In this paper we consider the properties of linear systems by means of
directed graphs and numerical structures. We also state efficient algorithms
for determining an approximate number of the non-zero terms within
determinants' expressions of the
ir matrices. The stated algorithms make use of
trees representing numerical structures which contains the indices of the nonzero
terms.
This paper yields interesting results used in practical engineering
applications which include linear systems with sparse matrices, for example:
networks, electronic circuits, earth velocities boxes (gearboxes), multi-works
systems ...etc.
This paper presents a method for finding online adaptive optimal
controllers for continuous-time linear systems without knowing the
system dynamical matrices. The proposed method employs one of
Intelligent Operations Research Techniques, this tech
nique is the
adaptive dynamic programming, to iteratively solve the algebraic
Riccati equation using the online information of state and input,
without requiring the a priori knowledge of the system dynamics. In
addition, all iterations can be conducted by using repeatedly the
same state and input information on some fixed time intervals. A
practical online algorithm is developed in this paper, and is applied
to the controller design for a turbocharged diesel engine with
exhaust gas recirculation.
