scholarly journals OPTIMAL CONTROL OF A CONVECTIVE-DIFFUSIVE FLUID PROBLEM

1995 ◽  
Vol 05 (02) ◽  
pp. 225-237 ◽  
Author(s):  
SUZANNE LENHART
Keyword(s):  
Optimal Control ◽  
Performance Criterion ◽  
Equation Modeling ◽  
Parabolic Differential Equation ◽  
Convective Velocity ◽  
Final Time ◽  
One Dimensional ◽  
Flow Through ◽  
Differential Equation Modeling ◽  
The Cost

We consider optimal control of a parabolic differential equation, modeling one-dimensional fluid flow through a soil-packed tube in which a contaminant is initially distributed. A fluid is pumped through the tube to remove the contaminant. The convective velocity due to the fluid pumping is the nonlinear control action. The goal is to minimize a performance criterion which is a combination of the total contaminant at the final time and the cost of the control. The optimal control is characterized by an optimality system.

LEARNING AND RECOGNITION OF HUMAN ACTIONS USING OPTIMAL CONTROL PRIMITIVES

2009 ◽  
Vol 06 (03) ◽  
pp. 459-479
Author(s):  
SUMITRA GANESH ◽  
RUZENA BAJCSY
Keyword(s):  
Optimal Control ◽  
Cost Function ◽  
Estimation Method ◽  
Nonlinear Least Squares ◽  
Performance Criterion ◽  
Human Motion ◽  
Human Actions ◽  
Mode Estimation ◽  
Nonlinear Least Squares Problem ◽  
The Cost

We propose a unified approach for recognition and learning of human actions, based on an optimal control model of human motion. In this model, the goals and preferences of the agent engaged in a particular action are encapsulated as a cost function or performance criterion, that is optimized to yield the details of the movement. The cost function is a compact, intuitive and flexible representation of the action. A parameterized form of the cost function is considered, wherein the structure reflects the goals of the actions, and the parameters determine the relative weighting of different terms. We show how the cost function parameters can be estimated from data by solving a nonlinear least squares problem. The parameter estimation method is tested on motion capture data for two different reaching actions and six different subjects. We show that the problem of action recognition in the context of this representation is similar to that of mode estimation in a hybrid system and can be solved using a particle filter if a receding horizon formulation of the optimal controller is adopted. We use the proposed approach to recognize different reaching actions from the 3D hand trajectory of subjects.

scholarly journals Optimal control analysis of deterministic and stochastic epidemic model with media awareness programs

2018 ◽  
Vol 9 (1) ◽  
pp. 24-35 ◽  
Author(s):  
Shrishail Ramappa Gani ◽  
Shreedevi Veerabhadrappa Halawar
Keyword(s):  
Differential Equation ◽  
Optimal Control ◽  
Control Problem ◽  
Bellman Equation ◽  
Optimality System ◽  
Equation Modeling ◽  
Control Analysis ◽  
Awareness Programs ◽  
Differential Equation Modeling ◽  
Stochastic Optimality

The present study considered the optimal control analysis of  both deterministic differential equation modeling and stochastic differential equation modeling of infectious disease by taking effects of media awareness programs  and treatment of infectives on the epidemic into account. Optimal media awareness strategy under the quadratic cost functional using Pontrygin's Maximum Principle  and Hamiltonian-Jacobi-Bellman equation are derived for both deterministic and stochastic optimal problem respectively. The Hamiltonian-Jacobi-Bellman equation is used to solve stochastic system, which is fully non-linear equation, however it ought to be pointed out that for stochastic optimality system it may be difficult to obtain the numerical results. For the analysis of the stochastic optimality system, the results of deterministic control problem are used to find an approximate numerical solution for the stochastic control problem.  Outputs of the simulations shows that media awareness programs place important role in the minimization of infectious population with minimum cost.

On the Optimal Control Problem With Unrestricted Final Time

1969 ◽  
Vol 91 (2) ◽  
pp. 155-160 ◽  
Author(s):  
C. T. Leondes ◽  
R. A. Niemann
Keyword(s):  
Optimal Control ◽  
Local Minimum ◽  
Computational Algorithm ◽  
Local Maximum ◽  
Fixed Time ◽  
Performance Criterion ◽  
Necessary Condition ◽  
Sufficient Condition ◽  
Final Time ◽  
Numerical Examples

In problems of optimal control, the final time T may be fixed or it may be unrestricted. For the unrestricted final time case, an additional necessary condition that the Hamiltonian be zero is added to the conditions for optimality used for the fixed time case. In this paper, it will be shown that this necessary condition may lead to a local maximum of the performance criterion with respect to final times as well as a local minimum. This paper first develops a computational algorithm using only the H = 0 condition, and then develops a sufficient condition for a local minimum with respect to final time and a computational algorithm employing this condition. Numerical examples are given to illustrate all results.

