A Series Solution Framework for Finite-time Optimal Feedback Control, H-infinity Control and Games

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Title: A Series Solution Framework for Finite-time Optimal Feedback Control, H-infinity Control and Games
Author: Sharma, Rajnish
Abstract: The Bolza -form of the finite -time constrained optimal control problem leads to the Hamilton -Jacobi -Bellman (HJB ) equation with terminal boundary conditions and tobe - determined parameters . In general , it is a formidable task to obtain analytical and /or numerical solutions to the HJB equation . This dissertation presents two novel polynomial expansion methodologies for solving optimal feedback control problems for a class of polynomial nonlinear dynamical systems with terminal constraints . The first approach uses the concept of higher -order series expansion methods . Specifically , the Series Solution Method (SSM ) utilizes a polynomial series expansion of the cost -to -go function with time -dependent coefficient gains that operate on the state variables and constraint Lagrange multipliers . A significant accomplishment of the dissertation is that the new approach allows for a systematic procedure to generate optimal feedback control laws that exactly satisfy various types of nonlinear terminal constraints . The second approach , based on modified Galerkin techniques for the solution of terminally constrained optimal control problems , is also developed in this dissertation . Depending on the time -interval , nonlinearity of the system , and the terminal constraints , the accuracy and the domain of convergence of the algorithm can be related to the order of truncation of the functional form of the optimal cost function . In order to limit the order of the expansion and still retain improved midcourse performance , a waypoint scheme is developed . The waypoint scheme has the dual advantages of reducing computational efforts and gain -storage requirements . This is especially true for autonomous systems . To illustrate the theoretical developments , several aerospace application -oriented examples are presented , including a minimum -fuel orbit transfer problem . Finally , the series solution method is applied to the solution of a class of partial differential equations that arise in robust control and differential games . Generally , these problems lead to the Hamilton -Jacobi -Isaacs (HJI ) equation . A method is presented that allows this partial differential equation to be solved using the structured series solution approach . A detailed investigation , with several numerical examples , is presented on the Nash and Pareto -optimal nonlinear feedback solutions with a general terminal payoff . Other significant applications are also discussed for one -dimensional problems with control inequality constraints and parametric optimization .
URI: http : / /hdl .handle .net /1969 .1 /ETD -TAMU -2008 -12 -156
Date: 2010-01-14

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A Series Solution Framework for Finite-time Optimal Feedback Control, H-infinity Control and Games. Available electronically from http : / /hdl .handle .net /1969 .1 /ETD -TAMU -2008 -12 -156 .

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