Mixed H2/H∞ filtering for uncertain systems with regional pole assignment

Copyright [2005] IEEE. This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of Brunel University's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to [email protected]. By choosing to view this document, you agree to all provisions of the copyright laws protecting it.The mixed H2/H∞ filtering problem for uncertain linear continuous-time systems with regional pole assignment is considered. The purpose of the problem is to design an uncertainty-independent filter such that, for all admissible parameter uncertainties, the following filtering requirements are simultaneously satisfied: 1) the filtering process is asymptotically stable; 2) the poles of the filtering matrix are located inside a prescribed region that compasses the vertical strips, horizontal strips, disks, or conic sectors; 3) both the H2 norm and the H∞ norm on the respective transfer functions are not more than the specified upper bound constraints. We establish a general framework to solve the addressed multiobjective filtering problem completely. In particular, we derive necessary and sufficient conditions for the solvability of the problem in terms of a set of feasible linear matrix inequalities (LMIs). An illustrative example is given to illustrate the design procedures and performances of the proposed method

On designing H∞ filters with circular pole and error variance constraints

Copyright [2003] IEEE. This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of Brunel University's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to [email protected]. By choosing to view this document, you agree to all provisions of the copyright laws protecting it.In this paper, we deal with the problem of designing a H∞ filter for discrete-time systems subject to error variance and circular pole constraints. Specifically, we aim to design a filter such that the H∞ norm of the filtering error-transfer function is not less than a given upper bound, while the poles of the filtering matrix are assigned within a prespecified circular region, and the steady-state error variance for each state is not more than the individual prespecified value. The filter design problem is formulated as an auxiliary matrix assignment problem. Both the existence condition and the explicit expression of the desired filters are then derived by using an algebraic matrix inequality approach. The proposed design algorithm is illustrated by a numerical example

Mixed H2/H∞ filtering for uncertain systems with regional pole assignment

The mixed H2/H∞ filtering problem for uncertain linear continuous-time systems with regional pole assignment is considered. The purpose of the problem is to design an uncertainty-independent filter such that, for all admissible parameter uncertainties, the following filtering requirements are simultaneously satisfied: 1) the filtering process is asymptotically stable; 2) the poles of the filtering matrix are located inside a prescribed region that compasses the vertical strips, horizontal strips, disks, or conic sectors; 3) both the H2 norm and the norm on the respective transfer functions are not more than the specified upper bound constraints. We establish a general framework to solve the addressed multiobjective filtering problem completely. In particular, we derive necessary and sufficient conditions for the solvability of the problem in terms of a set of feasible linear matrix inequalities (LMIs). An illustrative example is given to illustrate the design procedures and performances of the proposed method. © 2005 IEEE.published_or_final_versio

State-Feedback Output Tracking Via a Novel Optimal-Sliding Mode Control

This chapter describes a new framework for the design of a novel suboptimal state-feedback-sliding mode control for output tracking while H2/H∞ performances of the closed-loop system are under control. In contrast to most of the current sliding surface design schemes, in this new framework, the level of control effort required to maintain sliding is penalized. The proposed method for the design of optimal-sliding mode control is carried out in two stages. In the first stage, a state-feedback gain is derived using a linear matrix inequality (LMI)-based scheme that can assign a number of the closed-loop eigenvalues to a known value while satisfying performance specifications and ensuring that all the closed-loop poles are located in a preselected subregion. The sliding function matrix related to the particular state feedback derived in the first stage is obtained in the second stage by using one of the two different methods developed for this goal. We present a numerical example to demonstrate the remarkable performance of the proposed scheme

System Identification and LMI Based Robust PID Control of a Two-Link Flexible Manipulator

This paper presents investigations into the development of a linear matrix inequalities (LMI) based robust PID control of a nonlinear Two-Link Flexible Manipulator (TLFM) incorporating payload. A set of linear models of a TLFM is obtained by using system identification method in which the linear model represents the operating ranges of the dynamic system. Thus, the LMI constraints permit to robustly guarantee a certain perturbation rejection level and a region of pole location.  To study the effectiveness of the controller, initially a PID control is developed for TLFM with varying payloads. The performances of the controllers are assessed in terms of the input tracking controller capability of the system as compared to the response with PID control. Moreover, the robustness of the LMI based robust PID control schemes is discussed. Finally, a comparative assessment of the control strategies is presented

An extension algorithm of regional eigenvalue assignment controller design for nonlinear systems

This paper provides a new method to nonlinear control theory, which is developed from the eigenvalue assignment method. The main purpose of this method is to locate the pointwise eigenvalues of the linear-like structure built by freezing the nonlinear systems at a given time instant in a desired disk region. Since the control requirements for the transient response characteristics are the major constraints on the selection of the disk centre and radius, two different update algorithms are also developed to reshape the disk region by changing the disk centre and radius at each time step. The effectiveness of the proposed methods is tested in both simulations and experiments. A validated three-DOF laboratory helicopter is used for experiments