M. Edwin Sawan

Near-optimal state feedback design for singularly perturbed systems by unified approach

A near optimal state feedback design for singularly perturbed systems by a unified approach using the delta operator is presented with an example of the aircraft longitudinal motion. The main contribution of this paper is to explore the use of the i -operator that has attracted a new attention in systems science. The i -operator system unifies the continuous system and the discrete system together without loosing any characteristics of both systems. The paper offers the following; Finite-word-length-characteristics are improved using the i -operator. Floating-point-operations are reduced by block diagonalization and by time-invariant optimal feedback gain from the algebraic Riccati equation. The results of adopting those approaches are illustrated in the simulation figures and compared with the earlier one.

Singularly perturbed unified time systems with low sensitivity to model reduction using delta operators

A method of designing a state feedback gain achieving a specified insensitivity of the closed-loop trajectory by the singularly perturbed unified system using the δ operators is proposed. The order of system is reduced by the singular perturbation technique by ignoring the fast mode in it. The proposed method takes care of the actual trajectory variations over the range of the singular perturbation parameter. Necessary conditions for optimality are also derived. The previous study was done in the continuous time system. The present paper extends the previous study to the discrete system and the δ-operating system that unifies the continuous and discrete systems. Advantages of the proposed method are shown in the numerical example.

Five Heads Are Better Than One: An Interdisciplinary Graduate Course on Smart Grids: Lessons, Challenges, and Opportunities

According to the U.S. Department of Energy (DOE ), “Smart grid generally refers to a class of technology people are using to bring utility electricity delivery into the 21st century, using computer-based remote control and automation.” This initiative not only requires power engineers to have a better understanding of auxiliary fields like signal processing, controls, information technology, and communication networks but also needs experts in the auxiliary fields to understand the basic operations of power systems. There is great need in industry for such cross-trained professionals to meet the many challenges of modernizing the power grid.

AF MIMO Wireless Relay Networks under Received Power Constraint

This paper considers an amplify-and-forward (AF) relay scheme for M-source-M-destination pairs and N relay nodes. Cooperative minimum mean square error (MMSE) strategies for wireless relay networks under both a jamming environment and channel uncertainty with received power constraints at the destination nodes are studied. The main contribution of this paper is the derivation of the MMSE-based amplifying relay matrices (ARMs) under both a jamming environment and channel uncertainty. With the proposed ARMs, the system performance under study is evaluated by observing bit error rate (BER) using Monte Carlo simulations. In addition, it is proven that the proposed ARM is the global optimal ARM.

Unified modeling for singularly perturbed systems by delta operators: pole assignment case

A unified modeling method by using the δ-operators for the singularly perturbed systems is introduced. The unified model unifies the continuous and the discrete models. When compared with the discrete model, the unified model has an improved finite word-length characteristics and its δ-operator is handled conveniently like that of the continuous system. In additions, the singular perturbation method, a model approximation technique, is introduced. A pole placement example is used to show such advantages of the proposed methods. It is shown that the error of the reduced model in its eigenvalues is less than the order of e (singular perturbation parameter). It is shown that the error in the unified model is less than that of the discrete model.

MMSE Relaying Strategy for Two-Way Amplify-and-Forward Wireless Networks

This paper studies amplify-and-forward (AF) relay strategies for two-way wireless relay networks consisting of two sources with a single antenna and multiple relays with a single antenna. The closed form of relay amplifying matrices (vectors) with the perfect cancelation of self-interference under both no channel uncertainty and channel uncertainty is presented based on the minimum mean square error (MMSE) criterion. With the derived optimal relay amplifying matrices, the MMSE cost function behavior, the relay power usage, and the sum of the achievable rate are analyzed. Additionally, a filter for each destination will be provided to remove the influences of noises at the receivers.

Stability robustness bounds of discrete two-time-scale systems

This note considers the problem of robustness of discrete two-time-scale systems. Robustness is first analyzed for a nominal system as the general e-bound problem which characterizes an upper bound of the singular perturbation parameter. The stability robustness is then extended to handle the problem of systems subject to parameter variations. For any singular perturbation parameter bounded above by that obtained from the e-bound problem, a stability robustness bound with respect to parameter variations is derived. The results include both unstructured and structured variations.

Robust Stability in Discrete Singularly Perturbed Systems

Abstract In this note, discrete singularly perturbed systems with norm bounded perturbations in the system matrix are discussed. Based on the small gain theorem, sufficient conditions for robust stability are derived in terms of an explicit upper bound on the mode-separation parameter so that the stability of the lower-order systems in separation time scales ensures the stability of the full-order model.

Selection of Amplify-and-Forward Mobile Relay under Cascaded Rayleigh Fading

This paper assumes a practical channel model, called a cascaded Rayleigh fading channel, for a noncooperative distributed mobile relay network, which consists of one mobile source and one mobile destination, and multiple mobile amplify-and-forward (AF) relays. Then, an optimum AF relay amplifying vector (or matrix) is analytically designed using the minimum mean square error (MMSE) criteria and uses it for an efficient mobile relay selection. Power is intentionally not constrained. Instead, this paper presents a scaling factor scheme to meet a target signal-to-noise ratio (SNRTGT) at the destination. This SNRTGT strategy can implicitly embrace the power constraint problems and be a more practical implementation.

Half-duplex and full-duplex distributed relay systems under power constraints

This paper studies relay amplifying matrices and transmitter/receiver beamforming vectors of the amplify-and-forward (AF) multiple-input multiple-output (MIMO) half-duplex (HD)/full-duplex (FD) wireless distributed relay systems. The main objective of this paper is to determine a set of relay amplifying matrices and transmitter/receiver beamforming vectors under transmit power constraints at the source and the relays, individually and independently, based on the minimum mean square error (MMSE) criterion. Additionally, the achievable rate and the MMSE cost function (CF) behaviors will be investigated numerically and analytically for both FD and HD distributed relaying systems. Finally, an iterative algorithm is proposed to solve the desired optimization problem.