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Robust design is widely recognised as a leading method for reducing variability and improving quality. Most of the engineering statistics literature focuses on finding point estimates of the optimum operating conditions for robust design. Various procedures have been considered for calculating point estimates of the optimum operating conditions. Although the point estimation procedure is important for continuous quality improvement, the immediate question is ‘‘how accurate are these optimum operating conditions?” The answer is to consider interval estimation for a single variable or joint confidence regions for multiple variables. In this paper, using the bootstrap technique, we develop procedures for obtaining joint confidence regions for the optimum operating conditions. Two different procedures, using Bonferroni and multivariate normal approximation, are introduced. The proposed methods are illustrated and substantiated using a numerical example. [ABSTRACT FROM PUBLISHER]

Many of today’s industrial firms seek the continuous and systematic reduction of variability as a primary engineering goal across key production dimensions. Robust parameter design (RPD) is often considered among the most important methods for achieving these ends. Focused on statistical modelling and numerical optimisation strategies, most researchers typically assume processes possess moderate to low variability, which facilitates the use of ordinary least squares (OLS) regression. Realistically, however, industrial processes often exhibit high variability. In such cases, many of the modelling assumptions underpinning OLS methods do not hold. Consequently, the results and recommendations provided to decision-makers using these could generate suboptimal modifications to processes and products. This paper proposes an alternative method for dealing with high process variability. Specifically, using the coefficient of variation to identify influential sources of variability between design points, the proposed method advocates removing these sources and then applying optimal design theory to rebalance the experimental framework. Thereafter, RPD optimisation schemes may be applied to obtain more precise optimal operating conditions with less variability and bias. A numerical example combined with Monte Carlo simulation is used to illustrate the proposed procedure. [ABSTRACT FROM PUBLISHER]

Improving the dynamic performance of an automobile suspension system is considered as the main demand for comfortable and safe passenger travelling. From all previously proposed and implemented works, it is noticed that there are other factors that need to be considered to raising the car holding and stability in the road for improved passenger comfort when travelling. The minimization of car body displacement and oscillation time after exposure to road disturbances have been adopted in this work due to their contribution in raising the car holding and stability. The improvement in these features was maintained via a robust control methodology. The Fractional Order PID controller tuned by the Whales Optimization Algorithm (WOA) and Particle Swarm Optimization (PSO) algorithm is suggested in this work as a robust controller to reduce the effect of these demerits. In this paper, an active quarter car suspension nonlinear system is designed for the presented goals using a robust controller. Minimizing the displacement of the car body and reducing the damping frequency are achieved via a nonlinear control strategy using the fractional order PID controller, which can maintain the required characteristics. Tuning the parameters of the FOPID controller is performed by using the Whales Optimization Algorithm (WOA). Robustness of the FOPID controller is examined and proved to withstand a system parameter variation of ±12% in all system parameters and a maximum of ±80% in controller parameter variation. Simulation outcomes also indicate a considerably improved performance of the active suspension system with the fractional order PID controller over the traditional PID. [ABSTRACT FROM AUTHOR]

The proportional-integral-derivative (PID) controller is a widely used controller in automation industries. Several advanced PID tuning/design methods, such as response-based design, internal model control, and controller optimization by stochastic algorithms, have been proposed in the literature. However, regardless of the advantages and accuracy of developed tuning methods, due to the process modeling error and parametric uncertainties, the experimental response always differs from the theoretical response, which required online fine-tuning of the PID parameter. Manual adjustment of three PID parameters disturbs the robustness of the controller from its desired value; also, it does not guarantee the stability of the process. Therefore, this paper focuses on online PID controller tuning with the guaranteed robustness of the controller. A new single variable tuning method is developed for the online robustness and performance adjustment. Moreover, the proposed rules only depend upon the previously optimized PID parameters. The proposed method is an additional feature to all existing PID tuning methods, including optimal PID controller with stochastic optimization algorithms. The proposed method is validated with the help of optimal PID controller design by existing optimal tuning rules, optimized PID with particle swarm optimization and experimental validation on the canonical tank system. [ABSTRACT FROM AUTHOR]

