An extension of generalized minimum variance control for multi-input multi-output systems using coprime factorization approach

This paper proposes a new generalized minimum-variance controller (GMVC) having new design parameters by using the coprime factorization approach for a multi-input multi-output (MIMO) case. The method is directly extended from a conventional GMVC and used to construct the controller; it needs to solve only one Diophantine equation as in the conventional method. In this paper, by using double-coprime factorization, a simple formula for the closed-loop system given by the parametrized controller is obtained; and using the formula, it is proved that the closed-loop characteristic from the reference signal to plant output is independent of the selection of the design parameters and the poles of the controller can be chosen by the design parameters without changing the closed-loop system</p

A fractional representation approach to the robust regulation problem for MIMO systems

The aim of this paper is in developing unifying frequency domain theory for robust regulation of MIMO systems. The main theoretical results achieved are a new formulation of the internal model principle, solvability conditions for the robust regulation problem, and a parametrization of all robustly regulating controllers. The main results are formulated with minimal assumptions and without using coprime factorizations thus guaranteeing applicability with a very general class of systems. In addition to theoretical results, the design of robust controllers is addressed. The results are illustrated by two examples involving a delay and a heat equation.Comment: 23 pages, 3 figures, submitted to International Journal of Robust and Nonlinear Contro

UAS Model Identification and Simulation to Support In-Flight Testing of Discrete Adaptive Fault-Tolerant Control Laws

In mission-critical applications of unmanned and autonomous aerial systems(UAS), it is of significant importance to develop robust strategies for fault-tolerant systems that can countermeasure system degradation and consequently support the integration into the National Airspace (NAS). This thesis research illustrates the results of systems identification that is performed using DATCOM followed by the flight test data. This data is acquired from conducting an intensive flight testings program of a fixed-wing UAS to determine the state-space model of the aircraft. A discrete state-space system is reconstructed from these models to derive Auto-Regressive Moving-Average (ARMA) models used to design a Discrete Direct and Indirect Model Reference Adaptive Control. Description of the UAS, sub-systems, and integration is presented in this thesis along with analysis of results from numerical simulation to support the design, development, and validation of adaptive control laws for fault tolerance. A set of performance metrics are defined to perform the analysis in terms of control effort, tracking performance, and reconfiguration of control laws under commonly occurring failures such as partial control surface damage, pilot-induced oscillations, and uncertain ice accretion

A design of a strongly stable generalized predictive control using coprime factorization approach

This paper proposes a new generalized predictive control (GPC) having new design parameters. In selecting the design parameters, the controller becomes a strongly stable GPC, that is, not only the closed-loop system is stable, but also the controller itself is stable. The parameters are introduced by applying the coprime factorization approach and comparing Youla parametrization of stabilizing compensators to the controller by the standard GPC</p

Stabilization of systems with asynchronous sensors and controllers

We study the stabilization of networked control systems with asynchronous sensors and controllers. Offsets between the sensor and controller clocks are unknown and modeled as parametric uncertainty. First we consider multi-input linear systems and provide a sufficient condition for the existence of linear time-invariant controllers that are capable of stabilizing the closed-loop system for every clock offset in a given range of admissible values. For first-order systems, we next obtain the maximum length of the offset range for which the system can be stabilized by a single controller. Finally, this bound is compared with the offset bounds that would be allowed if we restricted our attention to static output feedback controllers.Comment: 32 pages, 6 figures. This paper was partially presented at the 2015 American Control Conference, July 1-3, 2015, the US

Design of optimal equalizers and precoders for MIMO channels

Channel equalization has been extensively studied as a method of combating ISI and ICI for high speed MIMO data communication systems. This dissertation focuses on optimal channel equalization in the presence of non-white observation noises with unknown PSD but bounded power-norm. A worst-case approach to optimal design of channel equalizers leads to an equivalent optimal H-infinity filtering problem for the MIMO communication systems. An explicit design algorithm is derived which not only achieves the zero-forcing (ZF) condition, but also minimizes the RMS error between the transmitted symbols and the received symbols. The second part of this dissertation investigates the design of optimal precoders which minimize the bit error rate (BER) subject to a fixed transmit-power constraint for the multiple antennas downlink communication channels under the perfect reconstruction (PR) condition. The closed form solutions are derived and an efficient design algorithm is proposed. The performance evaluations indicate that the optimal precoder design for multiple antennas communication systems proposed herein is an attractive/reasonable alternative to the existing precoder design techniques

Optimization methods for deadbeat control design: a state space approach

This thesis addresses the synthesis problem of state deadbeat regulator using state space techniques. Deadbeat control is a linear control strategy in discrete time systems and consists of driving the system from any arbitrary initial state to a desired final state infinite number of time steps. Having described the framework for development of the thesis which is in the form of a lower linear-fractional transformation (LFT), the conditions for internal stability based on the notion of coprime factorization over the set of proper and stable transfer matrices, namely RH, is discussed. This leads to the derivation of the class of all stabilizing linear controllers, which are parameterized affinely in terms of a stable but otherwise free parameter Q, usually known as the Q-parameterization. In this work, the classical Q- parameterization is generalized to deliver a parameterization for the family of deadbeat regulators. Time response characteristics of the deadbeat system are investigated. In particular, the deadbeat regulator design problem in which the system must satisfy time domain specifications and minimize a quadratic (LQG-type) performance criterion is examined. It is shown that the attained parameterization for deadbeat controllers leads to the formulation of the synthesis problem in a quadratic programming framework with Q regarded as the design variable. The equivalent formulation of this objective as a quadratic integral in the frequency domain provides the means for shaping the frequency response characteristics of the system. Using the LMI characterization of the standard H problem, a new scheme for shaping the system frequency response characteristics by minimizing the infinity norm of an appropriate closed-loop transfer function is introduced. As shown, the derived parameterization of deadbeat compensators simplifies considerably the formulation and solution of this problem. The last part of the work described in this thesis is devoted to addressing the synthesis problem of deadbeat regulators in a robust way, when the plant is subject to structured norm-bounded parametric uncertainties. A novel approach which is expressed as an LMI feasibility condition has been proposed and analysed

Control Theory: A Mathematical Perspective on Cyber-Physical Systems

Control theory is an interdisciplinary field that is located at the crossroads of pure and applied mathematics with systems engineering and the sciences. Recently the control field is facing new challenges motivated by application domains that involve networks of systems. Examples are interacting robots, networks of autonomous cars or the smart grid. In order to address the new challenges posed by these application disciplines, the special focus of this workshop has been on the currently very active field of Cyber-Physical Systems, which forms the underlying basis for many network control applications. A series of lectures in this workshop was devoted to give an overview on current theoretical developments in Cyber-Physical Systems, emphasizing in particular the mathematical aspects of the field. Special focus was on the dynamics and control of networks of systems, distributed optimization and formation control, fundamentals of nonlinear interconnected systems, as well as open problems in control