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.
Original language | Undefined |
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Pages (from-to) | 1-8 |
Number of pages | 8 |
Journal | Systems and control letters |
Volume | 0 |
Issue number | 1 |
DOIs | |
Publication status | Published - 1991 |
Keywords
- Nonlinear H∞ control
- State feedback
- Lagrangian submanifolds
- L2-induced norm
- METIS-140587
- stable manifolds
- hyperbolic Hamiltonian vector fields
- IR-72984
- Hamilton-Jacobi equation
- linearization