scholarly journals Simultaneous Robust Fault and State Estimation for Linear Discrete-Time Uncertain Systems

2017 ◽  
Vol 2017 ◽  
pp. 1-12 ◽  
Author(s):  
Feten Gannouni ◽  
Fayçal Ben Hmida
Keyword(s):  
Convex Optimization ◽  
State Estimation ◽  
Discrete Time ◽  
Upper Bound ◽  
Optimization Problem ◽  
Estimation Error ◽  
Original System ◽  
Error Variance ◽  
Linear Matrix ◽  
Convex Optimization Problem

We consider the problem of robust simultaneous fault and state estimation for linear uncertain discrete-time systems with unknown faults which affect both the state and the observation matrices. Using transformation of the original system, a new robust proportional integral filter (RPIF) having an error variance with an optimized guaranteed upper bound for any allowed uncertainty is proposed to improve robust estimation of unknown time-varying faults and to improve robustness against uncertainties. In this study, the minimization problem of the upper bound of the estimation error variance is formulated as a convex optimization problem subject to linear matrix inequalities (LMI) for all admissible uncertainties. The proportional and the integral gains are optimally chosen by solving the convex optimization problem. Simulation results are given in order to illustrate the performance of the proposed filter, in particular to solve the problem of joint fault and state estimation.

Robust Kalman Filtering for Discrete-Time Time-Varying Systems With Stochastic and Norm-Bounded Uncertainties

2017 ◽  
Vol 140 (3) ◽  
Author(s):  
Mahdi Abolhasani ◽  
Mehdi Rahmani
Keyword(s):  
Discrete Time ◽  
Upper Bound ◽  
Optimization Problem ◽  
Stochastic Systems ◽  
Estimation Error ◽  
Linear Matrix ◽  
Time Varying ◽  
Unknown Parameters ◽  
Bounded Uncertainties ◽  
Norm Bounded Uncertainties

In this paper, a new robust Kalman filter is proposed for discrete-time time-varying linear stochastic systems. The system under consideration is subject to stochastic and norm-bounded uncertainties in all matrices of the system model. In the proposed approach, the filter is first achieved by solving a stochastic min–max optimization problem. Next, we find an upper bound on the estimation error covariance, and then, by using a linear matrix inequality (LMI) optimization problem, unknown parameters of the filter are determined such that the obtained upper bound is minimized. Finally, two numerical examples are given to demonstrate the effectiveness and performance of the proposed filtering approach compared to the existing robust filters.

scholarly journals Analysis of Discrete-Time H2 Guaranteed Cost Performance

2009 ◽  
Author(s):  
Richard Conway ◽  
Roberto Horowitz
Keyword(s):  
Discrete Time ◽  
Upper Bound ◽  
Optimization Problem ◽  
Parametric Uncertainty ◽  
Linear Matrix ◽  
Matrix Inequality ◽  
Cost Performance ◽  
Lti System ◽  
Dynamic Uncertainty ◽  
Guaranteed Cost

This paper presents a methodology for analyzing the H2 guaranteed cost performance of a discrete-time LTI system with unstructured dynamic uncertainty. Using the methods of guaranteed cost control, an upper bound on H2 guaranteed cost performance over unstructured parametric uncertainty is formulated in terms of feasibility of a linear matrix inequality. It is then shown that the feasibility of this inequality also guarantees the same level of performance also over unstructured dynamic uncertainty. This is then used to formulate the problem of finding the best upper bound on H2 guaranteed cost performance over unstructured causal dynamic uncertainty as a semi-definite program. Finally, it is shown that this optimization problem can be solved efficiently and accurately using discrete algebraic Riccati equations.

