论文信息 - A Schur vector method to solve higher order Lyapunov equations

A Schur vector method to solve higher order Lyapunov equations

A general Schur vector method for solving a partial differential equation which appears in designing nonlinear optimal control laws for linear or nonlinear dynamical systems is proposed. The method reduces the dimensionality problem of the direct method. Numerical experiments show that it also reduces the numerical instability of the eigenvector method. >

Jietae Lee | Jietae Lee

[1] G. W. Stewart,et al. Algorithm 506: HQR3 and EXCHNG: Fortran Subroutines for Calculating and Ordering the Eigenvalues of a Real Upper Hessenberg Matrix [F2] , 1976, TOMS.

[2] Z. Rekasius,et al. Suboptimal design of intentionally nonlinear controllers , 1964 .

[3] D. Lukes. Optimal Regulation of Nonlinear Dynamical Systems , 1969 .

[4] A. Laub. A schur method for solving algebraic Riccati equations , 1978, 1978 IEEE Conference on Decision and Control including the 17th Symposium on Adaptive Processes.

[5] Charles Kenney,et al. Sensitivity of algebraic Riccati equations , 1987, 26th IEEE Conference on Decision and Control.

[6] David K. Probst,et al. A fast, low-space algorithm for multiplying dense multivariate polynomials , 1987, TOMS.

[7] Richard H. Bartels,et al. Algorithm 432 [C2]: Solution of the matrix equation AX + XB = C [F4] , 1972, Commun. ACM.

[8] R. Bass,et al. Optimal nonlinear feedback control derived from quartic and higher-order performance criteria , 1966 .

[9] E. Ryan,et al. On optimal nonlinear feedback regulation of linear plants , 1982 .

[10] C. S. Lu. Solution of the matrix equation AX+XB = C , 1971 .

[11] D. Williamson,et al. Design of nonlinear regulators for linear plants , 1977 .