Worst case analysis of nonlinear systems

The authors work out a framework for evaluating the performance of a continuous-time nonlinear system when this is quantified as the maximal value at an output port under bounded disturbances-the disturbance problem. This is useful in computing gain functions and L/sub /spl infin//-induced norms, wh...

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Bibliographic Details
Published in:IEEE transactions on automatic control 1999-06, Vol.44 (6), p.1180-1196
Main Authors: Fialho, I.J., Georgiou, T.T.
Format: Article
Language:English
Subjects:
Applied sciences
Computer science
control theory
systems
Control system analysis
Control systems
Control theory
Control theory. Systems
Disturbances
Dynamic programming
Dynamical systems
Equations
Exact sciences and technology
Feedback
Mathematical analysis
Mathematical models
Nonlinear dynamics
Nonlinear systems
Optimal control
Performance gain
Robustness
Trajectory
Upper bound
Viscosity
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Summary:The authors work out a framework for evaluating the performance of a continuous-time nonlinear system when this is quantified as the maximal value at an output port under bounded disturbances-the disturbance problem. This is useful in computing gain functions and L/sub /spl infin//-induced norms, which are often used to characterize performance and robustness of feedback systems. The approach is variational and relies on the theory of viscosity solutions of Hamilton-Jacobi equations. Convergence of Euler approximation schemes via discrete dynamic programming is established. The authors also provide an algorithm to compute upper bounds for value functions. Differences between the disturbance problem and the optimal control problem are noted, and a proof of convergence of approximation schemes for the control problem is given. Case studies are presented which assess the robustness of a feedback system and the quality of trajectory tracking in the presence of structured uncertainty.
ISSN:0018-9286
1558-2523
DOI:10.1109/9.769372