Abstract
Abstract It is shown that the matrix minimum principle can be used to study both deterministic and stochastic control systems described by partial differential equation models. It in shown that the matrix formulations of the control problem reduce to a state canonical equation which is identical with the Riccati equation of the conventional state vector representation. The technique employs the powerful optimization techniques of the calculus of variations and dynamic programming, and leads in a natural way to the separation principle for the case of stochastic optimal control problems. The results of this study show once more the close relationship between the tools used for finite-dimensional control problems and their distributed-parameter (infinite-dimensional) counterparts.
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