Control Strategies ◽  
Target Population ◽  
Therapy Resistance ◽  
Mathematical Concepts ◽  
Control Objective ◽  
Cancer Cell Population ◽  
Evolving Populations

Populations can evolve to adapt to external changes. The capacity to evolve and adapt makes successful treatment of infectious diseases and cancer difficult. Indeed, therapy resistance has become a key challenge for global health. Therefore, ideas of how to control evolving populations to overcome this threat are valuable. Here we use the mathematical concepts of stochastic optimal control to study what is needed to control evolving populations. Following established routes to calculate control strategies, we first study how a polymorphism can be maintained in a finite population by adaptively tuning selection. We then introduce a minimal model of drug resistance in a stochastically evolving cancer cell population and compute adaptive therapies. When decisions are in this manner based on monitoring the response of the tumor, this can outperform established therapy paradigms. For both case studies, we demonstrate the importance of high-resolution monitoring of the target population to achieve a given control objective, thus quantifying the intuition that to control, one must monitor.

scholarly journals Modelling of Dynamics of a Wheeled Mobile Robot with Mecanum Wheels with the use of Lagrange Equations of the Second Kind

2017 ◽  
Vol 22 (1) ◽  
pp. 81-99 ◽  
Author(s):  
Z. Hendzel ◽  
Ł. Rykała
Keyword(s):  
Mathematical Model ◽  
Kinetic Energy ◽  
Mobile Robot ◽  
Mobile Robots ◽  
Equations Of Motion ◽  
Wheeled Mobile Robot ◽  
Dynamic Equations ◽  
Lagrange Equations ◽  
Wheeled Mobile Robots ◽  
New Type

Abstract The work presents the dynamic equations of motion of a wheeled mobile robot with mecanum wheels derived with the use of Lagrange equations of the second kind. Mecanum wheels are a new type of wheels used in wheeled mobile robots and they consist of freely rotating rollers attached to the circumference of the wheels. In order to derive dynamic equations of motion of a wheeled mobile robot, the kinetic energy of the system is determined, as well as the generalised forces affecting the system. The resulting mathematical model of a wheeled mobile robot was generated with the use of Maple V software. The results of a solution of inverse and forward problems of dynamics of the discussed object are also published.

scholarly journals Modeling the Impact of Optimal Control Strategies on the Dynamics of Zika Virus Disease Using the Sterile Insect Technology

2020 ◽  
pp. 13-33
Author(s):  
Atokolo William ◽  
Akpa Johnson ◽  
Daniel Musa Alih ◽  
Olayemi Kehinde Samuel ◽  
C. E. Mbah Godwin
Keyword(s):  
Optimal Control ◽  
Control Strategy ◽  
Zika Virus ◽  
Human Population ◽  
Necessary Conditions ◽  
Virus Disease ◽  
Control Strategies ◽  
Control Measures ◽  
Optimal Control Strategy ◽  
The Impact

This work is aimed at formulating a mathematical model for the control of zika virus infection using Sterile Insect Technology (SIT). The model is extended to incorporate optimal control strategy by introducing three control measures. The optimal control is aimed at minimizing the number of Exposed human, Infected human and the total number of Mosquitoes in a population and as such reducing contacts between mosquitoes and human, human to human and above all, eliminates the population of Mosquitoes. The Pontryagin’s maximum principle was used to obtain the necessary conditions, find the optimality system of our model and to obtain solution to the control problem. Numerical simulations result shows that; reduction in the number of Exposed human population, Infected human population and reduction in the entire population of Mosquito population is best achieved using the optimal control strategy.

scholarly journals Optimal control of a collective migration model

2015 ◽  
Vol 26 (02) ◽  
pp. 383-417 ◽  
Author(s):  
Benedetto Piccoli ◽  
Nastassia Pouradier Duteil ◽  
Benjamin Scharf
Keyword(s):  
Optimal Control ◽  
Social Dynamics ◽  
Initial Conditions ◽  
Control Strategies ◽  
System Modeling ◽  
Initial Period ◽  
Target Velocity ◽  
Collective Migration ◽  
Optimal Control Strategy ◽  
Cohesive Group

Collective migration of animals in a cohesive group is rendered possible by a strategic distribution of tasks among members: some track the travel route, which is time and energy-consuming, while the others follow the group by interacting among themselves. In this paper, we study a social dynamics system modeling collective migration. We consider a group of agents able to align their velocities to a global target velocity, or to follow the group via interaction with the other agents. The balance between these two attractive forces is our control for each agent, as we aim to drive the group to consensus at the target velocity. We show that the optimal control strategies in the case of final and integral costs consist of controlling the agents whose velocities are the furthest from the target one: these agents sense only the target velocity and become leaders, while the uncontrolled ones sense only the group, and become followers. Moreover, in the case of final cost, we prove an “Inactivation” principle: there exist initial conditions such that the optimal control strategy consists of letting the system evolve freely for an initial period of time, before acting with full control on the agent furthest from the target velocity.

