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The purpose of this paper is to propose an interpolation-based projection framework for model reduction of quadratic-bilinear systems. The approach constructs projection matrices from the bilinear part of the original quadratic-bilinear descriptor system and uses these matrices to project the original system.

The projection matrices are constructed by viewing the bilinear system as a linear parametric system, where the input associated with the bilinear part is treated as a parameter. The advantage of this approach is that the projection matrices can be constructed reliably by using an a posteriori error bound for linear parametric systems. The use of the error bound allows us to select a good choice of interpolation points and parameter samples for the construction of the projection matrices by using a greedy-type framework.

The results are compared with the standard quadratic-bilinear projection methods and it is observed that the approximations through the proposed method are comparable to the standard method but at a lower computational cost (offline time).

In addition to the proposed model order reduction framework, the authors extend the one-sided moment matching parametric model order reduction (PMOR) method to a two-sided method that doubles the number of moments matched in the PMOR method.

The paper is aimed at the development of novel model reduction techniques for nonlinear systems.

The analysis is based on the bilinear and polynomial representation of nonlinear systems and the exact solution of the bilinear system in terms of Volterra series. Two sets of Krylov subspaces are identified which capture the most essential part of the input‐output behaviour of the system.

The paper proposes two novel model‐reduction strategies for nonlinear systems. The first involves the development, in a novel manner compared with previous approaches, of a reduced‐order model from a bilinear representation of the system, while the second involves reducing a polynomial approximation using Krylov subspaces derived from a related bilinear representation. Both techniques are shown to be effective through the evidence of a standard test example.

The proposed methodology is applicable to so‐called weakly nonlinear systems, where both the bilinear and polynomial representations are valid.

The suggested methods lead to an improvement in the accuracy of nonlinear model reduction, which is of paramount importance for the efficient simulation of state‐of‐the‐art dynamical systems arising in all aspects of engineering.

The proposed novel approaches for model reduction are particularly beneficial for the design of controllers for nonlinear systems and for the design and analysis of radio‐frequency integrated circuits.

Nonlinear dynamical systems may, under certain conditions, be represented by a bilinear system. The paper is concerned with the construction of the controllability and observability gramians for the corresponding bilinear system. Such gramians form the core of model reduction schemes involving balancing.

The paper examines certain properties of the bilinear system and identifies parameters that capture important information relating to the behaviour of the system.

Novel approaches for the determination of approximate constant gramians for use in balancing‐type model reduction techniques are presented. Numerical examples are given which indicate the efficacy of the proposed formulations.

The systems under consideration are restricted to the so‐called weakly nonlinear systems, i.e. those without strong nonlinearities where the essential type of behaviour of the system is determined by its linear part.

The suggested methods lead to an improvement in the accuracy of model reduction. Model reduction is a vital aspect of modern system simulation.

The proposed novel approaches for model reduction are particularly beneficial for the design of controllers for nonlinear systems and for the design of radio‐frequency integrated circuits.

The purpose of this study is to investigate the problem of fault accommodation in bilinear dynamic systems.

Solution to this problem is related to constructing the control law which provides full decoupling with respect to the fault effects. The so-called logic-dynamic approach will be used to solve this problem. The main steps of this approach are: replacing the initial bilinear system by certain linear one, solving the problem under consideration for this linear system by well-known linear methods with some restrictions, taking into account the bilinear term to correct the obtained linear solution.

Existing conditions of the fault accommodation problem in a form of rank equalities and inequalities are formulated. Calculating relations for the control law and the auxiliary systems are given.

The suggested method allows determining such a control law that preserves the main performances of the system in the faulty case, while the minor performances may degrade.

The main advantage of the logic-dynamic approach is a possibility to solve the problem of fault accommodation for nonlinear systems by linear methods without decreasing the main properties of the obtained solution.

This paper aims to study the Gramian solutions and solitonic interactions of a (2 + 1)-dimensional Broer–Kaup–Kupershmidt (BKK) system, which models the nonlinear and dispersive long gravity waves traveling along two horizontal directions in the shallow water of uniform depth.

Pfaffian technique is used to construct the Gramian solutions of the (2 + 1)-dimensional BKK system. Asymptotic analysis is applied on the two-soliton solutions to study the interaction properties.

N-soliton solutions in the Gramian with a real function ζ(y) of the (2 + 1)-dimensional BKK system are constructed and proved, where N is a positive integer and y is the scaled space variable. Conditions of elastic and inelastic interactions between the two solitons are revealed asymptotically. For the three and four solitons, elastic, inelastic interactions and soliton resonances are discussed graphically. Effect of the wave numbers, initial phases and ζ(y) on the solitonic interactions is also studied.

Shallow water waves are studied for the applications in environmental engineering and hydraulic engineering. This paper studies the shallow water waves through the Gramian solutions of a (2 + 1)-dimensional BKK system and provides some phenomena that have not been studied.

In recent years, Asian countries have experienced rising rates of premarital cohabitation, mirroring a similar trend that could be observed in many European countries several decades ago. As international differences in these trends are often attributed to institutional and societal differences, this study explores how China’s and Germany’s welfare and cultural regimes relate to national differences in the timing and prevalence of premarital cohabitation and direct marriage.

On the basis of two post-hoc harmonized surveys (pairfam for Germany; CFPS for China), descriptive analyses and logistic regressions were conducted. A higher standardization of partnership trajectories during the transition to adulthood was observed in China; this being probably related to China’s collectivist and Germany’s individualistic culture. While urban–rural differences prevail in China, and are attributable to China’s hukou system, East and West Germans differ considerably in this regard, a finding which can be traced back to regional differences in historical legacy. Discrepancies in economic modernization explain why the likelihood of experiencing these events differs for individuals in the Eastern and Western Chinese provinces.

