H-infinity Criterion Research Articles

Adapting H-infinity controller for the desired reference tracking of the sphere position in the maglev process

The Maglev process consists in a magnetic field geerated by the modulation of a coil current which yields the sphere levitation. Foucault current is the current transmitted from the coil to a sphere in the Maglev process which yields the undesired sphere vibrations. In this study, an adapting H-infinity controller is introduced as the combination of the adapting and H-infinity strategies for the desired reference tracking of the sphere position in the Maglev process. The adapting strategy is used for the unknown dynamics estimation, and the H-infinity strategy is used for the desired reference tracking. The Lyapunov technique is used to satisfy the error convergence and the H-infinity criterion. Two simulations show the effectiveness of the considered method for the desired reference tracking of the sphere position in the Maglev process.

Design of a Fault Tolerant Sampled-Data Fuzzy Observer With Exponential Time-Varying Gains

This paper deals with the sampled-data fuzzy observer design problem with time-varying gains under the sensor fault consideration. To this end, a nonlinear system with sensor fault is represented by a Takagi-Sugeno fuzzy model with immeasurable premise variables. The sensor fault considered in this paper is assumed to be a time-varying uncertain matrix included in measurements. The observer is designed to consist of gains varying exponentially between two consecutive sampling instants, by which the equilibrium point of the estimation error dynamics is asymptotically exponentially stabilized. In addition, the observer considered in this paper is assumed not to share the same premise variable with a system. Unlike previous studies, this paper proposes a method handling this mismatched premise problem by using an H-infinity criterion. The proposed observer design condition is formulated in terms of linear matrix inequalities, which is relaxed based on a novel fuzzified Lyapunov-Krasovskii functional and a matrix inequality. Finally, two simulation examples are given to validate the effectiveness of the proposed method.

A Decentralized H-Infinity Unscented Kalman Filter for Dynamic State Estimation Against Uncertainties

The widely used traditional Kalman filter-type power system dynamic state estimator is unable to address the unknown and non-Gaussian system process and measurement noise as well as dynamical model uncertainties. To this end, this paper proposes a decentralized H-infinity unscented Kalman filter that leverages the strength of the H-infinity criteria developed in robust control for handling system uncertainties with the advantage of the UKF for addressing strong model nonlinearities. Specifically, the statistical linerization approach is used to derive a linear-like batch-mode regression model similar to the linear Kalman filter. This allows us to resort to the linear H-infinity Kalman filter framework for the development of the proposed H-infinity UKF in the Krein space. An analytical form is also derived to tune the parameter of the H-infinity criterion. Two decoupled models are presented to enable the decentralized implementation of the H-infinity UKF using the local PMU measurements. Extensive simulation results carried out on the IEEE 39-bus system show that the proposed H-infinity UKF is able to bound the influences of various types of measurement and model uncertainties while obtaining accurate state estimates.

Fuzzy‐model‐based sampled‐data chaotic synchronisation under the input constraints consideration

In this study, the authors propose a novel sampled-data fuzzy chaotic synchronisation scheme under the input constraints consideration. The sampled-data chaos synchronisation controller feedbacks the synchronisation error between the state vectors of both the drive chaotic system and the response chaotic system at a constant sampling period. The chaotic synchronisation is achieved by stabilising the synchronisation error dynamics based on the H-infinity criterion. Linear matrix inequality-based sufficient conditions for synchronising two identical chaotic systems are derived based on the newly proposed time-dependent fuzzy Lyapunov–Krasovskii functional. Unlike previous approaches, the modelling error term is fully addressed so as to enhance the synchronisation performance. Finally, the effectiveness of the proposed method is validated through a numerical example.

On the use of H-inf criterion in channel estimation and precoding in massive MIMO systems

In this paper, a channel estimation (CE) and precoding scheme by using H-infinity (H-inf) criterion for mitigation of pilot contamination (PC) in massive multiple input multiple output (MIMO) orthogonal frequency division multiplexing (OFDM) systems is investigated. Firstly, different thresholds in H-inf CE and precoding are considered. Secondly, asymptotic analysis is presented to simplify the H-inf precoding, which shows that the complexity of an order of magnitude is reduced. Thirdly, approximate downlink achievable data rates per user are studied for different CE and precoding schemes, such as H-inf and minimum mean square error (MMSE) CE, MMSE, zero-forcing (ZF) and H-inf precoding. The analysis shows that the proposed scheme can provide dual mitigation to the PC. That is, the H-inf CE mitigates the PC by adjusting its thresholds, and the H-inf precoding is utilized to suppress the PC by considering inter-cell interference. The numerical results show that joint use of H-inf CE and H-inf precoding outperforms existing schemes in terms of mitigation to the PC.

Robust non-quadratic static output feedback controller design for Takagi–Sugeno systems using descriptor redundancy

This work concerns robust static output feedback controller (SOFC) design for uncertain and disturbed Takagi–Sugeno (TS) systems using an H-infinity criterion. The main result is based on a descriptor formulation of the closed-loop dynamics. The proposed approach allows avoiding appearance of crossing terms between the controller’s and the TS system’s input matrices leading to easier LMI formulation than existing studies in the literature. Moreover, the proposed SOFC design conditions do not require any restrictions on the output equation and allow dealing with unmeasurable premise variables. Indeed, taking advantage of the uncertain TS modeling, nonlinearities associated to unmeasurable premises variables can be reported from the nominal part to the uncertainties. To provide LMIs of less conservatism, the results are conducted in the non-quadratic framework. Finally, two numerical examples and a benchmark of a crane system are proposed to illustrate the efficiency of the SOFC design methodology.