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This study investigates the problem of fault estimation and control for unknown discrete-time systems. Such a problem was first formulated as an multiobjective optimization problem. Then, a data-driven parameterization controller design method was proposed to optimize both fault estimation and robust control performances. In terms of the single-objection control problem, necessary and sufficient conditions for designing the suboptimal controller were presented, and the performance index optimized by the developed data-driven method was shown to be consistent with that of the model-based method. In addition, by introducing additional slack variables into the controller design conditions, the conservatism of solving the multiobjective optimization problem was reduced. Furthermore, contrary to the existing data-driven controller design methods, the initial stable controller was not required, and the controller gain was directly parameterized by the collected state and input data in this work. Finally, the effectiveness and advantages of the proposed method are shown in the simulation results.

This paper describes a statistical and mathematical approach to optimize the mechanical properties of a wood plastic composite with Polyethylene Terephthalate (PET) as polymeric matrix. Wood plastic composite are materials that consist of a primary continuous polymer phase, where a secondary filler dispersed phase is embedded, the filler generally is wood fibers or sawdust. The slack variable approach in mixture experiments, consist in selecting a component of the mixture as slack variable, to subsequently design and analyze the experiment in terms of the remaining components. With the experimental design information three slack variable model were fit. Using response surface graphs, we show how different compositions modify the mechanical properties of wood plastic composite. Besides, by the desirability function, the optimal formulation of the compound that simultaneously maximizing the mechanical properties of wood plastic composite, was obtained. Finally, the components proportions that provides the best tensile, flexural and compression strength are presented.

This article presents a dual-stage coordinated control approach for voltage regulation and congestion management of active distribution networks (ADN) in the presence of photovoltaic (PV) generators and electric vehicle stations (EVS). The proposed scheme operates on rule-based model predictive control (RBMPC) to optimally manage the settings of the regulating devices, i.e., on-load tap changer (OLTC), distribution static synchronous compensator (DSTATCOM), PV generators, and EV inverters that possess different temporal characteristics. The first (hourly time-scale) and the second (one-minute time-scale) stages of the dual-stage coordinated control mechanism are designed to correct the long-term and short-term voltage fluctuations, respectively. The objectives of the proposed approach are to minimize the number of OLTC operations (first stage) and changes in set-points of PV and EV inverters, and DSTATCOM (second stage) in addition to minimization of slack variables, energy loss, and voltage error at EV stations. In both the stages, predefined rules are set for MPC to optimize different objectives on the basis of the magnitudes of bus voltages. Simulations are performed on 33-bus and 38-bus distribution networks to test the efficacy of the control approach. It is observed that the proposed approach could mitigate the voltage variations as well as line congestion for different scenarios.

In this paper, we aim to minimize the total power of all the Internet of Things devices (IoTDs) by jointly optimizing user association, computation capacity, transmit power, and the location of unmanned aerial vehicles (UAVs) in an UAV-assisted cloud radio access network (C-RAN). In order to solve this non-convex problem, we propose an effective algorithm by solving four subproblems iteratively. For the user association and the computation capacity subproblems, the non-convex constraints are relaxed and the optimal solutions are obtained. For the transmit power control and the location planning subproblems, successive convex approximation (SCA) technique is used to transform the non-convex constraints into convex ones. Moreover, to obtain the suboptimal solutions, slack variables are also introduced to deal with the feasibility-check problems. The simulation results demonstrate that the proposed algorithm can greatly reduce the total power consumption of IoTDs.

This article is concerned with the asynchronous reliable extended dissipative filtering problem for a class of continuous-time T-S fuzzy Markov jump systems. The modes of the encountered sensor failures and the designed filter are considered to be asynchronous with the original systems, which can be described by two mutually independent hidden Markov processes. By proposing double variables-based decoupling principle and variable substitution principle, a new condition is presented to guarantee the filtering error system to be stochastically stable and extended dissipative. Compared with the existing works, the proposed method does not impose constraints on Lyapunov variables and slack variables, and some unnecessary constraints on the system structure are removed. These directly lead to less conservative and more general results. An example is provided to illustrate the effectiveness of the proposed design method.

