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

2015 ◽  
Vol 23 (01) ◽  
pp. 1-29 ◽  
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.

scholarly journals Optimal Finite Cancer Treatment Duration by Using Mixed Vaccine Therapy and Chemotherapy: State Dependent Riccati Equation Control

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Ali Ghaffari ◽  
Mostafa Nazari ◽  
Farhad Arab
Keyword(s):  
Cancer Treatment ◽  
Riccati Equation ◽  
Treatment Duration ◽  
Equilibrium Points ◽  
Domain Of Attraction ◽  
Treatment Method ◽  
Vaccine Therapy ◽  
State Dependent ◽  
Healthy State ◽  
Cancerous Cells

The main objective of this paper is to propose an optimal finite duration treatment method for cancer. A mathematical model is proposed to show the interactions between healthy and cancerous cells in the human body. To extend the existing models, the effect of vaccine therapy and chemotherapy are also added to the model. The equilibrium points and the related local stability are derived and discussed. It is shown that the dynamics of the cancer model must be changed and modified for finite treatment duration. Therefore, the vaccine therapy is used to change the parameters of the system and the chemotherapy is applied for pushing the system to the domain of attraction of the healthy state. For optimal chemotherapy, an optimal control is used based on state dependent Riccati equation (SDRE). It is shown that, in spite of eliminating the treatment, the system approaches the healthy state conditions. The results show that the development of optimal vaccine-chemotherapy protocols for removing tumor cells would be an appropriate strategy in cancer treatment. Also, the present study states that a proper treatment method not only reduces the population of the cancer cells but also changes the dynamics of the cancer.

The effect of finite duration inputs on the dynamics of a system: Proposing a new approach for cancer treatment

2015 ◽  
Vol 08 (03) ◽  
pp. 1550036 ◽  
Author(s):  
Mostafa Nazari ◽  
Ali Ghaffari
Keyword(s):  
Dynamic Systems ◽  
Domain Of Attraction ◽  
Treatment Method ◽  
Free System ◽  
New Approach ◽  
Finite Duration ◽  
State Dependent ◽  
Healthy State ◽  
System Approaches ◽  
Limited Duration

In this paper, a principal question regarding the effect of inputs on the characteristics of dynamic systems is discussed. Whether an input implemented only for a limited duration, can change the characteristics of a dynamic system such that the behavior of the free system, after eliminating the input, differs from that before acting the input? In this paper, it is shown that a limited time acted input is not able to change the dynamical properties of a system after its elimination. Regarding the proposed approach, a novel finite duration treatment method is developed for a tumor-immune system. The vaccine therapy is used to change the parameters of the system and the chemotherapy is applied for pushing the system to the domain of attraction of the healthy state. For optimal chemotherapy, an optimal control is used based on state-dependent Riccati equation (SDRE). It is shown that, in spite of eliminating the treatment (therapeutic inputs), the system approaches to healthy state conditions. The present analysis suggests that a proper treatment method must change the dynamics of the cancer instead of only reducing the population of cancer cells.

Observer-based robust control for flexible-joint robot manipulators: A state-dependent Riccati equation-based approach

2020 ◽  
Vol 42 (16) ◽  
pp. 3135-3155
Author(s):  
Neda Nasiri ◽  
Ahmad Fakharian ◽  
Mohammad Bagher Menhaj
Keyword(s):  
Robust Control ◽  
Control Problem ◽  
Riccati Equation ◽  
Power Transmission ◽  
Control Method ◽  
Main Idea ◽  
Robotic Systems ◽  
Flexible Joint ◽  
State Dependent ◽  
Highly Nonlinear

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.

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

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.

scholarly journals State of Charge Estimation Algorithm for Unmanned Aerial Vehicle Power-Type Lithium Battery Packs Based on the Extended Kalman Filter

Energies ◽  
2019 ◽  
Vol 12 (20) ◽  
pp. 3960 ◽  
Author(s):  
Haitao Zhang ◽  
Ming Zhou ◽  
Xudong Lan
Keyword(s):  
Kalman Filter ◽  
Extended Kalman Filter ◽  
Control Method ◽  
Equivalent Circuit Model ◽  
State Of Charge ◽  
Energy Utilization ◽  
Battery Life ◽  
Power Type ◽  
Advantages And Disadvantages ◽  
Li Po

The lack of endurance is an important reason restricting further development of unmanned aerial vehicles (UAVs). Accurately estimating the state of charge (SOC) of the Li-Po battery can maximize the battery energy utilization and improve the endurance of UAVs. In this paper, the main current methods for estimating the SOC of vehicles were explored and discussed to unveil their advantages and disadvantages. In addition, the extended Kalman filter algorithm based on an equivalent circuit model was used to estimate SOC of power-type Li-Po batteries at different temperatures. The result showed that the closed-loop control method can effectively improve the battery life of small-sized electric UAVs.

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