Browsing by Subject "optimal control"
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Item Constrained expectation-maximization (EM), dynamic analysis, linear quadratic tracking, and nonlinear constrained expectation-maximation (EM) for the analysis of genetic regulatory networks and signal transduction networks(2009-05-15) Xiong, HaoDespite the immense progress made by molecular biology in cataloging andcharacterizing molecular elements of life and the success in genome sequencing, therehave not been comparable advances in the functional study of complex phenotypes.This is because isolated study of one molecule, or one gene, at a time is not enough byitself to characterize the complex interactions in organism and to explain the functionsthat arise out of these interactions. Mathematical modeling of biological systems isone way to meet the challenge.My research formulates the modeling of gene regulation as a control problem andapplies systems and control theory to the identification, analysis, and optimal controlof genetic regulatory networks. The major contribution of my work includes biologicallyconstrained estimation, dynamical analysis, and optimal control of genetic networks.In addition, parameter estimation of nonlinear models of biological networksis also studied, as a parameter estimation problem of a general nonlinear dynamicalsystem. Results demonstrate the superior predictive power of biologically constrainedstate-space models, and that genetic networks can have differential dynamic propertieswhen subjected to different environmental perturbations. Application of optimalcontrol demonstrates feasibility of regulating gene expression levels. In the difficultproblem of parameter estimation, generalized EM algorithm is deployed, and a set of explicit formula based on extended Kalman filter is derived. Application of themethod to synthetic and real world data shows promising results.Item Cooperative control of autonomous underwater vehicles.(Texas A&M University, 2004-09-30) Savage, ElizabethThe proposed project is the simulation of a system to search for air vehicles which have splashed-down in the ocean. The system comprises a group of 10+ autonomous underwater vehicles, which cooperate in order to locate the aircraft. The search algorithm used in this system is based on a quadratic Newton method and was developed at Sandia National Laboratories. The method has already been successfully applied to several two dimensional problems at Sandia. The original 2D algorithm was converted to 3D and tested for robustness in the presence of sensor error, position error and navigational error. Treating the robots as point masses, the system was found to be robust for all such errors. Several real-life adaptations were necessary. A round-robin communication strategy was implemented on the system to properly simulate the dissemination of information throughout the group. Time to convergence is delayed but the system still functioned adequately. Once simulations for the point masses had been exhausted, the dynamics of the robots were included. The robot equations of motion were described using Kane's equations. Path-planning was investigated using optimal control methods. The Variational Calculus approach was attempted using a line search tool "fsolve" found in Matlab and a Genetic Algorithm. A dynamic programming technique was also investigated using a method recently developed by Sandia National Laboratories. The Dynamic Programming with Interior Points (DPIP) method was a very effcient method for path planning and performed well in the presence of system constraints. Finally all components of the system were integrated. The motion of the robot exactly matched the motion of the particles, even when subjected to the same robustness tests carried out on the point masses. This thesis provides exciting developments for all types of cooperative projects.Item Incomplete Information Pursuit-Evasion Games with Applications to Spacecraft Rendezvous and Missile Defense(2014-12-04) Aures-Cavalieri, Kurt DPursuit-evasion games reside at the intersection of game theory and optimal control theory. They are often referred to as differential games because the dynamics of the relative system are modeled by the pursuer and evader differential equations of motion. Pursuit-evasion games diverge from traditional optimal control problems due to the participation of multiple intelligent agents with conflicting goals. Individual goals of each agent are defined through multiple cost functions and determine how each player will behave throughout the game. The optimal performance of each player is dependent upon how much knowledge they have about themselves, their opponent, and the system. Complete information games represent the ideal case in which each player can truly play optimally because all pertinent information about the game is readily available to each player. Player performance in a pursuit-evasion game greatly diminishes as information availability moves further from the ideal case and approaches the most realistic scenarios. Methods to maintain satisfactory performance in the presence of incomplete, imperfect, and uncertain information games is very desirable due to the application of optimal pursuit-evasion solutions to high-risk missions including spacecraft rendezvous and missile interception. Behavior learning techniques can be used to estimate the strategy of an opponent and augment the pursuit-evasion game into a one-sided optimal control problem. The application of behavior learning is identified in final-time-fixed, in finite-horizon, and final-time-free situations. A twostep dynamic inversion process is presented to fit systems with nonlinear kinematics and dynamics into the behavior learning framework for continuous, linear-quadratic games. These techniques are applied to minimum-time, spacecraft reorientation, and missile interception examples to illustrate the advantage of these techniques in real-world applications when essential information is unavailable.Item Modified Chebyshev-Picard Iteration Methods for Solution of Initial Value and Boundary Value Problems(2011-10-21) Bai, XiaoliThe solution of initial value problems (IVPs) provides the evolution of dynamic system state history for given initial conditions. Solving boundary value problems (BVPs) requires finding the system behavior where elements of the states are defined at different times. This dissertation presents a unified framework that applies modified Chebyshev-Picard iteration (MCPI) methods for solving both IVPs and BVPs. Existing methods for solving IVPs and BVPs have not been very successful in exploiting parallel computation architectures. One important reason is that most of the integration methods implemented on parallel machines are only modified versions of forward integration approaches, which are typically poorly suited for parallel computation. The proposed MCPI methods are inherently parallel algorithms. Using Chebyshev polynomials, it is straightforward to distribute the computation of force functions and polynomial coefficients to different processors. Combining Chebyshev polynomials with Picard iteration, MCPI methods iteratively refine estimates of the solutions until the iteration converges. The developed vector-matrix form makes MCPI methods computationally efficient. The power of MCPI methods for solving IVPs is illustrated through a small perturbation from the sinusoid motion problem and satellite motion propagation problems. Compared with a Runge-Kutta 4-5 forward integration method implemented in MATLAB, MCPI methods generate solutions with better accuracy as well as orders of magnitude speedups, prior to parallel implementation. Modifying the algorithm to do double integration for second order systems, and using orthogonal polynomials to approximate position states lead to additional speedups. Finally, introducing perturbation motions relative to a reference motion results in further speedups. The advantages of using MCPI methods to solve BVPs are demonstrated by addressing the classical Lambert?s problem and an optimal trajectory design problem. MCPI methods generate solutions that satisfy both dynamic equation constraints and boundary conditions with high accuracy. Although the convergence of MCPI methods in solving BVPs is not guaranteed, using the proposed nonlinear transformations, linearization approach, or correction control methods enlarge the convergence domain. Parallel realization of MCPI methods is implemented using a graphics card that provides a parallel computation architecture. The benefit from the parallel implementation is demonstrated using several example problems. Larger speedups are achieved when either force functions become more complicated or higher order polynomials are used to approximate the solutions.