This study proposes an exact model for timetable recovery after disturbances in the context of high-frequency public transport services. The objective of our model is the minimization of the deviation between the actual headway and the respective planned value. The resulting mathematical program for the rescheduling problem is nonlinear and non-smooth; thus, it cannot be solved to optimality. To rectify this, we reformulate the model using slack variables. The reformulated model can be solved to global optimality in real-time with quadratic programming. We apply the model to real data from the red metro line in Washington D.C. in a series of experiments. In our experiments, we investigate how many upstream trips should be rescheduled to respond to a service disturbance. Our findings demonstrate an improvement potential of service regularity of up to 30% if we reschedule the five upstream trips of a disturbed train.

This paper develops a model for a central controller in a fleet system that allows adaptive utilization of EV batteries distributed energy for concurrent services to the transportation and power grid. The paper proposes a cooperative-based model to coordinate and manage the operation of each EV to provide a large operating reserve to the grid while maintaining services to the transportation sector. The optimization model incorporates various slack variables and control parameters for managing real-time fare prices, adaptive energy, and reserve margin allocation, interaction with the grid operator, and meeting the fleet target revenue. A dynamic pricing mechanism is developed for real-time calculation of fare rates to allow the EV fleet optimization problem to achieve a daily revenue target while limiting fare prices in a competitive market. Numerical results indicate that the model can manage several EVs for various services while enhancing the fleet financial metrics.

This paper proposes a new robust Discrete-Time Sliding Mode Control ( dt-smc ) scheme for linear discrete-time delay system. The delays, affecting the state and the input, are assumed to be known, time-varying and bounded. The considered system is also subject to time-varying Unknown But norm-Bounded ( ubb ) unmatched uncertainties, that act on the state and the delayed state vectors. The designed controller is based on a novel sliding surface. Using a new Lyapunov functional candidate and by introducing slack variables, a less conservative delay-dependent sufficient condition ensuring the asymptotic stability of the closed loop system is derived in terms of Linear Matrix Inequalities ( lmi s). With respect to that condition a new dt-smc law is synthesized. The proposed control algorithm is applied to an Autonomous Underwater Vehicle ( auv ). The simulation results demonstrate the effectiveness of the proposed controller.

Usually the real-world (RW) datasets are imbalanced in nature, i.e., there is a significant difference between the number of negative and positive class samples in the datasets. Because of this, most of the conventional classifiers do not perform well on RW data classification problems. To handle the class imbalanced problems in RW datasets, this paper presents a novel density-weighted twin support vector machine (DWTWSVM) for binary class imbalance learning (CIL). Further, to boost the computational speed of DWTWSVM, a density-weighted least squares twin support vector machine (DWLSTSVM) is also proposed for solving the CIL problem, where, the optimization problem is solved by simply considering the equality constraints and by considering the 2-norm of slack variables. The key ideas behind the models are that during the model training phase, the training data points are given weights based on their importance, i.e., the majority class samples are given more importance compared to the minority class samples. Simulations are carried on a synthetic imbalanced and some real-world imbalanced datasets. The model performance in terms of F1-score, G-mean, recall and precision of the proposed DWTWSVM and DWLSTSVM are compared with support vector machine (SVM), twin SVM (TWSVM), least squares TWSVM (LSTWSVM), fuzzy TWSVM (FTWSVM), improved fuzzy least squares TWSVM (IFLSTWSVM) and density-weighted SVM for binary CIL. Finally, a statistical study is carried out based on F1-score and G-mean on RW datasets to verify the efficacy and usability of the suggested models.

