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An algorithm for construction of ε-value functions for the Bolza control problem

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Jacewicz E.
International Journal of Applied Mathematics and Computer Science
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2001
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tom 11
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nr 2
391-428
EN
The problem considered is that of approximate numerical minimisation of the non-linear control problem of Bolza. Starting from the classical dynamic programming method of Bellman, an ε-value function is defined as an approximation for the value function being a solution to the Hamilton-Jacobi equation. The paper shows how an ε-value function which maintains suitable properties analogous to the original Hamilton-Jacobi value function can be constructed using a stable numerical algorithm. The paper shows the numerical closeness of the approximate minimum to the infimum of the Bolza functional.
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Optimal control problems with upper semicontinuous Hamiltonians

100%
Misztela A.
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
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2010
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tom 30
|
nr 1
71-99
EN
In this paper we give examples of value functions in Bolza problem that are not bilateral or viscosity solutions and an example of a smooth value function that is even not a classic solution (in particular, it can be neither the viscosity nor the bilateral solution) of Hamilton-Jacobi-Bellman equation with upper semicontinuous Hamiltonian. Good properties of value functions motivate us to introduce approximate solutions of equations with such type Hamiltonians. We show that the value function is the unique approximate solution.
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A method for constructing ε-value functions for the Bolza problem of optimal control

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Pustelnik J.
International Journal of Applied Mathematics and Computer Science
|
2005
|
tom 15
|
nr 2
177-186
EN
The problem considered is that of approximate minimisation of the Bolza problem of optimal control. Starting from Bellman's method of dynamic programming, we define the ε-value function to be an approximation to the value function being a solution to the Hamilton-Jacobi equation. The paper shows an approach that can be used to construct an algorithm for calculating the values of an ε-value function at given points, thus approximating the respective values of the value function.
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