Exponential state estimation for discrete-time switched genetic regulatory networks with random delays

2014 ◽  
Vol 92 (9) ◽  
pp. 976-986 ◽  
Author(s):  
K. Mathiyalagan ◽  
R. Sakthivel ◽  
Hongye Su
Keyword(s):  
State Estimation ◽  
Discrete Time ◽  
Time Delays ◽  
Regulatory Networks ◽  
Estimation Error ◽  
Average Dwell Time ◽  
Genetic Regulatory Networks ◽  
Linear Matrix ◽  
State Estimator ◽  
Exponentially Stable

This paper is concerned with the problem of state estimator design for a class of discrete-time switched genetic regulatory networks (GRNs) with random time delays. The involved time delays are assumed to be randomly time-varying and are modeled by introducing Bernoulli distributed sequences. By using a piecewise Lyapunov–Krasovskii functional together with the linear matrix inequality (LMI) approach, we design a delay-distributed dependent state estimator such that the estimation error system is globally exponentially stable. Further, a class of switching signals specified by the average dwell time is identified to guarantee the exponential state estimation. All the conditions are established in the framework of LMIs, which can easily be solved by using standard numerical software. If a set of LMIs are feasible, then the desired state estimator can be obtained. Finally, a numerical example with simulation result is provided for the GRN model to illustrate the applicability and usefulness of the obtained theory.

scholarly journals Fault Detection for Discrete-Time Nonlinear Impulsive Switched Systems

2015 ◽  
Vol 2015 ◽  
pp. 1-12
Author(s):  
Qingyu Su ◽  
Xiaolong Jia ◽  
Zhengfan Song
Keyword(s):  
Fault Detection ◽  
Discrete Time ◽  
Switched Systems ◽  
Optimization Problem ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Robust Performance ◽  
Detection Problem ◽  
Convex Optimization Problem ◽  
Impulsive Switched Systems

This paper investigates the fault detection problem for discrete-time nonlinear impulsive switched systems. Attention is focused on designing the fault detection filters to guarantee the robust performance and the detection performance. Based on these performances, sufficient conditions for the existence of filters are given in the framework of linear matrix inequality; furthermore, the filter gains are characterized by a convex optimization problem. The presented technique is validated by an example. Simulation results indicate that the proposed method can effectively detect the faults.

scholarly journals State Estimation for Discrete-Time Fuzzy Cellular Neural Networks with Mixed Time Delays

2014 ◽  
Vol 2014 ◽  
pp. 1-13 ◽  
Author(s):  
Lijie Geng ◽  
Haiying Li ◽  
Bingchen Zhao ◽  
Guang Su
Keyword(s):  
Neural Networks ◽  
State Estimation ◽  
Discrete Time ◽  
Time Delays ◽  
Estimation Error ◽  
Sufficient Conditions ◽  
Cellular Neural Networks ◽  
Linear Matrix ◽  
Fuzzy Cellular Neural Networks ◽  
Mixed Time Delays

This paper is concerned with the exponential state estimation problem for a class of discrete-time fuzzy cellular neural networks with mixed time delays. The main purpose is to estimate the neuron states through available output measurements such that the dynamics of the estimation error is globally exponentially stable. By constructing a novel Lyapunov-Krasovskii functional which contains a triple summation term, some sufficient conditions are derived to guarantee the existence of the state estimator. The linear matrix inequality approach is employed for the first time to deal with the fuzzy cellular neural networks in the discrete-time case. Compared with the present conditions in the form ofM-matrix, the results obtained in this paper are less conservative and can be checked readily by the MATLAB toolbox. Finally, some numerical examples are given to demonstrate the effectiveness of the proposed results.

Robust Observer Design for Systems With Deterministic and Stochastic Uncertainties

2004 ◽  
Author(s):  
Jongchul Jung ◽  
Tae Hee Lee ◽  
Jeffrey L. Stein ◽  
Kunsoo Huh
Keyword(s):  
Optimization Problem ◽  
Design Method ◽  
Estimation Error ◽  
Error Variance ◽  
Error Modeling ◽  
Observer Design ◽  
Linear Matrix ◽  
Estimation Performance ◽  
L2 Norm ◽  
Stochastic Uncertainties

