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High-order variations for families of vector fields
Sufficient conditions involving Lie brackets of arbitrarily high-order are obtained for local controllability of families of vector fields. After providing a general framework for the generation of high-order ...
Geometric local controllability: second-order conditions
In a geometric point of view, a nonlinear control system, affine in the controls, is thought of as an affine subbundle of the tangent bundle of the state space. In deriving conditions for local controllability from ...
Geometric sliding mode control: The linear and linearised theory
The idea of sliding mode control for stabilisation is investigated to determine its geometric features. A geometric definition is provided for a sliding submanifold, and for various properties of a sliding submanifold. Sliding ...
An example with interesting controllability and stabilisation properties
A simple three-state system with two inputs is considered. The system's controllability is determined using properties of vector-valued quadratic forms. The quadratic structure is then used as the basis for the design of ...