Wolfram Language Paclet Repository
Community-contributed installable additions to the Wolfram Language
Guide to ZigangPan`NonlinearCholeskyFactorization`
This paclet is on the design of locally optimal matching and globally inverse optimal controllers for single-input and single-output strict-feedback nonlinear systems under perfect state measurements.
— generate all monomials of a given order for the given vector of variables.
— expand a give function into Taylor series and then truncate up to given order.
— solve the Hamilton-Jacobi-Isaacs equation for a nonlinear system at the equilibrium of origin in the form of Taylor series of expansion of the solution.
— yields a nonlinear function in terms of its nonlinear Cholesky factorization that matches the given Taylor series expansion of some nonlinear function up to a given order of accuracy.
— control design for SISO strict feedback nonlinear systems to achieve local optimal matching and global inverse optimality.
— control design for SISO strict feedback nonlinear systems to achieve local optimal matching and global inverse optimality.
— control design for SISO strict feedback nonlinear systems to achieve local optimal matching and global inverse optimality.
— control design for SISO strict feedback nonlinear systems to achieve local optimal matching and global inverse optimality.
The utility of the four design functions form a 2×2 table
Utility | Unboundedfirststate | bounded first state | |
Earlierdesign | backsteppinglocaloptimalmatchingglobalinverseoptimal | backsteppinglocaloptimalmatchingglobalinverseoptimalN | |
Newdesign | backsteppinglocaloptimalmatchingglobalinverseoptimalNew | backsteppinglocaloptimalmatchingglobalinverseoptimalNNew |
""