Control of Uncertain Systems with a Set-Membership Description of the Uncertainty
Abstract
The problem of optimal feedback control of uncertain discrete-time dynamic systems is considered, where the uncertain quantities do not have a stochastic description but instead they are known to belong to given sets. The problem is converted to a sequential minimax problem and dynamic programming is suggested as a general method for its solution. The notion of a sufficiently informative function, which parallels the notion of a sufficient statistic of stochastic optimal control, is introduced, and the possible decomposition of the optimal controller into an estimator and an actuator is demonstrated. Some special cases involving a linear system are further examined. A problem involving a convex cost functional and perfect state information for the controller is considered in detail. Particular attention is given to a special case, the problem of reachability of a target tube, and an ellipsoidal approximation algorithm is obtained which leads to linear control laws. State estimation problems are also examined, and some algorithms are derived which offer distinct advantages over existing estimation schemes. These algorithms are subsequently used in the solution of some reachability problems with imperfect state information for the controller.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jun 01, 1971
- Accession Number
- AD0728720
Entities
People
- Dimitri P. Bertsekas
Organizations
- Massachusetts Institute of Technology