INVESTIGATION OF PROBLEMS IN THE OPTIMAL CONTROL OF LINEAR MULTI-DIMENSIONAL SYSTEMS,
Abstract
The results are presented of the investigation of several problems encountered in both the mathematical theory and engineering applications of optimal control. A complete and exact mathematical treatment with engineering interpretations is given of the new concept of a minimalinput controlled plant for linear stationary systems. The minimal number of inputs to completely control a plant is shown to be equal to the largest number of blocks associated with any one eigenvalue in the Jordan canonical form of the plant matrix. In order for the controlled plant to be completely controllable with this minimal number of inputs, the input matrix must have a definite structure. A strictly numerical technique is given for all computations necessary to the realization of minimal-input control. The optimal control law for a linear time-varying plant with a quadratic performance criterion is derived in a feedback form. In applying minimaltime, bang-bang control to a linear plant, errors occur in the physical realization of the switching function. For a linear, stationary, twodimensional plant with distinct, non-zero poles and an almost optimal switching curve, there is derived both upper and lower bounds on the limitcycle behavior. These bounds are shown to hold for the real pole plant with a switching time delay. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Jun 01, 1963
- Accession Number
- AD0410584
Entities
People
- John J. O'donnell
Organizations
- Carnegie Institute of Technology