A Control Method of Dynamic Selfish Routing Based on a State-Dependent Tax

In this paper, the robust control problem is tackled by employing the state-dependent Riccati equation (SDRE) for uncertain systems with unmeasurable states subject to mismatched time-varying disturbances. The proposed observer-based robust (OBR) controller is applied to two highly nonlinear, coupled and large robotic systems: namely a manipulator presenting joint flexibility due to deformation of the power transmission elements between the actuator and the robot known as flexible-joint robot (FJR) and also an FJR incorporating geared permanent magnet DC motor dynamics in its dynamic model called electrical flexible-joint robot (EFJR). A novel state-dependent coefficient (SDC) form is introduced for uncertain EFJRs. Rather than coping with the OBR control problem for such complex uncertain robotic systems, the main idea is to solve an equivalent nonlinear optimal control problem where the uncertainty and disturbance bounds are incorporated in the performance index. The stability proof is presented. Solving the complicated robust control problem for FJRs and EFJRs subject to uncertainty and disturbances via a simple and flexible nonlinear optimal approach and no need of state measurement are the main advantages of the proposed control method. Finally, simulation results are included to verify the efficiency and superiority of the control scheme.

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State Dependent Riccati Equation (SDRE) Control Method Applied in Cancellation of a Parametric Resonance in a Magnetically Levitated Body

Volume 4: 8th International Conference on Multibody Systems, Nonlinear Dynamics, and Control, Parts A and B ◽

10.1115/detc2011-47406 ◽

2011 ◽

Author(s):

Fa´bio Roberto Chavarette ◽

Jose´ Manoel Balthazar ◽

Ce´lia Aparecida dos Reis ◽

Nelson Jose´ Peruzzi

Keyword(s):

Riccati Equation ◽

Control Method ◽

Equations Of Motion ◽

Control Design ◽

Inertial Force ◽

The Body ◽

State Dependent ◽

Oscillatory Movement ◽

Magnetically Levitated ◽

Static Equilibrium State

Here, a simplified dynamical model of a magnetically levitated body is considered. The origin of an inertial Cartesian reference frame is set at the pivot point of the pendulum on the levitated body in its static equilibrium state (ie, the gap between the magnet on the base and the magnet on the body, in this state). The governing equations of motion has been derived and the characteristic feature of the strategy is the exploitation of the nonlinear effect of the inertial force associated, with the motion of a pendulum-type vibration absorber driven, by an appropriate control torque [4]. In the present paper, we analyzed the nonlinear dynamics of problem, discussed the energy transfer between the main system and the pendulum in time, and developed State Dependent Riccati Equation (SDRE) control design to reducing the unstable oscillatory movement of the magnetically levitated body to a stable fixed point. The simulations results showed the effectiveness of the (SDRE) control design.

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Research on Control Method of Keeping Flight Formation by Using SDRE on the Sun-Earth Libration Points

Advances in Astronomy ◽

10.1155/2017/4162838 ◽

2017 ◽

Vol 2017 ◽

pp. 1-10 ◽

Cited By ~ 3

Author(s):

He Zhenqi ◽

Zhang Ke ◽

Lv Meibai

Keyword(s):

Control Method ◽

Libration Point ◽

Linear Quadratic Regulator ◽

Transition Process ◽

Continuous Control ◽

The Sun ◽

Nonlinear Dynamic Model ◽

Linear Quadratic ◽

State Dependent ◽

Lqr Controller

Keeping the flying formation of spacecraft is a key problem which needs to be solved in deep space exploration missions. In this paper, the nonlinear dynamic model of formation flying is established and a series of transformations are carried out on this model equation. By using SDRE (State-Dependent Riccati Equation) algorithm, the optimal control of flying formation is realized. Compared with the traditional control method based on the average orbit elements and LQR (Linear Quadratic Regulator) control method, the SDRE control method has higher control precision and is more suitable for the advantages of continuous control in practical engineering. Finally, the parameter values of the sun-earth libration point L2 are substituted in the equation and simulation is performed. The simulation curves of SDRE controller are compared with LQR controller. The results show that the SDRE controllers time cost is less than the LQR controllers and the former’s fuel consumption is less than the latter’s in the system transition process.

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Hypersonic guidance via the state-dependent Riccati equation control method

Proceedings of the 1999 IEEE International Conference on Control Applications (Cat. No.99CH36328) ◽

10.1109/cca.1999.806179 ◽

2003 ◽

Cited By ~ 10

Author(s):

J.R. Cloutier ◽

P.H. Zipfel

Keyword(s):

Riccati Equation ◽

Control Method ◽

The State ◽

State Dependent

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SDRE based Leader-Follower Formation Control of Multiple Mobile Robots

TEMA (São Carlos) ◽

10.5540/tema.2014.015.02.0195 ◽

2014 ◽

Vol 15 (2) ◽

Author(s):

Caio Igor Gonçalves Chinelato ◽

L.S. Martins-Filho

Keyword(s):

Mobile Robots ◽

Formation Control ◽

Control Method ◽

Nonlinear Dynamical System ◽

Control Performance ◽

Font Size ◽

Multiple Mobile Robots ◽

Nonlinear Dynamical ◽

Control Techniques ◽

State Dependent

Formation control of multiple mobile robots is relatively a new area of robotics and increase the control performance and advantages of multiple mobile robots systems. <a name="OLE_LINK72">In this work we present a study concerning the modeling and formation control of a robotic system composed by two mobile robots, where one robot is the leader and the other is follower</a>. The system is a nonlinear dynamical system and cannot be controlled by traditional linear control techniques. The control strategy proposed is the SDRE (State-Dependent Riccati Equation) method. Simulations results with the software Matlab show the efficiency of the control method.

