This dissertation describes several new connections between a polynomial's coefficients and its zeros. The most important of these, the Finite Nyquist Theorem (FNT), states that one can prove a polynomial has all its roots in an open, bounded or unbounded, convex region ${\cal D}$ of the complex plane given only the polynomial's degree and its phase at finitely many points along ${\cal D}$'s boundary. An immediate and very useful corollary to FNT is the Finite Inclusions Theorem (FIT), with which one can prove a class of polynomials has all its zeros in ${\cal D}$ given only the polynomials' degree and approximate knowledge of the class's value set at finitely many points along ${\cal D}$'s boundary. From FIT a procedure we call FIT synthesis is developed for synthesizing robustly ${\cal D}$-stabilizing controllers for parametrically uncertain systems (note, all the systems considered here are assumed to be linear time-invariant and finite dimensional). This procedure uses FIT to directly search for robust controllers by way of solving a sequence of systems of linear inequalities. Two numerical examples of this procedure are given to show its effectiveness. In these examples the systems of inequalities are solved via the projection method which is an elegantly simple technique for solving (finite or infinite) systems of convex inequalities in an arbitrary Hilbert space. Since this method has yet to appear in standard textbooks on numerical methods, it is covered here in detail with the aim of better popularizing the method and, where possible, extending the known theory concerning its convergence.

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A robot wanders around an unfamiliar environment, performing actions and observing their perceptual consequences. The robot's task is to construct a model of its environment that will allow it to predict the outcome of its actions and to determine what action sequences take it to particular goal states. In any reasonably complex situation, a robot that aims to manipulate its environment toward some desired end requires an internal representation of the environment because the robot can directly perceive only a small fraction of the global environmental state at any time; some portion of the rest must be stored internally if the robot is to act effectively. Rivest and Schapire (72, 74, 87) have studied this problem and have designed a symbolic algorithm to strategically explore and infer the structure of finite-state environments. At the heart of this algorithm is a clever representation of the environment called an update graph. This dissertation presents a connectionist implementation of the update graph using a highly specialized network architecture and a technique for using the connectionist update graph to guide the robot from an arbitrary starting state to a goal state. This technique requires a critic that associates the update graph's current state with the expected time to reach the goal state. At each time step, the robot selects the action that minimizes the output of the critic. The basic control acquisition technique is demonstrated on several environments, and it is generalized to handle a navigation task involving a more realistic environment characterized by a high-dimensional continuous state-space with real-valued actions and sensations in which a simulated cylindrical robot with a sensor belt operates in a planar environment. The task is short-range homing in the presence of obstacles. Unlike many approaches to robot navigation, our approach assumes no prior map of the environment. Instead, the robot has to use its limited sensory information to construct a model of its environment. A connectionist architecture is presented for building such a model. It incorporates a large amount of a priori knowledge in the form of hard-wired networks, architectural constraints, and initial weights. This navigation example demonstrates the use of a large modular architecture on a difficult task.

An indirect adaptive quenching algorithm for a nonlinear single-degree-of-freedom system with unknown constant system parameters is presented. The system is subject to external or parametric sinusoidal disturbances and the resulting control signal is also sinusoidal. The quenching algorithm provides a reduction in the control effort required compared to direct disturbance cancellation. The disturbance sinusoid and the unknown parameters are incorporated into the system model and an extended Kalman filter (EKF) with modified update equations is used to estimate the system state and parameters. The estimates are then used to form the quenching signal. The adaptive quenching algorithm is found to work well inside a quenching region defined by the separatrices and suggests the use of a hybrid control law. The algorithm was verified by implementing it on an analog computer. / Master of Science

This work is directed towards linear and nonlinear three dimensional magnetostatic field analysis and computation in electrical devices. Question regarding the validity and uniqueness of numerical field solutions, obtained on the basis of the curl curl approach, has been resolved through analytical proofs, numerical demonstrations, as well as experimental verifications. A nonlinear three dimensional magnetostatic field formulation is developed using the Newton-Raphson approach in conjunction with the three dimensional finite element method for inclusion of nonlinearities in laminated iron cores under saturated conditions. The developed, formulation was successfully implemented and applied to a practical example with considerable magnetic saturation. A method, for the calculation of saturated device winding inductance, is presented. This method is based on an energy perturbation technique and was successfully applied numerically and verified experimentally. Two methods for the calculation of forces on conductor segments as well as magnetized ferrous parts are developed in conjunction with the three dimensional finite element vector potential method. The proximity effect, resulting from considering small or large solution volumes on the field distribution, and the calculated values of force, is examined. It is demonstrated that a large solution volume, with Dirichlet boundary conditions imposed on the outermost surfaces of the volume considered, yield practically the same result, as when the Neumman boundary conditions were imposed on such surfaces. This result is of a considerable significance, from a practical standpoint, since the imposition of Dirichlet type boundary conditions on the outermost boundaries of the volume considered, results in a fewer number of equations to be solved. This, in turn, results in savings of the total execution time and memory costs required for the solution of large problems of two dimensional, and three dimensional fields by finite elements. It is demonstrated that three dimensional field solutions reduce to the corresponding two dimensional field solutions for problems which are inherently two dimensional in nature due to axial symmetry. This result provides a further verification of the validity of the three dimensional finite element formulation presented in this work. / Ph. D.

This work investigates energy-efficient approximate computation for solving differential equations. It extends the analog computing techniques to a new paradigm: continuous-time hybrid computation, where both analog and digital circuits operate in continuous time. In this approach, the time intervals in the digital signals contain important information. Unlike conventional synchronous digital circuits, continuous-time digital signals offer the benefits of adaptive power dissipation and no quantization noise. Two prototype chips have been fabricated in 65 nm CMOS technology and tested successfully. The first chip is capable of solving nonlinear differential equations up to 4th order, and the second chip scales up to 16th order based on the first chip. Nonlinear functions are generated by a programmable, clockless, continuous-time 8-bit hybrid architecture (ADC+SRAM+DAC). Digitally-assisted calibration is used in all analog/mixed-signal blocks. Compared to the prior art, our chips makes possible arbitrary nonlinearities and achieves 16 times lower power dissipation, thanks to technology scaling and extensive use of class-AB analog blocks. Typically, the unit achieves a computational accuracy of about 0.5% to 5% RMS, solution times from a fraction of 1 micro second to several hundred micro seconds, and total computational energy from a fraction of 1 nJ to hundreds of nJ, depending on equation details. Very significant advantages are observed in computational speed and energy (over two orders of magnitude and over one order of magnitude, respectively) compared to those obtained with a modern MSP430 microcontroller for the same RMS error.

Indiana University-Purdue University Indianapolis (IUPUI) / HEVC has achieved significant coding efficiency improvement beyond existing video coding standard by employing many new coding tools. Deblocking Filter, Sample Adaptive Offset and Adaptive Loop Filter for in-loop filtering are currently introduced for the HEVC standardization. However these filters are implemented in spatial domain despite the fact of temporal correlation within video sequences. To reduce the artifacts and better align object boundaries in video , a new algorithm in in-loop filtering is proposed. The proposed algorithm is implemented in HM-11.0 software. This proposed algorithm allows an average bitrate reduction of about 0.7% and improves the PSNR of the decoded frame by 0.05%, 0.30% and 0.35% in luminance and chroma.