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

Improved Distributed Estimation Method for Environmental\ud time-variant Physical variables in Static Sensor Networks

In this paper, an improved distributed estimation scheme for static sensor networks is developed. The scheme is developed for environmental time-variant physical variables. The main contribution of this work is that the algorithm in [1]-[3] has been extended, and a filter has been designed with weights, such that the variance of the estimation errors is minimized, thereby improving the filter design considerably\ud and characterizing the performance limit of the filter, and thereby tracking a time-varying signal. Moreover, certain parameter optimization is alleviated with the application of a particular finite impulse response (FIR) filter. Simulation results are showing the effectiveness of the developed estimation algorithm

IIR Digital Filter Design Using Convex Optimization

Digital filters play an important role in digital signal processing and communication. From the 1960s, a considerable number of design algorithms have been proposed for finite-duration impulse response (FIR) digital filters and infinite-duration impulse response (IIR) digital filters. Compared with FIR digital filters, IIR digital filters have better approximation capabilities under the same specifications. Nevertheless, due to the presence of the denominator in its rational transfer function, an IIR filter design problem cannot be easily formulated as an equivalent convex optimization problem. Furthermore, for stability, all the poles of an IIR digital filter must be constrained within a stability domain, which, however, is generally nonconvex. Therefore, in practical designs, optimal solutions cannot be definitely attained. In this dissertation, we focus on IIR filter design problems under the weighted least-squares (WLS) and minimax criteria. Convex optimization will be utilized as the major mathematical tool to formulate and analyze such IIR filter design problems. Since the original IIR filter design problem is essentially nonconvex, some approximation and convex relaxation techniques have to be deployed to achieve convex formulations of such design problems. We first consider the stability issue. A sufficient and necessary stability condition is derived from the argument principle. Although the original stability condition is in a nonconvex form, it can be appropriately approximated by a quadratic constraint and readily combined with sequential WLS design procedures. Based on the sufficient and necessary stability condition, this approximate stability constraint can achieve an improved description of the nonconvex stability domain. We also address the nonconvexity issue of minimax design of IIR digital filters. Convex relaxation techniques are applied to obtain relaxed design problems, which are formulated, respectively, as second-order cone programming (SOCP) and semidefinite programming (SDP) problems. By solving these relaxed design problems, we can estimate lower bounds of minimum approximation errors, which are useful in subsequent design procedures to achieve real minimax solutions. Since the relaxed design problems are independent of local information, compared with many prevalent design methods which employ local search, the proposed design methods using the convex relaxation techniques have an increased chance to obtain an optimal design

Design of optimal band-stop FIR filter using L1-norm based RCGA

AbstractIn this paper, an optimal design of linear phase digital finite impulse response (FIR) band stop (BS) filter using the L1-norm based real-coded genetic algorithm (L1-RCGA) is presented. Although RCGA has proved its ability to overcome the drawbacks associated with conventional gradient-based optimization methods of filter design, it is applied here with a novel fitness function based on the L1-norm. This leads to a global optimal solution along with the improvement in filter design with same specifications. The designed filter pursues a better response in terms of flat passband, high stopband attenuation and fast convergence. The simulation results justify that the proposed FIR BS filter using L1-RCGA outperforms the existing optimization techniques, the L1-method and particle swarm optimization (PSO) and the conventional methods such as least-squares (LS) approach, Kaiser window method and the Parks McClellan (PM) algorithm. A detailed analysis is performed to evaluate the performance of the designed filters

Discrete-time optimal preview control

There are many situations in which one can preview future reference signals, or future disturbances. Optimal Preview Control is concerned with designing controllers which use this preview to improve closed-loop performance. In this thesis a general preview control problem is presented which includes previewable disturbances, dynamic weighting functions, output feedback and nonpreviewable disturbances. It is then shown how a variety of problems may be cast as special cases of this general problem; of particular interest is the robust preview tracking problem and the problem of disturbance rejection with uncertainty in the previewed signal. . (', The general preview problem is solved in both the Fh and Beo settings. The H2 solution is a relatively straightforward extension ofpreviously known results, however, our contribution is to provide a single framework that may be used as a reference work when tackling a variety of preview problems. We also provide some new analysis concerning the maximum possible reduction in closed-loop H2 norm which accrues from the addition of preview action. / Name of candidate: Title of thesis: I DESCRIPTION OF THESIS Andrew Hazell Discrete-Time Optimal Preview Control The solution to the Hoo problem involves a completely new approach to Hoo preview control, in which the structure of the associated Riccati equation is exploited in order to find an efficient algorithm for computing the optimal controller. The problem tackled here is also more generic than those previously appearing in the literature. The above theory finds obvious applications in the design of controllers for autonomous vehicles, however, a particular class of nonlinearities found in typical vehicle models presents additional problems. The final chapters are concerned with a generic framework for implementing vehicle preview controllers, and also a'case study on preview control of a bicycle.Imperial Users onl

