scholarly journals Nonsmooth optimal regulation and discontinuous stabilization

2003 ◽  
Vol 2003 (20) ◽  
pp. 1159-1195 ◽  
Author(s):  
A. Bacciotti ◽  
F. Ceragioli
Keyword(s):  
Control Systems ◽  
Value Function ◽  
Infinite Horizon ◽  
Optimal Regulation ◽  
Affine Control Systems ◽  
Feedback Laws ◽  
The Relationship ◽  
The Value Function

For affine control systems, we study the relationship between an optimal regulation problem on the infinite horizon and stabilizability. We are interested in the case the value function of the optimal regulation problem is not smooth and feedback laws involved in stabilizability may be discontinuous.

Metric for Disassembly and Reuse Decisions: Formulation and Validation

2008 ◽  
Author(s):  
Vijitashwa Pandey ◽  
Deborah Thurston
Keyword(s):  
Maximum Likelihood ◽  
Value Function ◽  
Choice Theory ◽  
Decision Makers ◽  
Maximum Likelihood Estimates ◽  
Likelihood Method ◽  
Maximum Value ◽  
Long Range Planning ◽  
The Relationship ◽  
The Value Function

Design for disassembly and reuse focuses on developing methods to minimize difficulty in disassembly for maintenance or reuse. These methods can gain substantially if the relationship between component attributes (material mix, ease of disassembly etc.) and their likelihood of reuse or disposal is understood. For products already in the marketplace, a feedback approach that evaluates willingness of manufacturers or customers (decision makers) to reuse a component can reveal how attributes of a component affect reuse decisions. This paper introduces some metrics and combines them with ones proposed in literature into a measure that captures the overall value of a decision made by the decision makers. The premise is that the decision makers would choose a decision that has the maximum value. Four decisions are considered regarding a component’s fate after recovery ranging from direct reuse to disposal. A method on the lines of discrete choice theory is utilized that uses maximum likelihood estimates to determine the parameters that define the value function. The maximum likelihood method can take inputs from actual decisions made by the decision makers to assess the value function. This function can be used to determine the likelihood that the component takes a certain path (one of the four decisions), taking as input its attributes, which can facilitate long range planning and also help determine ways reuse decisions can be influenced.

The Relationship Between Numeracy and the Value Function and Probability Weighting in Prospect Theory

2012 ◽  
Author(s):  
Mona Gauth ◽  
Maria Henriksson ◽  
Peter Juslin ◽  
Neda Kerimi ◽  
Marcus Lindskog ◽  
...  
Keyword(s):  
Prospect Theory ◽  
Value Function ◽  
Probability Weighting ◽  
The Relationship ◽  
The Value Function

scholarly journals Stochastic optimal control problem with infinite horizon driven by G-Brownian motion

2018 ◽  
Vol 24 (2) ◽  
pp. 873-899 ◽  
Author(s):  
Mingshang Hu ◽  
Falei Wang
Keyword(s):  
Optimal Control ◽  
Brownian Motion ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Stochastic Optimal Control ◽  
Value Function ◽  
Infinite Horizon ◽  
Dynamic Programming Principle ◽  
Stochastic Optimal Control Problem ◽  
The Value Function

The present paper considers a stochastic optimal control problem, in which the cost function is defined through a backward stochastic differential equation with infinite horizon driven by G-Brownian motion. Then we study the regularities of the value function and establish the dynamic programming principle. Moreover, we prove that the value function is the unique viscosity solution of the related Hamilton−Jacobi−Bellman−Isaacs (HJBI) equation.

ASYMPTOTICS OF VALUE FUNCTION IN MODELS OF ECONOMIC GROWTH

2018 ◽  
pp. 605-616
Author(s):  
Alexander Leonidovich Bagno ◽  
Alexander Mikhailovich Tarasyev
Keyword(s):  
Economic Growth ◽  
Optimal Control ◽  
Asymptotic Behavior ◽  
Value Function ◽  
Growth Models ◽  
Infinite Horizon ◽  
Minimax Solution ◽  
Growth Stability ◽  
Economic Growth Models ◽  
The Value Function

Asymptotic behavior of the value function is studied in an infinite horizon optimal control problem with an unlimited integrand index discounted in the objective functional. Optimal control problems of such type are related to analysis of trends of trajectories in models of economic growth. Stability properties of the value function are expressed in the infinitesimal form. Such representation implies that the value function coincides with the generalized minimax solution of the Hamilton–Jacobi equation. It is shown that that the boundary condition for the value function is substituted by the property of the sublinear asymptotic behavior. An example is given to illustrate construction of the value function as the generalized minimax solution in economic growth models.

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