OPTIMIZATION OF SYSTEMS CONTAINING DISCONTINUOUS ELEMENTS,
Abstract
The uses of the sensitivity equations for systems containing discontinuous elements in solving various optimization problems are discussed. Known results about the first order sensitivities are employed in an iterative procedure proposed for the solution of two-point boundary value problems for systems described on different time intervals by different non-linear vector differential equations. The procedure, which involves the use of Newton's method, is demonstrated for fixed-time, fixed-end-point fuel optimization for linear time-varying plants with a bounded control. With modifications, the iterative procedure can also be used for solution of various free-time optimization problems involving a bounded control. An on-line method sub-optimal control is proposed for the case of fixed-time, fixed-end-point fuel optimization when the control is bounded and various parameters are known only to be near nominal values. This method of control, called the 'Switch Time Sensitivity' control, makes use of the partials of the optimal switch times with respect to the parameters in order to determine switch times which are near the optimal switch times for the perturbed system. The method of control is also applicable when some combination of fuel and time is to be minimized. Finally, a study is made of parameter optimization for a system containing a relay with hysteresis and dead zone. Under certain assumptions, the second order sensitivity equations are derived and the Newton-Raphson method is employed for the minimization of the chosen performance index. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- May 01, 1968
- Accession Number
- AD0675308
Entities
People
- Robert Gerald Stefanek
Organizations
- University of Illinois Urbana–Champaign