Algebraic Solutions to the Hamilton-Jacobi Equation with the Time-Varying Hamiltonian

@article{Kawano2013AlgebraicST,
  title={Algebraic Solutions to the Hamilton-Jacobi Equation with the Time-Varying Hamiltonian},
  author={Yu Kawano and Toshiyuki Ohtsuka},
  journal={SICE journal of control, measurement, and system integration},
  year={2013},
  volume={6},
  pages={28-37}
}
  • Y. Kawano, T. Ohtsuka
  • Published 31 January 2013
  • Mathematics
  • SICE journal of control, measurement, and system integration
The Hamilton-Jacobi equation (HJE) with the time-varying Hamiltonian plays an important role in the analysis and control of nonlinear systems and is very difficult to solve for general nonlinear systems. In this paper, the HJE with coefficients belonging to meromorphic functions is considered, and its solutions with algebraic gradients are characterized in terms of commutative algebra. It is shown that there exists a solution with an algebraic gradient if and only if an Hinvariant and… 
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