MathDB4 problems
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Ruina's convergence conjecture for piece-wise holonomic systems
Piece-wise holonomic systems and smooth non-holonomic systems are considered as models of motion generated by manipulating system components. Ruina's convergence conjecture. The mo…
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The conjecture that local controllability implies the existence of a stabilizing control law
For the nonholonomic integrator (or Heisenberg system), consider the control system … A reasonable form of local controllability should imply the existence of a stabilizing control…
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Conjecture on homogeneous approximations improving MPC prediction-horizon estimates
Consider model predictive control for the nonholonomic mobile robot, with the stage cost … The discussion concerns using the homogeneous approximation of the system at the origin i…
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Conformal Hamiltonization conjecture for the nonholonomic rolling problem
The nonholonomic problem of an ellipsoid of revolution rolling on a rough plane and the corresponding Hamiltonian problem of rolling on a smooth plane have identical topological be…