Minimax optimal control of stochastic uncertain systems with relative entropy constraints
- 1 March 2000
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Automatic Control
- Vol. 45 (3), 398-412
- https://doi.org/10.1109/9.847720
Abstract
This paper considers a new class of discrete time stochastic uncertain systems in which the uncertainty is described by a constraint on the relative entropy between a nominal noise distribution and the perturbed noise distribution. This uncertainty description is a natural extension to the case of stochastic uncertain systems, of the sum quadratic constraint uncertainty description. This paper solves problems of worst-case robust performance analysis and output feedback minimax optimal controller synthesis in a general nonlinear setting. Specializing these results to the linear case leads to a minimax linear quadratic Gaussian (LQG) optimal controller. This controller is defined by Riccati difference equations and a Kalman filter-like state equation. The paper also shows that the minimax LQG problem will have a solution if and only if a corresponding H/sup /spl infin// control problem has a solution. A linear example is presented to illustrate the minimax LQG methodology.Keywords
This publication has 24 references indexed in Scilit:
- Global optimization for H/sub ∞/ control with constant diagonal scalingIEEE Transactions on Automatic Control, 1998
- System analysis via integral quadratic constraintsIEEE Transactions on Automatic Control, 1997
- A Weak Convergence Approach to the Theory of Large DeviationsWiley Series in Probability and Statistics, 1997
- Connections between stochastic control and dynamic gamesMathematics of Control, Signals, and Systems, 1996
- Performance analysis and controller synthesis for nonlinear systems with stochastic uncertainty constraintsAutomatica, 1996
- A connection betweenAutomatica, 1995
- Mixed H 2/H ∞ ControlPublished by Springer Science and Business Media LLC ,1995
- Mixed ℋ/sub 2/ and ℋ/sub ∞/ performance objectives. II. Optimal controlIEEE Transactions on Automatic Control, 1994
- LQG cost bounds in discrete-time H2/H-infinity controlTransactions of the Institute of Measurement and Control, 1991
- Mixed-norm H2/H∞ regulation and estimation: The discrete-time caseSystems & Control Letters, 1991