Legged robots that balance
Practical numerical algorithms for chaotic systems
Practical numerical algorithms for chaotic systems
Analysis of a simplified hopping robot
International Journal of Robotics Research
Periodic motions
Efficient sensitivity analysis of large-scale differential-algebraic systems
Applied Numerical Mathematics
LAPACK Users' guide (third ed.)
LAPACK Users' guide (third ed.)
Parametric sensitivity functions for hybrid discrete/continuous systems
Applied Numerical Mathematics
Hidden Discontinuities and Parametric Sensitivity Calculations
SIAM Journal on Scientific Computing
Modeling, simulation, sensitivity analysis, and optimization of hybrid systems
ACM Transactions on Modeling and Computer Simulation (TOMACS)
Sensitivity Analysis for Oscillating Dynamical Systems
SIAM Journal on Scientific Computing
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A theory is developed for local, first-order sensitivity analysis of limit-cycle oscillating hybrid systems, which are dynamical systems exhibiting both continuous-state and discrete-state dynamics whose state trajectories are closed, isolated, and time-periodic. Methods for the computation of initial-condition sensitivities and parametric sensitivities are developed to account exactly for any jumps in the sensitivities at discrete transitions and to exploit the time-periodicity of the system. It is shown that the initial-condition sensitivities of any limit-cycle oscillating hybrid system can be represented as the sum of a time-decaying component and a time-periodic component so that they become periodic in the long-time limit. A method is developed for decomposition of the parametric sensitivities into three parts, characterizing the influence of parameter changes on period, state variable amplitudes, and relative phases, respectively. The computation of parametric sensitivities of period, amplitudes, and different types of phases is also described. The methods developed in this work are applied to particular models for illustration, including models exhibiting state variable jumps.