ON A ROBUSTNESS OF REDUCED ORDER MODELS BY STATE OPTIMIZATION APPROACH

Abstract

State optimization approach has been proposed to treating various different system problems in optimal projection equations (OPEQ). While OPEQ for problems of open-loop thinking is found consisting of two modified Lyapunov equations, excepting conditions for the rank of measurements matrices whereas required in system identification problems, the one for closed-loop thinking consists of two modified Riccatti or Lyapunov equations excepting conditions for compensating system happened to be in a problem like that of order reduction for controller. Apart from addditonally constrained-conditions and simplicity in the solution form have been obtainable for each problem, it has been found the system problems switching over to computing the solution of OPEQ and the physical nature of medeled states possibly retaining in optimal order reduction problem.

On adopting the state optimization approach to a robustness of reduced order for a nonlinear series-based expressible uncertain model to enjoy the above mentioned advantages is reported in this paper. Necessary conditions for the robustness obtain from those for uncertain model to be the one of stability, joint controllability and observability characteristcs. Sufficient ones for reduced order by state optimization to be applicable for uncertainty of quasilinear model are reported next. Robustness of reduced order interpreting in terms of a concave optimization problem with different initial conditions, bounds and limits are also reported.