Yvonne Ilke Yaz

Nonlinear observer design with general criteria

A class of nonlinear system and measurement equations involving incrementally conic nonlinearities with finite energy disturbances is considered. A linear matrix inequality based observer design approach is presented that guarantees the satisfaction of a variety of performance criteria ranging from simple estimation error boundedness to dissipativity. Simple simulation examples are included to explore the freedom in design and to illustrate and provide support to the proposed design methodology.

Resilient design of discrete-time observers with general criteria using LMIs

Much of the recent work on robust control or observer design has focused on preservation of stability of the controlled system or the convergence of the observer in the presence of parameter perturbations in the plant equations. The present work addresses the important problem of resilience or nonfragility which is the maintenance of convergence or performance when the observer is erroneously implemented due possibly to computational errors, e.g., round off errors in digital implementation or sensor errors. A linear matrix inequality approach is presented that maximizes performance in the implementation based on the knowledge of an upper bound on the error in the observer gain. Some design examples are provided for illustration purposes.

Discrete-time nonlinear observer design with general criteria

A class of discrete-time nonlinear system and measurement equations involving incrementally conic nonlinearities with finite energy disturbances is considered. A linear matrix inequality based design approach is presented that guarantees the satisfaction of a variety of performance criteria ranging from simple estimation error boundedness to dissipativity. Simple simulation examples are included to illustrate and provide support to the proposed design methodology.

Resilient design of observers with general criteria using LMIs

Much of the recent work on robust control or observer design has focused on preservation of stability of the controlled system or the convergence of the observer in the presence of parameter perturbations in the system and/or measurement equations. The present work addresses the important problem of resilience or non-fragility of observers, which is the maintenance of convergence or performance when the observer gain is perturbed due possibly to computational or implementation errors. A linear matrix inequality approach is presented that maximizes performance of the observer based on the knowledge of an upper bound on the error in the observer gain. Simulation studies are included to test the conservativeness of this design procedure

A generalization of tent map and its use in EKF based chaotic parameter modulation/demodulation

First, the one-dimensional tent map is generalized to extend the range of parameters for chaotic behavior. Then, a chaotic spread spectrum communication scheme is proposed by employing a generalized symmetric tent map to implement high efficiency binary message modulation. Binary bit streams are represented by noise-like and broadband chaotic sequences generated from a symmetric tent map with different parameter sets. Generalizing the tent map by finding the largest parameter set that drives this map to chaos allows modulation of multiple bits by one chaotic sequence at a time, thus the message carrying capacity is greatly improved in the proposed system. The original binary message is recovered by employing an extended Kalman filter to estimate the state of the chaotic system and identify the parameters of the received noise contaminated chaotic sequence, therefore extracting the binary message by matching the parameter sets with the corresponding binary bit stream. Bit error rate performance is presented in simulation studies.

Discrete-time resilient controller design with general criteria for a class of uncertain nonlinear systems

A discrete-time resilient state feedback control scheme is presented to control nonlinear systems with locally conic type of nonlinearities and driven by finite energy disturbances. The resilience property is achieved in the presence of bounded perturbations in the feedback gain. The controller design is also robust as the design process addresses system models containing a higher degree of uncertainty by allowing perturbations in both the system parameters as well as the center and the boundaries of the cone in which the nonlinearity resides. Results are presented for various performance criteria in a unified framework using linear matrix inequalities (LMIs). Illustrative examples are included to demonstrate the efficiency of the proposed approach.

LMI based observer design for nonlinear systems with integral quadratic constraints

In this work, a general class of continuous-time uncertain nonlinear systems with integral quadratic constraints is considered. A full-order nonlinear state observer design is presented for various error performance criteria in a unified framework. These performance criteria include guaranteed-cost suboptimal versions of estimation objectives like H/sub 2/, H/sub /spl infin//, passivity, etc. The design of nonlinear state observers that satisfy these criteria are given using a common matrix inequality formulation.

H2−H∞ control of continuous-time nonlinear systems using the state-dependent Riccati equation approach

ABSTRACT This paper presents a novel state-dependent Riccati equation (SDRE) control approach with the purpose of providing a more effective control design framework for continuous-time nonlinear systems to achieve a mixed nonlinear quadratic regulator and H∞ control performance criteria. By solving the generalized SDRE, the optimal control solution is found to achieve mixed performance objectives guaranteeing nonlinear quadratic optimality with inherent stability property in combination with H∞ type of disturbance reduction. An efficient computational algorithm is given to find the solution to the SDRE. The efficacy of the proposed technique is used to design the control system for inverted pendulum, an under-actuated nonlinear mechanical system.

Robust controller design with general criteria for uncertain conic nonlinear systems with disturbances

A robust state feedback scheme is proposed to control a large class of continuous-time uncertain nonlinear systems with locally conic type nonlinearities and driven by finite energy disturbances. It is assumed that there is also uncertainty regarding the center and the boundary of the cone in which the nonlinearity resides in order to allow the robust control of systems whose models contain a higher degree of uncertainty. Results are presented for various performance criteria using linear matrix inequalities. Illustrative examples are included to demonstrate the efficiency of the proposed approach.

Lyapunov-based design of resilient observers for a class of nonlinear systems and general performance criteria

A class of continuous-time nonlinear system and measurement equations having incrementally conic nonlinearities and finite energy disturbances is considered. A Lyapunov based resilient observer design approach is presented, which guarantees the satisfaction of a variety of performance criteria ranging from estimation error boundedness to dissipativity of various types. Linear matrix inequalities are used in the feasibility study of the solution. Some simulation studies are included to illustrate and provide support to the effectiveness of the proposed design methodology.