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A control method of selfish routing based on replicator dynamics with capitation tax and subsidy

2009 IEEE International Conference on Control Applications ◽

10.1109/cca.2009.5281032 ◽

2009 ◽

Cited By ~ 2

Author(s):

Takafumi Kanazawa ◽

Takurou Misaka ◽

Toshimitsu Ushio ◽

Yasuhiko Fukumoto

Keyword(s):

Control Method ◽

Replicator Dynamics ◽

Selfish Routing

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FINITE DURATION TREATMENT OF CANCER BY USING VACCINE THERAPY AND OPTIMAL CHEMOTHERAPY: STATE-DEPENDENT RICCATI EQUATION CONTROL AND EXTENDED KALMAN FILTER

Journal of Biological System ◽

10.1142/s0218339015500011 ◽

2015 ◽

Vol 23 (01) ◽

pp. 1-29 ◽

Cited By ~ 5

Author(s):

MOSTAFA NAZARI ◽

ALI GHAFFARI ◽

FARHAD ARAB

Keyword(s):

Kalman Filter ◽

Riccati Equation ◽

Extended Kalman Filter ◽

Control Method ◽

Domain Of Attraction ◽

Treatment Method ◽

Drug Dosage ◽

Vaccine Therapy ◽

Finite Duration ◽

State Dependent

The main purpose of this paper is to propose an optimal finite duration treatment method for preventing tumor growth. The obtained results show that changing the dynamics of the cancer model is essential for a finite duration treatment. Therefore, vaccine therapy is used for changing the parameters of the system and chemotherapy is applied for pushing the system to the domain of attraction of the healthy state. The state-dependent Riccati equation (SDRE)-based optimal control method is used for optimal chemotherapy. In this method, the special conditions of the patients could be considered by choosing suitable weighting matrices in the cost function and restricting the drug dosage. Also, there are infinite ways to choose these state-dependent matrices. In this paper, these interesting features of this method are used for each patient. Since measuring the states of the system is impossible at each time for states feedback; an extended Kalman filter (EKF) is designed as an observer in the nonlinear system. So, the SDRE method is employed just by measuring the population of normal cells. Numerical simulations show the flexibility and effectiveness of this treatment method.

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Optimal sliding mode control design based on the state-dependent Riccati equation for cooperative manipulators to increase dynamic load carrying capacity

Robotica ◽

10.1017/s0263574718001030 ◽

2018 ◽

Vol 37 (2) ◽

pp. 321-337 ◽

Cited By ~ 8

Author(s):

A. H. Korayem ◽

S. R. Nekoo ◽

M. H. Korayem

Keyword(s):

Sliding Mode Control ◽

Dynamic Load ◽

Carrying Capacity ◽

Control Method ◽

Sliding Mode ◽

Load Carrying Capacity ◽

Mode Control ◽

State Dependent ◽

Load Carrying ◽

Cooperative Manipulators

SUMMARYCooperative manipulators have uncertainties in their structure; therefore, an optimal sliding mode control method is derived from a combination of the sliding mode control (SMC) and the state-dependent Riccati equation (SDRE) technique. This proposed combination is applied to a class of non-linear closed-loop systems. One of the distinguished features of this control method is its robustness toward uncertainty. Due to the lack of optimality in the SMC method, in this paper, a robust and optimal method is presented by considering the SDRE in design of the sliding surface. Due to the fact that cooperative manipulators have been used for carrying loads, the percentage of load distributions between each manipulator has been derived to increase the dynamic load carrying capacity (DLCC). The proposed control structure is implemented on a Scout robot with two manipulators in cooperative mode, theoretically and practically using LabVIEW software; and the results were compared by considering the uncertainty in its structure. In comparison with the SDRE, the proposed method increased the DLCC almost 10% in the Scout case.

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Optimization of theAedes aegyptiControl Strategies for Integrated Vector Management

Journal of Applied Mathematics ◽

10.1155/2015/918194 ◽

2015 ◽

Vol 2015 ◽

pp. 1-8 ◽

Cited By ~ 5

Author(s):

Marat Rafikov ◽

Elvira Rafikova ◽

Hyun Mo Yang

Keyword(s):

Control Method ◽

Population Management ◽

Mosquito Population ◽

Quadratic Functional ◽

Chemical Insecticide ◽

Dengue Disease ◽

State Dependent ◽

Sustainable Policy ◽

Vector Management ◽

Optimization Control

We formulate an infinite-time quadratic functional minimization problem ofAedes aegyptimosquito population. Three techniques of mosquito population management, chemical insecticide control, sterile insect technique control, and environmental carrying capacity reduction, are combined in order to obtain the most sustainable strategy to reduce mosquito population and consequently dengue disease. The solution of the optimization control problem is based on the ideas of the Dynamic Programming and Lyapunov Stability using State-Dependent Riccati Equation (SDRE) control method. Different scenarios are analyzed combining three mentioned population management efforts in order to assess the most sustainable policy to reduce the mosquito population.

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