Numerical computation of the optimal feedback law¶for nonlinear infinite time horizon control problems

Prager, Wolfgang

doi:10.1007/s100920070010

Cited by 6 publications

(2 citation statements)

References 3 publications

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“…One has to face the severe problem to solve the nonlinear Hamilton-Jacobi-Bellman (HJB) equation or alternatively to solve many two-point boundary value problems for the Euler-Lagrange equations, which still is a serious challenge, especially on the infinite time interval. We refer to [Beard et al, 1998;Beeler et al, 2000;Prager, 2000] for some solutions to both problems and their limitations.…”

Section: Introductionmentioning

confidence: 99%

Method to Solve the Nonlinear Infinite Horizon Optimal Control Problem With Application to the Track Control of a Mobile Robot

Holzhüter

Klinker

2007

Int. J. Bifurcation Chaos

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We present a numerical method to solve the infinite time horizon optimal control problem for low dimensional nonlinear systems. Starting from the linear-quadratic approximation close to the origin, the extremal field is efficiently calculated by solving the Euler-Lagrange equations backward in time. The resulting controller is given numerically on an interpolation grid. We use the method to obtain the optimal track controller for a mobile robot. The result is a globally asymptotically stable nonlinear controller, obtained without any specific insight into the system dynamics.

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Section: Introductionmentioning

confidence: 99%

Method to Solve the Nonlinear Infinite Horizon Optimal Control Problem With Application to the Track Control of a Mobile Robot

Holzhüter

Klinker

2007

Int. J. Bifurcation Chaos

View full text Add to dashboard Cite

show abstract

“…There are several other approaches to solving HJB PDEs, and a large literature, for example see [3], [6], [13], [9], [10], [16], [18], [19], [21] and their references. One approach is to discretize the underlying optimal control problem and convert it into a nonlinear program in discrete time and space.…”

Section: Other Approachesmentioning

confidence: 99%