Inverse optimal design of input-to-state stabilizing nonlinear controllers
- 1 March 1998
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Automatic Control
- Vol. 43 (3) , 336-350
- https://doi.org/10.1109/9.661589
Abstract
We show that input-to-state stabilizability (as defined by Sontag,1989, 1995) is both necessary and sufficient for the solvability of a Hamilton-Jacobi-Isaacs equation associated with a meaningful differential game problem similar to, but more general than, the "nonlinear H/sub /spl infin//" problem. The significance of the result stems from the fact that constructive solutions to the input-to-state stabilization problem are available (presented in the paper) and that, as shown here, inverse optimal controllers possess margins on input-to-state stability against a certain class of input unmodeled dynamics. Rather than completion of squares, the main tools in our analysis are Legendre-Fenchel transformations and the general form of Young's inequality.Keywords
This publication has 32 references indexed in Scilit:
- Stabilization by output feedback for systems with ISS inverse dynamicsPublished by Elsevier ,2003
- A ‘universal’ construction of Artstein's theorem on nonlinear stabilizationPublished by Elsevier ,2003
- Constructive Nonlinear ControlPublished by Springer Nature ,1997
- A nonlinear small gain theorem for the analysis of control systems with saturationIEEE Transactions on Automatic Control, 1996
- $\mathcal{H}_\infty $ Control of Nonlinear Systems: Differential Games and Viscosity SolutionsSIAM Journal on Control and Optimization, 1996
- Stabilization in spite of matched unmodeled dynamics and an equivalent definition of input-to-state stabilityMathematics of Control, Signals, and Systems, 1996
- On characterizations of the input-to-state stability propertySystems & Control Letters, 1995
- On Characterizations of Input-to-State Stability with Respect to Compact SetsPublished by Elsevier ,1995
- On a state space approach to nonlinearSystems & Control Letters, 1991
- Smooth stabilization implies coprime factorizationIEEE Transactions on Automatic Control, 1989