Besides these differences, the two national contexts resemble each other in the prevalence of educational hypergamy, as well as in greater rates of cohabitation prior to first marriage, in contrast to direct marriage, seen among wealthier individuals and those with higher education. For the first time, the effects of cultural and institutional differences on the transition to adulthood were compared between a collectivistic vs. individualistic cultural regime and a productivist vs. corporatist conservative welfare regime, enabling researchers to draw conclusions about the link between cultural and welfare regime types and partnership patterns.

The purpose of this paper is to identify the fault modes of a nonlinear twin-rotor system (TRS) using the subspace technique to facilitate fault identification, diagnosis and control applications.

For identification of fault modes, three types of system malfunctions are introduced. First malfunction resembles actuator, second internal system dynamics and third represents sensor malfunction or offset. For each fault scenario, the resulting TRS model is applied with persistently exciting inputs and corresponding outputs are recorded. The collected input–output data are invoked in NS4SID subspace system identification algorithm to obtain the unknown fault model. The identified actuator fault modes of the TRS can be used for fault diagnostics, fault isolation or fault correction applications.

The identified models obtained through system identification are validated for correctness by comparing the response of the actual model under the fault condition and identified model. The results certify that the identified fault modes correctly resemble the respective fault conditions in the actual system.

The utilization of proposed work for current research emphasized the area of fault detection, diagnosis and correction applications that makes its value significantly. These modes when used for diagnosis purposes allow users to timely get intimated and rectify the performance degradation of the plant before it gets totally malfunctioned. Moreover, the slight performance degradation is also indicated when fault diagnosis is performed.

The purpose of this paper is to develop an easily implemented and practical stabilizing strategy for the hardware-in-the-loop (HIL) system. As the status of HIL system in the ground verification experiment for space equipment keeps rising, the stability problems introduced by high stiffness of industrial robot and discretization of the system need to be solved ungently. Thus, the study of the system stability is essential and significant.

To study the system stability, a mathematical model is built on the basis of control circle. And root-locus and 3D root-locus method are applied to the model to figure out the relationship between system stability and system parameters.

The mathematical model works well in describing the HIL system in the process of capturing free-floating targets, and the stabilizing strategy can be adopted to improve the system dynamic characteristic which meets the needs of the practical application.

A method named 3D root-locus is extended from traditional root-locus method. And the improved method graphically displays the stability of the system under the influence of multivariable. And the strategy that stabilize the system with elastic component has a strong feasible and promotional value.

For most practical control system problems, the state variables of a system are not often available or measureable due to technical or economical constraints. In these cases, an observer-based controller design problem, which is involved with using the available information on inputs and outputs to reconstruct the unmeasured states, is desirable, and it has been wide investigated in many practical applications. However, the investigation on a discrete-time singular Markovian jumping system is few so far. This paper aims to consider an observer-based control problem for a discrete-time singular Markovian jumping system and provides a set of easy-used conditions to the proposed control law.

According to the connotation of the separation principle extended from linear systems, a mode-dependent observer and a state-feedback controller is designed and carried out independently via two sets of derived necessary and sufficient conditions in terms of linear matrix inequalities (LMIs).

A set of necessary and sufficient conditions for an admissibility analysis problem related to a discrete-time singular Markovian jumping system is derived to be a doctrinal foundation for the proposed design problems. A mode-dependent observer and a controller for such systems could be designed via two sets of strictly LMI-based synthesis conditions.

The proposed method can be applied to discrete-time singular Markovian jumping systems with transition probability p_ij > 0 rather than the ones with p_ii = 0.

The formulated problem and proposed methods have extensive applications in various fields such as power systems, electrical circuits, robot systems, chemical systems, networked control systems and interconnected large-scale systems. Take robotic networked control systems for example. It is recognized that the variance phenomena derived from network transmission, such as packets dropout, loss and disorder, are suitable for modeling as a system with Markovian jumping modes, while the dynamics of the robot systems can be described by singular systems. In addition, the packets dropout or loss might result in unreliable transmission signals which motivates an observer-based control problem.

Both of the resultant conditions of analysis and synthesis problems for a discrete-time singular Markovian jumping system are necessary and sufficient, and are formed in strict LMIs, which can be used and implemented easily via MATLAB toolbox.

In the field of cryptography, authentication, secrecy and identification can be accomplished by use of secret keys for any computer-based system. The need to acquire certificates endorsed through CA to substantiate users for the barter of encoded communications is one of the most significant constraints for the extensive recognition of PKC, as the technique takes too much time and susceptible to error. PKC’s certificate and key management operating costs are reduced with IBC. IBE is a crucial primeval in IBC. The thought behind presenting the IBE scheme was to diminish the complexity of certificate and key management, but it also gives rise to key escrow and key revocation problem, which provides access to unauthorised users for the encrypted information.

This paper aims to compare the result of IIBES with the existing system and to provide security analysis for the same and the proposed system can be used for the security in federated learning.

Furthermore, it can be implemented using other encryption/decryption algorithms like elliptic curve cryptography (ECC) to compare the execution efficiency. The proposed system can be used for the security in federated learning.

As a result, a novel enhanced IBE scheme: IIBES is suggested and implemented in JAVA programming language using RSA algorithm, which eradicates the key escrow problem through eliminating the need for a KGC and key revocation problem by sing sub-KGC (SKGC) and a shared secret with nonce. IIBES also provides authentication through IBS as well as it can be used for securing the data in federated learning.