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This study is concerned with the finite-time H∞ control problem for uncertain discrete-time Markovian jump singular systems with time-varying norm-bounded disturbance. Firstly, the concepts of singular finite-time stability, singular finite-time boundedness and singular H∞ finite-time stabilisation are given. Then, sufficient conditions of singular finite-time boundedness and singular H∞ finite-time stability are derived for the class of discrete-time Markovian jump singular systems. The main contribution of the study is to propose a numerical efficient and reliable controller design process for state feedback finite-time H∞ control of discrete-time Markovian jump singular systems. By applying the descriptor system technique presented by Fridman and Shaked, sufficient criteria are presented for the solvability of the problems, which can be reduced to feasibility problems in terms of linear matrix inequalities. Finally, numerical examples are included to illustrate the validity of the presented results.

Singular systems behave more powerfully in termsof dynamical system modeling than ordinary state space systems. Since thealgebraic equations in singular models can describe the systems constraints,nonlinear singular systems can present a general method for modeling andcontrol of constrained dynamical systems. This paper discusses an adaptivecontrol for nonlinear singular systems which satisfy Lipschitz condition. Adaptivemethods for singular systems are hardly ever investigated in literatures;however they are very useful methods in practice because the adaptive mechanismduring the adaptive control can adjust the controller for a system with unknownstructures and parameters to improve the system performance. The presentedcontroller is composed of a state feedback approach with adaptive gains and amechanism to adjust the gains based on the Lyapunov stability theorem. Firstthe controller is designed to stabilize the system then it is extended for the trackingproblem. A simulation on a mobile robot singular model is provided toillustrate the effectiveness of the proposed control approach.

This paper aims at proposing an observer-based T-S fuzzy singular system. Firstly, we give a general model of nonlinear singular systems. We use the T-S fuzzy control method to form a T-S fuzzy singular system and we give the augmented system and compact form of a T-S fuzzy singular system. Secondly, we design a T-S fuzzy observer for the augmented system. In order to prove the parameters and state estimation errors are globally stable for the T-S fuzzy observer, we construct a Lyapunov function with T-S fuzzy form. Then we give the sufficient condition that the fuzzy control fuzzy system is globally exponentially stable and give the controller gains. Finally, we give two numerical examples for the observer, and the simulation results demonstrate the effectiveness of the observer for the nonlinear singular system,through a comparison of the literature (Zulfiqar et al. in Appl. Math. Model. 40(3):2301-2311, 2016 ).

In the present study, stochastic numerical computing approach is developed by applying artificial neural networks (ANNs) to compute the solution of Lane–Emden type boundary value problems arising in thermodynamic studies of the spherical gas cloud model. ANNs are used in an unsupervised manner to construct the energy function of the system model. Strength of efficient local optimization procedures based on active-set (AS), interior-point (IP) and sequential quadratic programming (SQP) algorithms is used to optimize the energy functions. The performance of all three design methodologies ANN-AS, ANN-IP and ANN-SQP is evaluated on different nonlinear singular systems. The effectiveness of the proposed schemes in terms of accuracy and convergence is established from the results of statistical indicators.

This paper studies the H ∞ filtering problem of discrete-time singular nonlinear systems in encrypted state which are represented by Takagi-Sugeno (T-S) fuzzy model, meantime, quantization, signal missing and filter failure are considered. This paper selects the measurement output and the filter output for quantization, the sensor failure of the systems, the loss of the estimated signal and filter output signals are considered. Then, the admissible condition of the filtering error system is calculated and verified, and the condition meets the specific H ∞ performance index. By quoting a new Lyapunov function, the design conditions of the filter and the adjustment parameters of the quantizers are obtained. Finally, the feasibility of this method is verified by a circuit example.

The current research focuses on a recommendation system based on Decision Tree, Naive Bayes, Ridge Classifier, and Random Forest, using a new hybrid method combining Singular Value Decomposition (SVD) and K-Nearest Neighbors (KNN). The Decision Tree model reaches a good trade-off for precision, recall, and F1 metrics, acting as a benchmark. On the other hand, the hybrid model greatly surpasses the remaining ones in such a way that precision is as high as 89.35%, recall is 59.01%, and F1 is up to 71.30%, thus reinforcing the notion that it finds user preferences for recommendations more effectively. By combining collaborative filtering with similarity-based recommendations, the system can model user-item interaction and thus improve the quality of book recommendations. The above findings imply that the hybrid model holds good potential to deliver better recommendations in a more relevant and acceptable way, countering the implicit limitations of their single-algorithm counterparts and increasing user satisfaction.

In general, the construction of observers for nonlinear descriptor systems depends on the solvability of a linear matrix inequality involving system matrices, and it is based on the system’s nonlinearity. Therefore, the type of nonlinearity present in the system heavily affects the observer design process. There are significant developments in the literature for observer design for descriptor systems with various types of nonlinearity. Motivated by this, the current work reviews the literature on observer design for nonlinear descriptor systems with an extensive discussion on the type of nonlinearities that are considered. Here, an analysis and the comparison on the most common nonlinearities is presented, providing a roadmap to all researchers in the field. Furthermore, less common nonlinearities have been identified, presenting under-explored areas within the literature, and can open new domains for future research.

In this paper, a bio-inspired computational intelligence technique is presented for solving nonlinear doubly singular system using artificial neural networks (ANNs), genetic algorithms (GAs), sequential quadratic programming (SQP) and their hybrid GA–SQP. The power of ANN models is utilized to develop a fitness function for a doubly singular nonlinear system based on approximation theory in the mean square sense. Global search for the parameters of networks is performed with the competency of GAs and later on fine-tuning is conducted through efficient local search by SQP algorithm. The design methodology is evaluated on number of variants for two point doubly singular systems. Comparative studies with standard results validate the correctness of proposed schemes. The consistent correctness of the proposed technique is proven through statistics using different performance indices.

In this paper, a novel sliding mode preview control (SMPC) problem with H ∞ performance is investigated for a category of discrete-time singular Markovian jump systems (SMJSs). A novel augmented error system (AES) model is first developed for discrete-time SMJSs based on the analysis of preview information, and the problem of SMPC is reformulated as the stability problem of AES. Secondly, a novel mode-independent sliding surface function is established for AES such that the reachability of sliding mode surfaces (SMS) can always be achievable. Thirdly, sufficient conditions of the H ∞ admissible stability for sliding mode dynamics is derived, based on which a suitable SMPC law is designed to satisfy discrete-time reachability condition. Finally, simulation results have shown that the proposed SMPC law is superior to the control law without previewable information.

This work studies an unknown input observer (UIO) design dedicated to the Takagi–Sugeno fuzzy-approximation-based nonlinear singular systems with unknown inputs in the discrete-time domain. Not only the input equation, but also the output equation are assumed to be affected by unknown inputs. By restoring to a fuzzy Lyapunov function together with the well-developed linear matrix inequality (LMI) technique, some new relaxed sufficient criteria for the convergence of the designed UIO are exactly given and accurately proved. Significantly, consider that the actuator fault may occur frequently, which may result in a disastrous consequence for modern control systems. Therefore, an extended UIO called unknown input proportional integral observer is further investigated to reconstruct the actuator fault. All the design procedures are formulated in terms of LMIs. Finally, simulation studies on a numerical example as well as a practical one are provided to test the performance of the developed two procedures.