1and differentiating, we get Cr = li -€PV -EPV, ) = -Q i C -Q u + U .Substituting for li and U from the original system, and simplifying, we get where and A different viewpoint is taken in developing the decoupling transformations for singularly perturbed linear systems. The proposed transformations have the advantage over the previous ones since they also decouple the transformation equations (13) and (14), enabling us to perform the computations in parallel. This is numeri-cally very efficient for the case of time-varying systems where the corresponding differential equations are stiff. REFERENCES Gajic, D. Petkovski, and X. Shen, Singularly Perturbed and Weakly Coupled Linear Control Systems-A Recursive Approach. Abstract-( A , E , B)-invariant and ( E , A , B)-invariant subspaces forthe two-dimensional singular Roesser model are investigated. These subspaces are related to the existence of the solutions when the boundary conditions are in these subspaces. Also existence of a solution sequence in certain subspaces derived from the invariant subspaces is shown. The boundary conditions that appear in the solution when some semistates in the solution are restricted to zero are also investigated.
A train operation optimization by minimizing its traction energy subject to various constraints is carried out using nature-inspired evolutionary algorithms. The optimization process results in switching points that initiate cruising and coasting phases of the driving. Due to nonlinear optimization formulation of the problem, nature-inspired evolutionary search methods, Genetic Simulated Annealing, Firefly, and Big Bang-Big Crunch algorithms were employed in this study. As a case study a real-like train and test track from a part of Eskisehir light rail network were modeled. Speed limitations, various track alignments, maximum allowable trip time, and changes in train mass were considered, and punctuality was put into objective function as a penalty factor. Results have shown that all three evolutionary methods generated effective and consistent solutions. However, it has also been shown that each one has different accuracy and convergence characteristics.
We consider the existence of solutions with certain geometric properties for the implicit Roesser model (IRM) and the second implicit Fornasini-Marchesini model. We define invariant subspaces and some geometric notions which do not have one-dimensional counterparts. Using these notions, we analyze a Fornasini-Marchesini-like model which encompasses two alternative representations of the IRM. For the IRM we consider boundary conditions on any side of the boundary to investigate existence of the solutions.We provide recursions to compute relevant subspaces for each model. We relate the 2-D output nulling (A,E,B)-invariant subspaces of a dual system to observer design. We construct an asymptotic state-space observer for each model by using geometric techniques, and include an illustrative example.
The real structured singular value (RSSV, or real μ) is a useful measure to analyze the robustness of linear systems subject to structured real parametric uncertainty, and surely a valuable design tool for the control systems engineers. We formulate the RSSV problem as a nonlinear programming problem and use a new computation technique, F-modified subgradient (F-MSG) algorithm, for its lower bound computation. The F-MSG algorithm can handle a large class of nonconvex optimization problems and requires no differentiability. The RSSV computation is a well known NP hard problem. There are several approaches that propose lower and upper bounds for the RSSV. However, with the existing approaches, the gap between the lower and upper bounds is large for many problems so that the benefit arising from usage of RSSV is reduced significantly. Although the F-MSG algorithm aims to solve the nonconvex programming problems exactly, its performance depends on the quality of the standard solvers used for solving subproblems arising at each iteration of the algorithm. In the case it does not find the optimal solution of the problem, due to its high performance, it practically produces a very tight lower bound. Considering that the RSSV problem can be discontinuous, it is found to provide a good fit to the problem. We also provide examples for demonstrating the validity of our approach.Keywords Robust control · Real structured singular value · Nonlinear programming · Modified subgradient algorithm R. Kasimbeyli published under the name Rafail N. Gasimov until 2007.
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