Stability-Preserving Optimization in the Presence of Fast Disturbances

• Published in: IEEE transactions on automatic control Vol. 56; no. 11; pp. 2683 - 2687
• Main Authors: Wirth, B., Gerhard, J., Marquardt, W.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.11.2011; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Adaptative systems; Applied sciences; Asymptotic stability; Computer science; control theory; systems; Control system analysis; Control theory. Systems; Design parameters; Disturbances; Dynamical systems; Dynamics; Exact sciences and technology; fast disturbances; Manifolds; Mathematical analysis; Numerical stability; Optimization; robust optimization; robust stability; Robustness; Steady-state; Trajectory; Robust control; fast disturbances; Robust stability; Optimal control; robust optimization; Robustness; Dynamical system; Dynamical systems; Constrained optimization
• ISSN: 0018-9286; 1558-2523
• DOI: 10.1109/TAC.2011.2160029

We present algebraic conditions on the trajectory of a dynamical system to approximately describe a certain type of system robustness. The corresponding equations can be used as constraints in a robust optimization procedure to select a set of optimal design parameters for a dynamical system which is subject to fast disturbances. Robustness is ensured by requiring the disturbance parameters to stay sufficiently far away from critical manifolds in the disturbance parameter space, at which the system would lose stability. The closest distance to the critical manifolds is measured along their normal vectors.