Structure-Preserving Model Reduction of Physical Network Systems

This paper considers physical network systems where the energy storage is naturally associated to the nodes of the graph, while the edges of the graph correspond to static couplings. The first sections deal with the linear case, covering examples such as mass-damper and hydraulic systems, which have a structure that is similar to symmetric consensus dynamics. The last section is concerned with a specific class of nonlinear physical network systems; namely detailed-balanced chemical reaction networks governed by mass action kinetics. In both cases, linear and nonlinear, the structure of the dynamics is similar, and is based on a weighted Laplacian matrix, together with an energy function capturing the energy storage at the nodes. We discuss two methods for structure-preserving model reduction. The first one is clustering; aggregating the nodes of the underlying graph to obtain a reduced graph. The second approach is based on neglecting the energy storage at some of the nodes, and subsequently eliminating those nodes (called Kron reduction).</p

Digital Filter Design Using Improved Artificial Bee Colony Algorithms

Digital filters are often used in digital signal processing applications. The design objective of a digital filter is to find the optimal set of filter coefficients, which satisfies the desired specifications of magnitude and group delay responses. Evolutionary algorithms are population-based meta-heuristic algorithms inspired by the biological behaviors of species. Compared to gradient-based optimization algorithms such as steepest descent and Newton’s like methods, these bio-inspired algorithms have the advantages of not getting stuck at local optima and being independent of the starting point in the solution space. The limitations of evolutionary algorithms include the presence of control parameters, problem specific tuning procedure, premature convergence and slower convergence rate. The artificial bee colony (ABC) algorithm is a swarm-based search meta-heuristic algorithm inspired by the foraging behaviors of honey bee colonies, with the benefit of a relatively fewer control parameters. In its original form, the ABC algorithm has certain limitations such as low convergence rate, and insufficient balance between exploration and exploitation in the search equations. In this dissertation, an ABC-AMR algorithm is proposed by incorporating an adaptive modification rate (AMR) into the original ABC algorithm to increase convergence rate by adjusting the balance between exploration and exploitation in the search equations through an adaptive determination of the number of parameters to be updated in every iteration. A constrained ABC-AMR algorithm is also developed for solving constrained optimization problems.There are many real-world problems requiring simultaneous optimizations of more than one conflicting objectives. Multiobjective (MO) optimization produces a set of feasible solutions called the Pareto front instead of a single optimum solution. For multiobjective optimization, if a decision maker’s preferences can be incorporated during the optimization process, the search process can be confined to the region of interest instead of searching the entire region. In this dissertation, two algorithms are developed for such incorporation. The first one is a reference-point-based MOABC algorithm in which a decision maker’s preferences are included in the optimization process as the reference point. The second one is a physical-programming-based MOABC algorithm in which physical programming is used for setting the region of interest of a decision maker. In this dissertation, the four developed algorithms are applied to solve digital filter design problems. The ABC-AMR algorithm is used to design Types 3 and 4 linear phase FIR differentiators, and the results are compared to those obtained by the original ABC algorithm, three improved ABC algorithms, and the Parks-McClellan algorithm. The constrained ABC-AMR algorithm is applied to the design of sparse Type 1 linear phase FIR filters of filter orders 60, 70 and 80, and the results are compared to three state-of-the-art design methods. The reference-point-based multiobjective ABC algorithm is used to design of asymmetric lowpass, highpass, bandpass and bandstop FIR filters, and the results are compared to those obtained by the preference-based multiobjective differential evolution algorithm. The physical-programming-based multiobjective ABC algorithm is used to design IIR lowpass, highpass and bandpass filters, and the results are compared to three state-of-the-art design methods. Based on the obtained design results, the four design algorithms are shown to be competitive as compared to the state-of-the-art design methods

Digital Filters and Signal Processing

Digital filters, together with signal processing, are being employed in the new technologies and information systems, and are implemented in different areas and applications. Digital filters and signal processing are used with no costs and they can be adapted to different cases with great flexibility and reliability. This book presents advanced developments in digital filters and signal process methods covering different cases studies. They present the main essence of the subject, with the principal approaches to the most recent mathematical models that are being employed worldwide