Driven by the practicality of unmanned aerial vehicle (UAV), we consider a dual-UAV based non-orthogonal multiple access (NOMA) scenario, which consists of one communication UAV for services and one jamming UAV against eavesdropping. The goal is to maximize the secrecy energy efficiency through the successive convex approximation based communication resource, UAV trajectory, and artificial noise optimization. Considering the probabilistic constraint of outage probability from imperfect channel state information, we transform it to a non-probabilistic problem by Markov inequality and Marcum $Q$ -function, then the problem is decomposed into three subproblems. We apply matching-swapping method to assign subchannel in non-orthogonal multiple access (NOMA) UAV networks before the joint process, then convert the power optimization problem to a standard convex optimization form by upper bound of the concave function. The communication UAV trajectory is studied under the constraints of flying energy consumption, maximum speed, and flying altitude. To track this NP-hard problem, Taylor expansion and various slack variables sets are introduced to transform the non-convex problem to convex one. For the artificial noise optimization problem, we use the lower bound to replace the convex term turning it into an easy-to-solve convex optimization problem. In the end, simulations results reveal that: 1) The reasonable jamming scheme can improve the secrecy energy efficiency of the NOMA UAV networks, even if it can cause interference for legitimate users; 2) UAV will fly to a place where the performance gain from users is high when flying energy consumption permits.

In this paper, we develop a distributed solver for a group of strict (non-strict) linear matrix inequalities over a multi-agent network, where each agent only knows one inequality, and all agents co-operate to reach a consensus solution in the intersection of all the feasible regions. The formulation is transformed into a distributed optimization problem by introducing slack variables and consensus constraints. Then, by the primal–dual methods, a distributed algorithm is proposed with the help of projection operators and derivative feedback. Finally, the convergence of the algorithm is analyzed, followed by illustrative simulations.

This paper presented a model predictive control strategy with guaranteed nominal stability, applicable to systems with repeated integrating poles. The offset-free control law is obtained inside a one-layer optimization formulation through the development of a state-space model based on an analytical expression of the system step response. While the stability of the closed-loop system is achieved by considering an infinite prediction horizon along with the inclusion of terminal equality constraints, its feasibility to tackle model uncertainty is ensured by means of an always feasible-optimization formulation through the insertion of a suitable set of slack variables. The effectiveness of the method is illustrated for the output tracking and disturbance rejection problem in a benchmark system, “ball-and-plate” apparatus, including a nonlinear plant-model mismatch scenario.

K-nearest neighbor (KNN) based weighted multi-class twin support vector machines (KWMTSVM) is a novel multi-class classification method. In this paper, we propose a novel least squares version of KWMTSVM called LS-KWMTSVM by replacing the inequality constraints with equality constraints and minimized the slack variables using squares of 2-norm instead of conventional 1-norm. This simple modification leads to a very fast algorithm with much better results. The modified primal problems in the proposed LS-KWMTSVM solves only two systems of linear equations whereas two quadratic programming problems (QPPs) need to solve in KWMTSVM. The proposed LS-KWMTSVM, same as KWMTSVM, employed the weight matrix in the objective function to exploit the local information of the training samples. To exploit the inter class information, we use weight vectors in the constraints of the proposed LS-KWMTSVM. If any component of vectors is zero then the corresponding constraint is redundant and thus we can avoid it. Elimination of redundant constraints and solving a system of linear equations instead of QPPs makes the proposed LS-KWMTSVM more robust and faster than KWMTSVM. The proposed LS-KWMTSVM, commensurate as the KWMTSVM, all the training data points into a “1-versus-1-versus-rest” structure, and thus our LS-KWMTSVM generate ternary output {-1,0,+1} which helps to deal with imbalance datasets. Numerical experiments on several UCI and KEEL imbalance datasets(with high imbalance ratio) clearly indicate that the proposed LS-KWMTSVM has better classification accuracy compared with other baseline methods but with remarkably less computational time. This work was supported by Science and Engineering Research Board (SERB) under Early Career Research Award Grant No. ECR/2017/000053 and Ramanujan fellowship Grant No. SB/S2/ RJN-001/2016. This work was also supported by Council of Scientific & Industrial Research (CSIR), New Delhi, INDIA under Extra Mural Research (EMR) Scheme Grant No. 22(0751)/17/ EMR-II.

