โ Scribed by P. Sannuti; P. Kokotovic
No coin nor oath required. For personal study only.
M6thode des perturbations singuli res pour le calcul, quasi-optimal de syst mes non-lin6aires d'ordres 61 v6s Singul ire St6rungsmethode ftir den fastoptimalen Entwurf nichtlinearer Regelungssysteme h6herer Ordnung MeToR cnHry~apHbIX BO3MyHIeHI4~ ~.qa np~I~In~KeHHO-OnTnMaJIbnoro paccqeTa HeJII,IHeFI/-IblX CHCTeM BblCOIGiX IIOpfl~KOB P. SANNUTI t and P. KOKOTOVIC+ +
A sufficient condition is given for continuity and differentiability of the optimum control with respect to perturbations which change the system order, the "singular perturbations", and make optimal synthesis procedures practical.
Summary--This paper extends the singular perturbation method proposed in an earlier paper by the same authors.
For a class of non-linear systems, a sufficient condition is given under which the optimal control is continuous and differentiable with respect to perturbations which change the order of the system, the "singular perturbations". Then a low-order near optimum design for high-order systems is developed. The dimensionality 2(n+m) of the boundary value problem is reduced to 2n, while the performance achieved is close to optimum. Example of the near-optimum design for a fifth order non-linear plant is included.
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