This book defines and develops the generalized adjoint of an
input-output system. It is the result of a theoretical development
and examination of the generalized adjoint concept and the
conditions under which systems analysis using adjoints is valid.
Results developed in this book are useful aids for the analysis and
modeling of physical systems, including the development of guidance
and control algorithms and in developing simulations. The
generalized adjoint system is defined and is patterned similarly to
adjoints of bounded linear transformations. Next the elementary
properties of the generalized adjoint system are derived. For a
space of input-output systems, a generalized adjoint map from this
space of systems to the space of generalized adjoints is defined.
Then properties of the generalized adjoint map are derived.
Afterward the author demonstrates that the inverse of an
input-output system may be represented in terms of the generalized
adjoint. The use of generalized adjoints to determine bounds for
undesired inputs such as noise and disturbance to an input-output
system is presented and methods which parallel adjoints in linear
systems theory are utilized. Finally, an illustrative example is
presented which utilizes an integral operator representation for
the system mapping.
General
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