Robust Feedback Control of Nonlinear PDEs by Polynomial Approximation of the Hamilton‐Jacobi‐Isaacs Equation | Zendy

Kalise Dante | Zendy; Kundu Sudeep | Zendy; Kunisch Karl | Zendy

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Robust Feedback Control of Nonlinear PDEs by Polynomial Approximation of the Hamilton‐Jacobi‐Isaacs Equation

Author(s) -

Kalise Dante,

Kundu Sudeep,

Kunisch Karl

Publication year - 2019

Publication title -

pamm

Language(s) - English

Resource type - Journals

ISSN - 1617-7061

DOI - 10.1002/pamm.201900333

Subject(s) - ansatz , nonlinear system , mathematics , discretization , polynomial , optimal control , galerkin method , pseudospectral optimal control , hamilton–jacobi equation , mathematical analysis , pseudo spectral method , mathematical optimization , physics , quantum mechanics , fourier analysis , fourier transform , mathematical physics

We present a computational method for the synthesis of optimal robust feedback laws for nonlinear dynamics based on the solution of a nonlinear Hamilton‐Jacobi‐Isaacs equation. This equation is approximated with an iterative method involving the solution of high‐dimensional linear PDEs, for which we use of a Galerkin method with global polynomial ansatz functions. The method is applied for controlling dynamics arising from a pseudospectral discretization of nonlinear parabolic PDEs.

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