New Nonlinear Observer Design With Application to Electrostatic Micro-Actuators

2005 ◽  
Author(s):  
Venkat Durbha ◽  
S. N. Balakrishnan
Keyword(s):  
Optimal Control ◽  
Cost Function ◽  
Correction Term ◽  
Observer Design ◽  
Nonlinear Observer ◽  
Optimal Feedback Control ◽  
Actuator Dynamics ◽  
One Dimensional ◽  
Practical Applications ◽  
The Cost

In many practical applications it is not possible to measure all the states required to control the system. In such instances observer/filter is used to give a good estimate of the states of the system. The objective of the observer is to estimate the states such that the error between the actual and computed measurements goes to zero and obtain the “best” estimates of the states of a given system. In the current study a new nonlinear observer structure is proposed. The development of the observer is based on optimal control theory. A cost function is defined in terms of the measurement residual and the magnitude of correction term. The observer gains are obtained by minimizing the cost function with respect to the magnitude of corrections. The proposed observer is used to estimate the states of a one-dimensional electrostatic micro-actuator. The states of the actuator dynamics are, charge on the capacitor plates, the distance between the plates and the relative velocity between the plates. The regulation of the actuator states to desired trajectories is achieved through optimal control based state feedback. However in practice it is very difficult to measure the relative position and velocity of the plates. In this paper optimal feedback control based on the state estimates provided by the observer is used to regulate the actuator states to the desired location.

Certain Problems with the Application of Stochastic Diffusion Processes for the Description of Chemical Engineering Phenomena. Stochastic Model of Non-Isothermal Flow Chemical Reactor

1996 ◽  
Vol 61 (2) ◽  
pp. 242-258 ◽  
Author(s):  
Vladimír Kudrna ◽  
Libor Vejmola ◽  
Pavel Hasal
Keyword(s):  
Stochastic Model ◽  
Chemical Engineering ◽  
Diffusion Processes ◽  
Dispersion Model ◽  
Chemical Reactor ◽  
Segregation Index ◽  
One Dimensional ◽  
A Value ◽  
Isothermal Case ◽  
Flow Through

Recently developed stochastic model of a one-dimensional flow-through chemical reactor is extended in this paper also to the non-isothermal case. The model enables the evaluation of concentration and temperature profiles along the reactor. The results are compared with the commonly used one-dimensional dispersion model with Danckwerts' boundary conditions. The stochastic model also enables to evaluate a value of the segregation index.

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.

scholarly journals Dynamical Analysis and Optimal Control for a SEIR Model Based on Virus Mutation in WSNs

Mathematics ◽  
2021 ◽  
Vol 9 (9) ◽  
pp. 929
Author(s):  
Guiyun Liu ◽  
Jieyong Chen ◽  
Zhongwei Liang ◽  
Zhimin Peng ◽  
Junqiang Li
Keyword(s):  
Optimal Control ◽  
Rapid Development ◽  
Hamiltonian Function ◽  
Propagation Model ◽  
Dynamical Analysis ◽  
Optimal Control Strategy ◽  
Epidemic Dynamics ◽  
Optimization Control ◽  
The Cost ◽  
The Pontryagin Maximum Principle

With the rapid development of science and technology, the application of wireless sensor networks (WSNs) is more and more widely. It has been widely concerned by scholars. Viruses are one of the main threats to WSNs. In this paper, based on the principle of epidemic dynamics, we build a SEIR propagation model with the mutated virus in WSNs, where E nodes are infectious and cannot be repaired to S nodes or R nodes. Subsequently, the basic reproduction number R0, the local stability and global stability of the system are analyzed. The cost function and Hamiltonian function are constructed by taking the repair ratio of infected nodes and the repair ratio of mutated infected nodes as optimization control variables. Based on the Pontryagin maximum principle, an optimal control strategy is designed to effectively control the spread of the virus and minimize the total cost. The simulation results show that the model has a guiding significance to curb the spread of mutated virus in WSNs.

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