Function approximation for the deterministic Hamilton-Jacobi-Bellman equation

Function approximation for the deterministic Hamilton-Jacobi-Bellman equation

Based on Gaussian basis functions, a new method for calculating the Hamilton-Jacobi-Bellman equation for deterministic continuous-time and continuous-valued optimal control problems is proposed. A semi-Lagrangian discretization scheme is used to obtain a discrete-time finite-state approximation of t...

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Hauptverfasser: Rungger, M., Stursberg, O.
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Sprache:eng
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Continuous time systems
Convergence
Cost function
Differential equations
Dynamic programming
Function approximation
Optimal control
Partial differential equations
State feedback
State-space methods
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description Based on Gaussian basis functions, a new method for calculating the Hamilton-Jacobi-Bellman equation for deterministic continuous-time and continuous-valued optimal control problems is proposed. A semi-Lagrangian discretization scheme is used to obtain a discrete-time finite-state approximation of the continuous dynamics. The value function of the discretized system is approximated by a Gaussian network. Limit behavior analysis provides a proof of convergence for the scheme. The performance of the presented approach is demonstrated for an underpowered inverted pendulum as numerical example. Furthermore, a comparison to the approximation by continuous piecewise affine functions (the current state of the art) shows the benefits of the approximation technique proposed here.
doi_str_mv 10.1109/CDC.2009.5400068
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subjects Continuous time systems
Convergence
Cost function
Differential equations
Dynamic programming
Function approximation
Optimal control
Partial differential equations
State feedback
State-space methods
title Function approximation for the deterministic Hamilton-Jacobi-Bellman equation
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