Solvable Approximations to Control Systems
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Publication:3323796
DOI10.1137/0322004zbMath0537.93040OpenAlexW2180949094MaRDI QIDQ3323796
Publication date: 1984
Published in: SIAM Journal on Control and Optimization (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1137/0322004
Nonlinear systems in control theory (93C10) Canonical structure (93B10) Transformations (93B17) Algebraic methods (93B25) Nilpotent and solvable Lie groups (22E25) Series expansions (e.g., Taylor, Lidstone series, but not Fourier series) (41A58)
Related Items (13)
Intrinsic nilpotent approximation ⋮ Geometric control theory ⋮ Geometrical and topological methods in optimal control theory ⋮ Normal forms for vector fields with respect to an arbitrary dilation ⋮ Fliess series, a generalization of the Ree's theorem, and an algebraic approach to a homogeneous approximation problem ⋮ Homogeneous tangent vectors and high-order necessary conditions for optimal controls ⋮ Subspaces of maximal singularity for homogeneous control systems ⋮ Higher-order local approximations of smooth control systems and pointwise higher-order optimality conditions ⋮ Free algebras and noncommutative power series in the analysis of nonlinear control systems: an application to approximation problems ⋮ Sufficient conditions for local controllability and high-order necessary conditions for optimality. A differential-geometric approach. ⋮ Global stability of a class of difference equations on solvable Lie algebras ⋮ Local asymptotic approximation of non-linear control systems! ⋮ Implementation of the algorithm for constructing homogeneous approximations of nonlinear control systems
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