Solving of the Modified Filter Algebraic Riccati Equation for H-infinity fault detection filtering

2017 ◽  
Vol 9 (1) ◽  
pp. 57-77
Author(s):  
Zsolt Horváth ◽  
András Edelmayer
Keyword(s):  
Fault Detection ◽  
Riccati Equation ◽  
Optimization Problem ◽  
Computational Cost ◽  
Optimal Solution ◽  
Algebraic Riccati Equation ◽  
Linear Matrix ◽  
Optimization Approach ◽  
Linear Quadratic ◽  
Quadratic Optimization Problem

AbstractThe objective of this paper is solving of the Modified Filter Algebraic Riccati Equation (MFARE) for calculating of the filter gain. The results are used for model-based fault detection filtering of faults in the air path of diesel engines. The Hinfinity optimization approach requires the solution of a linear-quadratic optimization problem that leads to the solution of MFARE. In our paper two basic concepts for solving MFARE are examined, namely the analytically implemented gamma-iteration and casting the problem as a convex optimization problem based on Linear Matrix Inequalities (LMIs).The algorithms are implemented in MATLAB. Each algorithm has to ensure the condition for a global convergence and also has to deliver an optimal solution. Not at least, the computational cost has to be as small as possible.

scholarly journals A method for estimating Hill function-based dynamic models of gene regulatory networks

2018 ◽  
Vol 5 (2) ◽  
pp. 171226 ◽  
Author(s):  
Faizan Ehsan Elahi ◽  
Ammar Hasan
Keyword(s):  
Gene Regulatory Networks ◽  
Regulatory Networks ◽  
Optimization Problem ◽  
Dynamic Models ◽  
Initial Conditions ◽  
Computational Cost ◽  
Optimization Approach ◽  
Continuous Models ◽  
Gene Regulatory ◽  
The Cost

Gene regulatory networks (GRNs) are quite large and complex. To better understand and analyse GRNs, mathematical models are being employed. Different types of models, such as logical, continuous and stochastic models, can be used to describe GRNs. In this paper, we present a new approach to identify continuous models, because they are more suitable for large number of genes and quantitative analysis. One of the most promising techniques for identifying continuous models of GRNs is based on Hill functions and the generalized profiling method (GPM). The advantage of this approach is low computational cost and insensitivity to initial conditions. In the GPM, a constrained nonlinear optimization problem has to be solved that is usually underdetermined. In this paper, we propose a new optimization approach in which we reformulate the optimization problem such that constraints are embedded implicitly in the cost function. Moreover, we propose to split the unknown parameter in two sets based on the structure of Hill functions. These two sets are estimated separately to resolve the issue of the underdetermined problem. As a case study, we apply the proposed technique on the SOS response in Escherichia coli and compare the results with the existing literature.

scholarly journals An Efficient Hybrid Optimization Approach Using Adaptive Elitist Differential Evolution and Spherical Quadratic Steepest Descent and Its Application for Clustering

2019 ◽  
Vol 2019 ◽  
pp. 1-15
Author(s):  
T. Nguyen-Trang ◽  
T. Nguyen-Thoi ◽  
T. Truong-Khac ◽  
A. T. Pham-Chau ◽  
HungLinh Ao
Keyword(s):  
Differential Evolution ◽  
Clustering Analysis ◽  
Hybrid Approach ◽  
Computational Cost ◽  
Internal Validity ◽  
Optimal Solution ◽  
Population Based ◽  
Steepest Descent ◽  
Optimization Approach ◽  
Global Optimal

