Pareto optimal strategy for linear stochastic systems with H∞ constraint in finite horizon

Jiang, Xiushan; Tian, Senping; Zhang, Tianliang; Zhang, Weihai

doi:10.1016/j.ins.2019.10.005

Cited by 22 publications

(16 citation statements)

References 37 publications

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“…In rules (1)-( 5), the eUKF equals the previous estimation error of the UKF. The eUH∞F represents the previous estimation error of the UH∞F filter and σ is indicative of the STD of the previous state estimation of the two UKF and UH∞F filters illustrated in Equation (5). Equally, the same rules are considered to estimate the magnitude in which the magnitude estimation error is deployed instead of the state estimation error: σ ¼ ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi…”

Section: Fuzzy Logic Systemmentioning

confidence: 99%

“…Therefore, Simon et al [4] presented two different methods to combine two filters, initially, using the steady gain linear combination of two filters and then extracting the gain of the hybrid filter from a Riccati equation [4]. Among other methods, optimization methods were used to combine the two objective functions of these filters [5][6][7]. Employing the linear combination of gains, the prior state estimation, and the magnitude of the two UKF and UH∞F filters, Tehrani et al [8] presented a dual filter that exhibited higher robustness relative to the UKF and UH∞F filters in both two Gaussian and non-Gaussian noise states as well as optimization ability.…”

Section: Introductionmentioning

confidence: 99%

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A new adaptive fuzzy hybrid unscented Kalman/H‐infinity filter for state estimating dynamical systems

Masoumnezhad

Tehrani

Akoushideh

et al. 2021

IET Signal Processing

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State estimation and dynamical model identification from observed data has been an attractive research area with a wide range of applications such as communication, navigation, radar target tracking, and system control. A method of Adaptive Fuzzy Unscented Kalman/H∞ Filter (AFUKH∞) to estimate non-linear systems is presented using a combination of the Unscented Kalman Filter (UKF) and Unscented H∞ Filter (UH∞F). The proposed filter does not need linearisation and is based on a combination of gain, a priori state estimation, and a priori measurement estimation in each time step. The performance of the filter is adaptively adjustable. Thus, its efficiency is better than the other two filters. Two fuzzy logic systems are proposed that determine the weight of the UKF and UH∞F filters at each step. These two fuzzy systems are designed to be independent of the dynamics of the system (problem). The proposed filter is referred to as a hybrid AFUKH∞-II. In the proposed method, the state of the feedback is used as input that improves the efficiency of the filter. The challenge of reentry vehicle tracking and the state estimation of a magnetic motor as two non-linear high-order problems are used as benchmarks, and the results are compared with the UKF, UH∞F, and AFUKH∞ filters. The experiments show that an estimation of the proposed hybrid filter (AFUKH∞-II) is improved against state-of-the-art filters. Also, estimation error and variance values of the proposed filter in the presence of Gaussian noise is decreased by 270% and 370%, respectively, compared with the AFUKH∞ filter. How to cite this article: Masoumnezhad M, Tehrani M, Akoushideh A, Narimanzadeh N. A new adaptive fuzzy hybrid unscented Kalman/H-infinity filter for state estimating dynamical systems.

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Section: Fuzzy Logic Systemmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A new adaptive fuzzy hybrid unscented Kalman/H‐infinity filter for state estimating dynamical systems

Masoumnezhad

Tehrani

Akoushideh

et al. 2021

IET Signal Processing

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“…Ahmed et al [18] studied the Pareto optimal control with external disturbances, and gave the form of Pareto optimal control under H ∞ constraint for continuous-time stochastic systems by means of linear matrix inequalities. Jiang et al [19] introduced the generalized differential Riccati equations to obtain Pareto solutions under H ∞ constraint for continuous-time stochastic systems. It should be noted that the above two articles are about continuous-time rather than discrete-time.…”

Section: Introductionmentioning

confidence: 99%

Pareto Optimal Strategy under H∞ Constraint for Discrete-Time Stochastic Systems

et al. 2022

Self Cite

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This paper investigates the Pareto optimal strategy of discrete-time stochastic systems under H∞ constraint, in which the weighting matrices of the weighted sum cost function can be indefinite. Combining the H∞ control theory with the indefinite LQ control theory, the generalized difference Riccati equations (GDREs) are obtained. By means of the solution of the GDREs, the Pareto optimal strategy with H∞ constraint is derived, and the necessary and sufficient conditions for the existence of the strategy are presented. Then the Pareto optimal solution under the worst-case disturbance is solved. Finally, the efficiency of the obtained results is illustrated by a numerical example.

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“…Finite-time stability focuses on the system state behavior only in a specified finite-time horizon instead of the whole time interval, which differentiates the finite-time stability from the classical Lyapunov stability studied in [12], [36], [37] for discrete stochastic stability and [14], [18] for stochastic stability of continuous Itô systems. In some practical applications, the considered operating duration of the controlled system is often limited [11], [20], so, in some cases, the transient characteristics of systems may be more important than the state convergence in an infinite-time horizon. As it is wellknown that finite-time stability contains two kinds of different concepts: one is defined as in [1]- [3], [16], [24], [30], [35], which is in fact finite-time bounded in some sense, while the other one is defined as in [5], [8], [20], [25], [28], [31], [32], [34], where finite-time stability satisfies both "stability in Lyapunov sense" and "finite-time attractiveness".…”

Section: Introductionmentioning

confidence: 99%

Non-fragile Finite-time Stabilization for Discrete Mean-field Stochastic Systems

Zhang¹,

Deng²,

Shi³

2022

Preprint

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In this paper, the problem of non-fragile finitetime stabilization for linear discrete mean-field stochastic systems is studied. The uncertain characteristics in control parameters are assumed to be random satisfying the Bernoulli distribution. A new approach called the "state transition matrix method" is introduced and some necessary and sufficient conditions are derived to solve the underlying stabilization problem. The Lyapunov theorem based on the state transition matrix also makes a contribution to the discrete finite-time control theory. One practical example is provided to validate the effectiveness of the newly proposed control strategy.

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Pareto optimal strategy for linear stochastic systems with H∞ constraint in finite horizon

Cited by 22 publications

References 37 publications

A new adaptive fuzzy hybrid unscented Kalman/H‐infinity filter for state estimating dynamical systems

A new adaptive fuzzy hybrid unscented Kalman/H‐infinity filter for state estimating dynamical systems

Pareto Optimal Strategy under H∞ Constraint for Discrete-Time Stochastic Systems

Non-fragile Finite-time Stabilization for Discrete Mean-field Stochastic Systems

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