On a state space approach to nonlinear H∞ control


Schaft, A.J. van der (1991) On a state space approach to nonlinear H∞ control. Systems & Control Letters, 16 (1). pp. 1-8. ISSN 0167-6911

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Abstract:We study the standard H∞ optimal control problem using state feedback for smooth nonlinear control systems. The main theorem obtained roughly states that the L2-induced norm (from disturbances to inputs and outputs) can be made smaller than a constant γ > 0 if the corresponding H∞ norm for the system linearized at the equilibrium can be made smaller than γ by linear state feedback. Necessary and sufficient conditions for the latter problem are by now well-known, e.g. from the state space approach to linear H∞ optimal control. Our approach to the nonlinear H∞ optimal control problem generalizes the state space approach to the linear H∞ problem by replacing the Hamiltonian matrix and corresponding Riccati equation as used in the linear context by a Hamiltonian vector field together with a Hamiltonian-Jacobi equation corresponding to its stable invariant manifold.
Item Type:Article
Copyright:© 1991 Elsevier
Electrical Engineering, Mathematics and Computer Science (EEMCS)
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Link to this item:http://purl.utwente.nl/publications/72984
Official URL:http://dx.doi.org/10.1016/0167-6911(91)90022-7
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