scholarly journals Optimal Control Techniques on a Mathematical Model for the Dynamics of Tungiasis in a Community

2017 ◽  
Vol 2017 ◽  
pp. 1-19 ◽  
Author(s):  
Jairos Kahuru ◽  
Livingstone S. Luboobi ◽  
Yaw Nkansah-Gyekye
Keyword(s):  
Mathematical Model ◽  
Optimal Control ◽  
Control Strategy ◽  
Control Strategies ◽  
Control Process ◽  
Control Measures ◽  
Human Beings ◽  
Optimal Control Strategy ◽  
Control Techniques ◽  
Existence Of Optimal Control

Tungiasis is a permanent penetration of female sand flea“Tunga penetrans”into the epidermis of its host. It affects human beings and domestic and sylvatic animals. In this paper, we apply optimal control techniques to a Tungiasis controlled mathematical model to determine the optimal control strategy in order to minimize the number of infested humans, infested animals, and sand flea populations. In an attempt to reduce Tungiasis infestation in human population, the control strategies based on personal protection, personal treatment, educational campaign, environmental sanitation, and insecticidal treatments on the affected parts as well as on animal fur are considered. We prove the existence of optimal control problem, determine the necessary conditions for optimality, and then perform numerical simulations. The numerical results showed that the control strategy comprises all five control measures and that which involves the three control measures of insecticide control, insecticidal dusting on animal furs, and environmental hygiene has the significant impact on Tungiasis transmission. Therefore, fighting against Tungiasis infestation in endemic settings, multidimensional control process should be employed in order to achieve the maximum benefits.

Experimental results on the nonlinear∞control via quasi-LPV representation and game theory for wheeled mobile robots

Robotica ◽  
2009 ◽  
Vol 27 (4) ◽  
pp. 547-553 ◽  
Author(s):  
Roberto S. Inoue ◽  
Adriano A. G. Siqueira ◽  
Marco H. Terra
Keyword(s):  
Mobile Robot ◽  
Control Strategies ◽  
The State ◽  
Wheeled Mobile Robot ◽  
Experimental Results ◽  
Algebraic Riccati Equation ◽  
Linear Matrix ◽  
Wheeled Mobile Robots ◽  
Nonlinear Dynamic Equations ◽  
Angular Velocities

SUMMARYIn this paper, nonlinear dynamic equations of a wheeled mobile robot are described in the state-space form where the parameters are part of the state (angular velocities of the wheels). This representation, known as quasi-linear parameter varying, is useful for control designs based on nonlinear∞approaches. Two nonlinear∞controllers that guarantee induced2-norm, between input (disturbances) and output signals, bounded by an attenuation level γ, are used to control a wheeled mobile robot. These controllers are solved via linear matrix inequalities and algebraic Riccati equation. Experimental results are presented, with a comparative study among these robust control strategies and the standard computed torque, plus proportional-derivative, controller.

scholarly journals A Co-infection model for HPV and Syphilis with Optimal Control and Cost-Effectiveness Analysis

2020 ◽  
Author(s):  
Andrew Omame ◽  
Daniel Okuonghae ◽  
Ugochukwu Emmanuel Nwafor ◽  
Benedict Udoka Odionyenma
Keyword(s):  
Optimal Control ◽  
Cost Effectiveness ◽  
Asymptotic Stability ◽  
Global Asymptotic Stability ◽  
Control Strategies ◽  
Cost Effective ◽  
Infection Model ◽  
Control Analysis ◽  
Optimal Control Strategy ◽  
Disease Free

In this work, we develop and present a co-infection model for human papillomavirus (HPV) and syphilis with cost-effectiveness optimal control analysis. The full co-infection model is shown to undergo the phenomenon of backward bifurcation when a certain condition is satisfied. The global asymptotic stability of the disease-free equilibrium of the full model is shown \textbf{not to exist}, when the associated reproduction number is less than unity. The existence of endemic equilibrium of the syphilis-only sub-model is shown to exist and the global asymptotic stability of the disease-free and endemic equilibria of both the syphilis-only sub-model and HPV-only sub-model were established. The global asymptotic stability of disease-free equilibrium of the HPV-only sub-model is also proven. Numerical simulations of the optimal control model showed that the optimal control strategy which implements syphilis treatment controls for singly infected individuals is the most cost-effective of all the control strategies in reducing the burden of HPV and syphilis co-infections.

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