An observer design method for stochastic and deterministic robustness is developed so that the observer is less sensitive to uncertainties in transient and in steady-state observer performance. The uncertainties include not only deterministic factors such as unknown initial estimation error, round-off error, modeling error and sensing bias, but also stochastic factors such as disturbance and sensor noise. From a stochastic perspective, a small value in estimation error variance represents robustness to the stochastic uncertainties. It is shown that the upper bound of the error variance can be minimized by reducing the observer gain and by increasing the decay rate of the observer. From a deterministic perspective, a small value in the L2 norm condition number of the observer eigenvector matrix guarantees robust estimation performance to the deterministic uncertainties. An optimization problem constrained by a linear matrix inequality condition is formulated for both the deterministic and the stochastic robustness. The observer gain can be selected as a trade-off solution and the estimation performance to stochastic and deterministic uncertainties is demonstrated on simulation examples.

scholarly journals $H_\infty$ State Estimation of Delayed Recurrent Memristive Neural Networks: continuous-time case and discrete-time case

2021 ◽  
Author(s):  
fangyuan Ma ◽  
Xingbao Gao
Keyword(s):  
Neural Networks ◽  
State Estimation ◽  
Discrete Time ◽  
Continuous Time ◽  
Estimation Error ◽  
Linear Matrix ◽  
Memristive Neural Networks ◽  
Connection Weight ◽  
Discrete Time Case ◽  
The Given

This paper investigates the problem of $H_\infty$ state estimation of delayed recurrent memristive neural networks (DRMNNs) with both continuous-time and discrete-time cases. By utilizing Lyapunov-Krasovskii functional (LKF) and linear matrix inequalities (LMIs), two criterions are provided to guarantee the asymptotically stable of the estimation error systems with a $H_\infty$ performance. The connection weight parameters of DRMNNs are dealed with logical switching signals, which greatly reduces the computational complexity. The given conditions can be easily checked by solving LMIs, the obtained theoretical results are supported demonstrated by two numerical examples.

Observer-Based Stabilization of Linear Discrete Time-Varying Delay Systems

2021 ◽  
Author(s):  
Venkatesh Modala ◽  
Sourav Patra ◽  
Goshaidas Ray
Keyword(s):  
Discrete Time ◽  
Upper Bound ◽  
Delay Systems ◽  
Linear Matrix ◽  
Time Varying ◽  
Stabilizing Controller ◽  
Time Varying Delay ◽  
Convex Inequality ◽  
Summation Inequality ◽  
Delay Dependent

Abstract This paper presents the design of an observer-based stabilizing controller for linear discrete-time systems subject to interval time-varying state-delay. In this work, the problem has been formulated in convex optimization framework by constructing a new Lyapunov-Krasovskii (LK) functional to derive a delay-dependent stabilization criteria. The summation inequality and the extended reciprocally convex inequality are exploited to obtain a less conservative delay upper bound in linear matrix inequality (LMI) framework. The derived stability conditions are delay-dependent and thus, ensure global asymptotic stability in presence of any time delay less than the obtained delay upper bound. Numerical examples are included to demonstrate the usefulness of the developed results.

scholarly journals Heliostat Field Layout Optimization with Evolutionary Algorithms

10.29007/7p6t ◽  
2018 ◽  
Author(s):  
Pascal Richter ◽  
David Laukamp ◽  
Levin Gerdes ◽  
Martin Frank ◽  
Erika Ábrahám
Keyword(s):  
Power Plant ◽  
Convex Optimization ◽  
Evolutionary Algorithms ◽  
Convergence Rate ◽  
Evolutionary Algorithm ◽  
Computer Science ◽  
Energy Supply ◽  
Optimization Problem ◽  
Convex Optimization Problem ◽  
New Genotype

The exploitation of solar power for energy supply is of increasing importance. While technical development mainly takes place in the engineering disciplines, computer science offers adequate techniques for optimization. This work addresses the problem of finding an optimal heliostat field arrangement for a solar tower power plant.We propose a solution to this global, non-convex optimization problem by using an evolutionary algorithm. We show that the convergence rate of a conventional evolutionary algorithm is too slow, such that modifications of the recombination and mutation need to be tailored to the problem. This is achieved with a new genotype representation of the individuals.Experimental results show the applicability of our approach.

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