Hamilton-Jacobi Equations with Semilinear Costs and State Constraints, with Applications to Large Deviations in Games

2021 ◽  
Author(s):  
William H. Sandholm ◽  
Hung V. Tran ◽  
Srinivas Arigapudi
Keyword(s):  
Game Theory ◽  
Optimal Control ◽  
Large Deviations ◽  
Evolutionary Game Theory ◽  
State Constraints ◽  
Optimal Control Problems ◽  
Evolutionary Game ◽  
Control Problems ◽  
Optimal Solutions ◽  
Jacobi Equations

We characterize solutions of a class of time-homogeneous optimal control problems with semilinear running costs and state constraints as maximal viscosity subsolutions to Hamilton-Jacobi equations and show that optimal solutions to these problems can be constructed explicitly. We present applications to large deviations problems arising in evolutionary game theory.

scholarly journals Nonlinearly constrained optimal control problems

1992 ◽  
Vol 33 (4) ◽  
pp. 517-530 ◽  
Author(s):  
K. L. Teo ◽  
K. H. Wong
Keyword(s):  
Optimal Control ◽  
General Class ◽  
State Constraints ◽  
Computational Algorithm ◽  
Optimal Control Problems ◽  
Control Problems ◽  
Constrained Optimal Control ◽  
Continuous State ◽  
Constraint Transcription ◽  
Inequality Type

AbstractIn a paper by Teo and Jennings, a constraint transcription is used together with the concept of control parametrisation to devise a computational algorithm for solving a class of optimal control problems involving terminal and continuous state constraints of inequality type. The aim of this paper is to extend the results to a more general class of constrained optimal control problems, where the problem is also subject to terminal equality state constraints. For illustration, a numerical example is included.

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