In this paper, a hybrid approach that combines a population-based method, adaptive elitist differential evolution (aeDE), with a powerful gradient-based method, spherical quadratic steepest descent (SQSD), is proposed and then applied for clustering analysis. This combination not only helps inherit the advantages of both the aeDE and SQSD but also helps reduce computational cost significantly. First, based on the aeDE’s global explorative manner in the initial steps, the proposed approach can quickly reach to a region that contains the global optimal value. Next, based on the SQSD’s locally effective exploitative manner in the later steps, the proposed approach can find the global optimal solution rapidly and accurately and hence helps reduce the computational cost. The proposed method is first tested over 32 benchmark functions to verify its robustness and effectiveness. Then, it is applied for clustering analysis which is one of the problems of interest in statistics, machine learning, and data mining. In this application, the proposed method is utilized to find the positions of the cluster centers, in which the internal validity measure is optimized. For both the benchmark functions and clustering problem, the numerical results show that the hybrid approach for aeDE (HaeDE) outperforms others in both accuracy and computational cost.

scholarly journals Linear Quadratic Optimal Control Design: A Novel Approach Based on Krotov Conditions

2019 ◽  
Vol 2019 ◽  
pp. 1-17
Author(s):  
Avinash Kumar ◽  
Tushar Jain
Keyword(s):  
Optimal Control ◽  
Cost Function ◽  
Riccati Equation ◽  
Nonconvex Optimization ◽  
Optimization Problem ◽  
A Priori ◽  
Control Law ◽  
Linear Quadratic ◽  
Linear Quadratic Optimal Control ◽  
Quadratic Optimal Control

This paper revisits the problem of synthesizing the optimal control law for linear systems with a quadratic cost. For this problem, traditionally, the state feedback gain matrix of the optimal controller is computed by solving the Riccati equation, which is primarily obtained using calculus of variations- (CoV-) based and Hamilton–Jacobi–Bellman (HJB) equation-based approaches. To obtain the Riccati equation, these approaches require some assumptions in the solution procedure; that is, the former approach requires the notion of costates and then their relationship with states is exploited to obtain the closed-form expression of the optimal control law, while the latter requires a priori knowledge regarding the optimal cost function. In this paper, we propose a novel method for computing linear quadratic optimal control laws by using the global optimal control framework introduced by V. F. Krotov. As shall be illustrated in this article, this framework does not require the notion of costates and any a priori information regarding the optimal cost function. Nevertheless, using this framework, the optimal control problem gets translated to a nonconvex optimization problem. The novelty of the proposed method lies in transforming this nonconvex optimization problem into a convex problem. The convexity imposition results in a linear matrix inequality (LMI), whose analysis is reported in this work. Furthermore, this LMI reduces to the Riccati equation upon imposing optimality requirements. The insights along with the future directions of the work are presented and gathered at appropriate locations in this article. Finally, numerical results are provided to demonstrate the proposed methodology.

scholarly journals Non-Convex Feasibility Robust Optimization Via Scenario Generation and Local Refinement

2019 ◽  
Vol 142 (5) ◽  
Author(s):  
Eliot Rudnick-Cohen ◽  
Jeffrey W. Herrmann ◽  
Shapour Azarm
Keyword(s):  
Robust Optimization ◽  
Optimization Problems ◽  
Computational Cost ◽  
Optimal Solution ◽  
Optimization Techniques ◽  
Scenario Generation ◽  
Test Problems ◽  
Optimization Approach ◽  
Uncertain Parameters ◽  
Worst Case

Abstract Feasibility robust optimization techniques solve optimization problems with uncertain parameters that appear only in their constraint functions. Solving such problems requires finding an optimal solution that is feasible for all realizations of the uncertain parameters. This paper presents a new feasibility robust optimization approach involving uncertain parameters defined on continuous domains. The proposed approach is based on an integration of two techniques: (i) a sampling-based scenario generation scheme and (ii) a local robust optimization approach. An analysis of the computational cost of this integrated approach is performed to provide worst-case bounds on its computational cost. The proposed approach is applied to several non-convex engineering test problems and compared against two existing robust optimization approaches. The results show that the proposed approach can efficiently find a robust optimal solution across the test problems, even when existing methods for non-convex robust optimization are unable to find a robust optimal solution. A scalable test problem is solved by the approach, demonstrating that its computational cost scales with problem size as predicted by an analysis of the worst-case computational cost bounds.

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