This article addresses the problem of robust stabilization of uncertain linear systems by static state- and output-feedback control laws. The uncertainty is supposed to belong to a polytope and both continuous- and discrete-time systems are investigated. Contrarily to the main stream of the linear matrix inequality (LMI)-based robust stabilization methods available in the literature, where the product between the Lyapunov (or slack variable) and control gain matrices is transformed in a new variable, this article proposes a change of paradigm, avoiding the standard change of variables and providing synthesis conditions that deal directly with the control gain as an optimization variable. The design procedure is formulated in terms of a locally convergent iterative algorithm based on LMIs, having as main novelties the following points: Both the Lyapunov and the closed-loop dynamic matrices appear affinely in the conditions; the iterative scheme involves the slack variables only, avoiding the classic alternation between the Lyapunov matrix and the control gain; an extra degree of freedom is created in terms of an additional scalar variable, which also appears affinely in the conditions and represents a scaling on the closed-loop dynamic matrix; a smart termination for the algorithm through a stability analysis condition. Numerical experiments based on exhaustive simulations show that all these features combined provide a robust stabilization technique capable to outperform the best available methods in the literature in terms of effectiveness, being specially suitable to address static output-feedback and decentralized control problems.

Zhang neural network (ZNN), a special recurrent neural network, has recently been established as an effective alternative for time-varying linear equations with inequality constraints (TLEIC) solving. Still, the convergent time produced by the ZNN model always tends to infinity. In contrast to ZNN, a finite-time convergent neural network (FCNN) is proposed for the TLEIC problem. By introducing a non-negative slack variable, the initial form of the TLEIC has been transformed into a system of time-varying linear equation. Afterwards, the stability and finite-time performance of the FCNN model is substantiated by the theoretical analysis. Then, simulation results further verify the effectiveness and superiority of the proposed FCNN model as compared with the ZNN model for solving TLEIC problem. Finally, the proposed FCNN model is successfully applied to the trajectory planning of redundant manipulators with joint limitations, thereby illustrating the applicability of the new neural network model.

This letter deals with a shaped beampattern synthesis problem through controlling the mainlobe ripple and the output filter energy based on the minimization of the peak sidelobe level in the spatial region of interest. To tackle the challenging optimization problem with nonconvex constraints, a novel first-order iterative convex approximation (FOICA) procedure that handles the nonconvex constraints with their convex upper bound functions resorting to the first-order Taylor expansion is developed. Hence, in each iteration, the original problem is approximated through a convex problem globally solved via a polynomial time method. Additionally, a nonnegative slack variable to ensure a decreasing trend in the objective function during the iteration is introduced. Finally, the numerical simulations are provided to verify that the proposed algorithm outperforms the state-of-the-art algorithms in terms of achieved beampattern performance.

Operational performance in the low-voltage distribution network (LVDN) can be undermined by its inherent unbalances, which may become worse as the penetration of rooftop solar continuously increases. To address this issue, load balancing via phase-reconfiguration devices (PRDs), which can change phase positions of residential customers as required, provides a cost-efficient option. However, most reported approaches to control PRDs require that demands of all residential customers are available, which are not viable for many LVDNs without smart meters or advanced metering infrastructure (AMI) installed. To bridging the gap in this field, this paper proposes a novel method to control PRDs purely based on measurable data from PRDs, and its controller. Based on limited information, sensitivity analysis in the network with PRDs is studied, followed by the optimization model that comprehensively considers operational requirements in the network. Moreover, slack variables are introduced to the model, and penalized in the objective function to assure either a strategy that is secure or with minimized violations can always be provided. The model is a challenging mixed-integer non-convex programming (MINCP) problem, which is reformulated as an efficient solvable mixed-integer second-order cone programming (MISOCP) based on exact reformulations or accurate linear approximations. Simulations based on two modified IEEE systems, and a real system in Australia demonstrate that an efficient strategy can be provided to mitigate unbalances in the network.

