Abstract
For the optimal control problem of a nonlinear distributed parameter system (DPS) with an index constainnig partial differential operators in the spatial variables, deriving a costate system equation and the associated boundary and final conditions in component notations is very tedious and complicated. Matrix methods, which provide structural and operational convenience, are introduced into the derivations. The costate system with the final condition for a class of DPS's and indices consisting of the first order partial differential operator is given in a compact matrix form.
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