TIME OPTIMAL CONTROL FOR A CLASS OF COMMON RANDOM DISTURBANCES
Abstract
The report concerns the time optimal control of a system variable where the controlling input to the system is bounded, as is normally the case in practice. Optimal control is defined here as that control which yields time optimal trajectories. It is shown that time optimal control also yields optimal trajectories in the sense of minimizing the maximum error (if this is the initial error, minimize the overswing next) and the number of oscillations. The problem of optimal control of a second-order system initially in equilibrium and subjected to a large class of commonly occurring random disturbances is solved. Disturbances are considered to be controllable or uncontrollable. The broad class of random disturbances treated herein may have initial nonequilibrium values and consist of a unidirectional uncontrollable portion, followed by a controllable portion of sufficient duration to enable an optimal controller to bring the system to equilibrium. A single control function is derived which suffices to yield optimal trajectories.
Document Details
- Document Type
- Technical Report
- Publication Date
- Feb 02, 1968
- Accession Number
- AD0667521
Entities
People
- Norval P. Smith
Organizations
- Massachusetts Institute of Technology