In this letter, the UAV-enabled relay communication is investigated, where the UAV relay forwards the information received from the ground source node to the ground destination node under malicious jamming. We aim to maximize the end-to-end throughput by optimizing the trajectory of UAV and transmit power of both UAV and source node jointly. However, the formulated problem is intractable due to the non-convex objective function and constraints. Thus, with the aid of slack variables, we propose an efficient algorithm to solve it based on the block coordinate descent (BCD) and successive convex approximation (SCA) techniques. Numerical results are provided to show that the joint design of trajectory and power control improves the throughput significantly.

In this article, the actuator fault estimation of a networked control system (NCS) with packet dropout is studied. First, a Markov chain is utilized to describe the packet loss behaviour. Then, the global system is modelled as a Markovian jump linear system (MJLS). Next, a proportional–integral observer is used to estimate the actuator’s fault. Sufficient conditions are written in the form of linear matrix inequality (LMI) after using the stochastic Lyapunov–Krasovskii functional. By applying matrix theory skills, we introduce some slack variables in the LMI for more relaxation. The obtained LMI has more advantages than others existing in the literature. Finally, a simulation is provided to show the validity of the proposed approach and compare the obtained results with other presented works.

Wireless powered mobile edge computing (MEC) leveraging hybrid passive backscatter communications (BackCom) and active transmissions (AT) for efficient data offloading has been investigated in Internet of Things (IoT) networks, where however the delay minimization problem has not been sufficiently studied. In this letter, we propose to minimize the overall delay for data offloading and computing of all IoT nodes in a hybrid BackCom-AT based wireless powered MEC network. We formulate an optimization problem to jointly optimize the operation time of a power beacon, and the computing frequency, transmit power, and portions of task bits for BackCom offloading, AT offloading and local computing of each IoT node. By introducing auxiliary variables and slack variables, the formulated non-convex optimization problem is transformed into an equivalent but more tractable form and is optimally solved by our proposed bisection-based iterative algorithm (BBIA). Computer simulations verify the quick convergence of the BBIA, and show that our proposed algorithm achieves a much shorter overall delay of all IoT nodes than the baseline schemes.

This paper deals with the observer design problem for semi-Markov jump systems with incremental quadratic constraints. Based on the design objective that the state estimation error is stochastically stable, the sufficient conditions formulated by linear matrix inequalities are presented. To reduce the conservatism of sufficient conditions as well as the computational burden, the relaxation method with slack variable is employed. Finally, a simulation example verifies the effectiveness and superiority of the method studied in this paper.

This article proposes an alternative for robust control of synchronous reluctance motors using linear matrix inequalities to obtain fixed gains that ensure current and speed regulation, under parameter uncertainties and variations. The proposed design procedure is based on a polytopic model, which takes into account: i) uncertainties and variations of the mechanical and electrical parameters of the motor, ii) one step delay from digital implementation of the control law, and iii) internal model based controllers to guarantee reference tracking. Less conservative linear matrix inequalities, relying on slack variables, ensure robust pole location and certify the closed-loop stability for the entire domain of uncertain and time-varying motor parameters, based on parameter-dependent Lyapunov functions. The linear matrix inequalities ensure a fast and systematic computation of the control gains, that are also easy to be implemented, not adding computational complexity when compared, for instance, to usual strategies based on PI controllers. Experimental results for a 2.2 kW commercial motor are provided, validating the proposed procedure, and illustrating good tracking of currents and speed references, with suitable dynamic responses and reduced cross-coupling effects, when compared to sliding mode and PI controllers.