Piecewise linear quadratic optimal control
Top Cited Papers
- 1 April 2000
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Automatic Control
- Vol. 45 (4) , 629-637
- https://doi.org/10.1109/9.847100
Abstract
The use of piecewise quadratic cost functions is extended from stability analysis of piecewise linear systems to performance analysis and optimal control. Lower bounds on the optimal control cost are obtained by semidefinite programming based on the Bellman inequality. This also gives an approximation to the optimal control law. An upper bound to the optimal cost is obtained by another convex optimization problem using the given control law. A compact matrix notation is introduced to support the calculations and it is proved that the framework of piecewise linear systems can be used to analyze smooth nonlinear dynamics with arbitrary accuracKeywords
This publication has 12 references indexed in Scilit:
- Robust stability analysis and controller design with quadratic Lyapunov functionsPublished by Springer Nature ,2005
- On the computation of piecewise quadratic Lyapunov functionsPublished by Institute of Electrical and Electronics Engineers (IEEE) ,2002
- Computation of piecewise quadratic Lyapunov functions for hybrid systemsIEEE Transactions on Automatic Control, 1998
- Piecewise linear quadratic optimal controlPublished by Institute of Electrical and Electronics Engineers (IEEE) ,1997
- A new class of universal Lyapunov functions for the control of uncertain linear systemsPublished by Institute of Electrical and Electronics Engineers (IEEE) ,1996
- Analyzing piecewise linear dynamical systemsIEEE Control Systems, 1995
- Numerical approximation of the H∞ norm for nonlinear systemsAutomatica, 1995
- L/sub 2/-gain analysis of nonlinear systems and nonlinear state-feedback H/sub infinity / controlIEEE Transactions on Automatic Control, 1992
- Structure and control of piecewise-linear systemsInternational Journal of Control, 1989
- Nonlinear regulation: The piecewise linear approachIEEE Transactions on Automatic Control, 1981