scholarly journals Feedback control problem of an SIR epidemic model based on the Hamilton-Jacobi-Bellman equation

2020 ◽  
Vol 17 (3) ◽  
pp. 2284-2301
Author(s):  
Yoon-gu Hwang ◽  
◽  
Hee-Dae Kwon ◽  
Jeehyun Lee ◽  
◽  
...  
Keyword(s):  
Feedback Control ◽  
Control Problem ◽  
Epidemic Model ◽  
Bellman Equation ◽  
Sir Epidemic Model ◽  
Model Based ◽  
Sir Epidemic ◽  
Hamilton Jacobi Bellman Equation ◽  
Hamilton Jacobi Bellman

scholarly journals The Dubins Traveling Salesperson Problem With Stochastic Dynamics

2013 ◽  
Author(s):  
Ross P. Anderson ◽  
Dejan Milutinović
Keyword(s):  
Feedback Control ◽  
Bellman Equation ◽  
Stochastic Dynamics ◽  
Numerical Results ◽  
Traveling Salesperson Problem ◽  
Expected Time ◽  
Hamilton Jacobi Bellman Equation ◽  
Dubins Vehicle ◽  
Robotic Vehicle ◽  
Hamilton Jacobi Bellman

Motivated by applications in which a nonholonomic robotic vehicle should sequentially hit a series of waypoints in the presence of stochastic drift, we formulate a new version of the Dubins vehicle traveling salesperson problem. In our approach, we first compute the minimum expected time feedback control to hit one waypoint based on the Hamilton-Jacobi-Bellman equation. Next, minimum expected times associated with the control are used to construct a traveling salesperson problem based on a waypoint hitting angle discretization. We provide numerical results illustrating our solution and analyze how the stochastic drift affects the solution.

scholarly journals A unified framework of rapid exponential stability and optimal feedback control for nonlinear systems

2019 ◽  
Vol 11 (3) ◽  
pp. 168781401983320
Author(s):  
Yan Li ◽  
Yuanchun Li
Keyword(s):  
Feedback Control ◽  
Nonlinear Systems ◽  
Exponential Stability ◽  
Real Time ◽  
Lyapunov Functions ◽  
Bellman Equation ◽  
Optimal Feedback Control ◽  
Optimal Feedback ◽  
Hamilton Jacobi Bellman Equation ◽  
Hamilton Jacobi Bellman

A novel framework of rapid exponential stability and optimal feedback control is investigated and analyzed for a class of nonlinear systems through a variant of continuous Lyapunov functions and Hamilton–Jacobi–Bellman equation. Rapid exponential stability means that the trajectories of nonlinear systems converge to equilibrium states in accelerated time. The sufficient conditions of rapid exponential stability are developed using continuous Lyapunov functions for nonlinear systems. Furthermore, according to a variant of continuous Lyapunov functions, a rapid exponential stability is guaranteed which satisfies some canonical conditions and Hamilton–Jacobi–Bellman equation for controlled nonlinear systems. It is can be seen that the solution of Hamilton–Jacobi–Bellman equation is a continuous Lyapunov function, and, therefore, rapid exponential stability and optimality are guaranteed for nonlinear systems. Last, the main result of this article is investigated via a nonlinear model of a spacecraft with one axis of symmetry through simulations and is used to check rapid exponential stability. Moreover, for the disturbance problem of initial point, a rapid exponential stable controller can reject the large-scale disturbances for controlled nonlinear systems. In addition, the proposed optimal feedback controller is applied to the tracking trajectories of 2-degree-of-freedom manipulator, and the numerical results have illustrated high efficiency and robustness in real time. The simulation results demonstrate the use of the rapid exponential stability and optimal feedback approach for real-time nonlinear systems.

scholarly journals Optimal control of an SIR epidemic through finite-time non-pharmaceutical intervention

2020 ◽  
Author(s):  
David I. Ketcheson
Keyword(s):  
Optimal Control ◽  
Finite Time ◽  
Bellman Equation ◽  
Time Interval ◽  
Finite Time Interval ◽  
Sir Epidemic ◽  
Hamilton Jacobi Bellman Equation ◽  
Long Time ◽  
Hamilton Jacobi Bellman ◽  
Number Of Individuals

AbstractWe consider the problem of controlling an SIR-model epidemic by temporarily reducing the rate of contact within a population. The control takes the form of a multiplicative reduction in the contact rate of infectious individuals. The control is allowed to be applied only over a finite time interval, while the objective is to minimize the total number of individuals infected in the long-time limit, subject to some cost function for the control. We first consider the no-cost scenario and analytically determine the optimal control and solution. We then study solutions when a cost of intervention is included, as well as a cost associated with overwhelming the available medical resources. Examples are studied through the numerical solution of the associated Hamilton-Jacobi-Bellman equation. Finally, we provide some examples related directly to the current pandemic.AMS subject classification. 92D30, 34H05, 49N90, 92-10, 49L12

scholarly journals Dynamic programming principle and associated Hamilton-Jacobi-Bellman equation for stochastic recursive control problem with non-Lipschitz aggregator

2018 ◽  
Vol 24 (1) ◽  
pp. 355-376 ◽  
Author(s):  
Jiangyan Pu ◽  
Qi Zhang
Keyword(s):  
Dynamic Programming ◽  
Control Problem ◽  
Bellman Equation ◽  
Backward Stochastic Differential Equation ◽  
Dynamic Programming Principle ◽  
Unknown Variable ◽  
Hamilton Jacobi Bellman Equation ◽  
Hamilton Jacobi Bellman ◽  
The Stability ◽  
The Value Function

In this work we study the stochastic recursive control problem, in which the aggregator (or generator) of the backward stochastic differential equation describing the running cost is continuous but not necessarily Lipschitz with respect to the first unknown variable and the control, and monotonic with respect to the first unknown variable. The dynamic programming principle and the connection between the value function and the viscosity solution of the associated Hamilton-Jacobi-Bellman equation are established in this setting by the generalized comparison theorem for backward stochastic differential equations and the stability of viscosity solutions. Finally we take the control problem of continuous-time Epstein−Zin utility with non-Lipschitz aggregator as an example to demonstrate the application of our study.

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