Karisetty, Bhanu Chandra

English

Open Access Repository of Indian Theses

AbstractDifferential Equations constrained by algebraic equations and inequalities on the statesoccur naturally in the modeling of many engineering systems such as simulation andcontrol of multibody dynamical systems and electrical circuits, in robotic path planningand sliding mode control systems, in guidance design for aerospace vehicles and in chem-ical reactor systems. These systems are often known as path constrained DifferentialAlgebraic Equation (DAE) systems. In this work we investigate the numerical methodsfor (1) simulation of path constrained DAEs with high differential index, (2) computa-tional solution of optimal control problems with high index constraints and (3) dynamicoptimization problem with disjunctive algebraic constraints.At first, this thesis develops the generalized-α method and analyzes it in detail. Thegeneralized-α method is shown to have regularization property which becomes a keyadvantage in solving high index path constrained dynamical systems.We show that the α-method is a good simulator for high index DAEs due to theregularization property involved in the discretization. This solves effectively the index 3Euler-Lagrange equations, Kane’s equations formulation and other higher index DAEsoccurring naturally.We study a direct method known as transcription method, a numerical approach,equipped with the generalized-α discretization to solve an Optimal Control Problem(OCP). State-constrained path constraints in an OCP pose numerical challenges because(1) along the (active) constraints a high index DAE is often formed and (2) the numberand interval of active inequality constraints (even if not state constrained) is not known inpriori. It is shown that the regularization property of the generalized-α method is usefulivvin these situations. The proposed method does not perturb the inequality constraintsand hence the physics of the problem is not diluted. The convergence analysis of thediscretized dynamic optimization problem to the continuous OCP is proved for a widerange of control problems by assuming low continuity conditions on the controls.Also this thesis solves OCPs having either-or (disjunctive) constraints by consideringan equivalent simple convex hull of the disjunctive constraints. This idea is implementedto a control problem in vehicle dynamics to stabilize the rollover of a road vehicle un-dergoing severe maneuver. From a practical point of view we obtain the control forcesas sensory output.This thesis also focuses on the computation of the radial hedgehog solution, solutionof a Singular Boundary Value Problem (SBVP) arising from the energy minimization ofnematic liquid crystal, by solving an equivalent boundary value DAE. The equivalentDAE, which is index 3 at the point of singularity and index 1 in the rest of the simulationinterval, is solved by the α-method. It is shown that the point of singularity can beremoved by the DAE approach. Advantages of the DAE approach over classical solversfor SBVP and transcription method for the radial hedgehog problem are also shown.Some computational findings of the radial hedgehog solution completes the thesis.Overall, the thesis shows that the singularity and ill-conditioning inherent in pathconstrained DAEs can be dealt with numerically in a consistent and correct way by adiscretization with regularization property.

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http://eprints.csirexplorations.com/1092/2/Abstract_from_Nigam_PhDThesis_.pdf

Sex difference in behavioral and molecular neural response to chronic stress in mouse models of depression and related disorders

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