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The Numerical Solution of Continuous Time Optimal Control Problems with the Cutting Angle Method (Paperback)
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The Numerical Solution of Continuous Time Optimal Control Problems with the Cutting Angle Method (Paperback)
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This book consists of two parts. The first part is on the
development of the proposition that if there exists a type of
function, then there exists a functional with the same type based
on the proposition of the inheritance and generalizability
properties of a function in a functional. This study presents the
abstract convex, increasing positively homogeneous and
convex-along-rays functionals via this proposition. The second part
concerns the investigation of the use of a global search
optimization algorithm called the Cutting Angle Method (CAM) on
Optimal Control Problems (OCP). Many algorithms are available for
solving OCP, but they are basically local search algorithms. To
overcome the problem associated with local searches, most OCP are
modeled as Linear Quadratic Regulator (LQR) problems in the hope
that the solution found estimates of the true global solution to
the original problem. However, in doing so, a lot of information
carried by the original problem might be lost in its translation
into LQR models. CAM being a global search algorithm is expected to
overcome this problem. It can be used alone or in combination with
a local search to find the global solution. CAM has been
successfully used on functions, however, OCP are functionals. To do
this, a model has been introduced based on inheritance and
generalizability properties to demonstrate that the optimization
algorithms that are used for functions can also be extended for use
in functionals. Based on these properties, the study discovered
that with the Unit Vectors Combinations Technique (UVCT) proposed
in this research, CAM could successfully work on functionals in
general and OCP particularly. To help speed up the convergence of
CAM, the literature proposed the use of local searches for the
determination of the initial solution. In a case study done in the
research, CAM was successfully combined with a local search known
as the Dynamic Integrated System Optimization and Parameter
Estimation (DISOPE) algorithm. Moreover, the initial solution given
by the DISOPE algorithm has been verified as a global influence by
CAM.
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