In this paper, we analyze the problem of the stabilization for discrete-time Takagi–Sugeno fuzzy parametric uncertain systems. The stabilization conditions of these systems are investigated with two observers and two different Lyapunov functions: nonquadratic and delayed nonquadratic. The stabilization conditions are analyzed between k and k + t sample variations in the Lyapunov function. The obtained stabilization results represent an extension of previous works with one-sample variation in discrete time. All the results are obtained in the form of linear matrix inequalities which are solved by using various convex optimization algorithms. Two theorems are proposed, and comparison via simulation is given to demonstrate the robustness of the proposed approaches. Nevertheless, this paper shows that the second proposed observer gives the less conservative results (less restrictive). These reduced conservative results are demonstrated by a larger feasible area of stabilization (stabilization domain) and a fast convergence of estimation errors compared to the first. [ABSTRACT FROM AUTHOR]

This paper presents a new design technique to determine the optimal values of proportional–integral–derivative controller gains of an automatic voltage regulator, using the evolutionary algorithm namely 'Cuckoo Search'. The dynamic performance of the proposed controller is evaluated by estimating its transient response characteristics, such as, rise time, settling time, maximum peak overshoot, and steady-state error. In addition, a thorough comparison of the time response characteristics, obtained with proposed controller and other existing evolutionary algorithm based controllers is made to demonstrate its external attributes and adeptness. Comparative analysis illustrates that the proposed controller can be considered as a significant device in the subject area of the power systems as it offers, more energy efficient, robust, and fast convergence characteristics than the controllers, considered here for the discussions. Furthermore, robustness of proposed controller has also been investigated by allowing 50% uncertainty in the automatic voltage regulator system. Finally, the stability of an automatic voltage regulator system with proposed controller is investigated through root-locus and bode plots. It is revealed that the proposed controller not only capable to provide good dynamic response, but also exhibits stable performance for wide range of open loop gains. • A new optimization technique is utilised to design PID controller for AVR system. • The proposed controller is also capable to handle model uncertainties. • The results are compared with CAS-PID, GA-PID and PSO-PID controllers. • The fast and efficient dynamic response of AVR system is observed comparatively. [ABSTRACT FROM AUTHOR]

This paper addresses the robust control problem of Twin Rotor Multi input multi output System (TRMS) via H 2 and H ∞ control techniques. An output error optimization technique is proposed to develop H 2 and H ∞ controllers for the well posed plant. Computer simulation results are presented for closed loop TRMS in hovering positions which show marked improvements over previous works. The simulated plant exhibits stable responses in hovering position at the desired pitch and yaw angles. Corrections are incorporated in model formulation to compensate control and sensor singularities. The output error optimization technique proposed in the present paper can be essentially adopted in controlling of 2 by 2 plants exhibiting non-minimum phase dynamics. [ABSTRACT FROM AUTHOR]

In control practices, problems of parametric or time-varying uncertainties must be dealt with. Robust control based on norm theory and convex and non-convex optimization algorithms is a powerful tool to solve these problems in theory, but it is employed rarely in applications. In most engineering cases, Proportional-Integration-Derivative (PID) control is still the most popular method for its easy-to-tune and controllable properties. The control method proposed in this paper integrates the PID control into robust control formulation as a robust Structured Static Output Feedback (SSOF) problem of Linear-Parameter-Varying (LPV) systems, which can be converted into a Parameter Dependent Bilinear-Matrix-Inequality (PDBMI) optimization problem. A convex-concave decomposition based method is given to solve the proposed PDBMI problem. The proposed solution has a simple structure in PID form and can guarantee stability and robustness of the system being controlled in the whole operation range with less conservativeness than existing solution. [ABSTRACT FROM AUTHOR]

This paper presents a new robust load frequency control (LFC) technique based on an optimal design of the coefficient diagram method (CDM) in a three area thermal power system equipped with redox flow batteries (RFB). In order to emphasize on a realistic power system and obtain an accurate insight, important nonlinearities due to generation rate constraint (GRC), governor dead band (GDB) and time delay (TD) were considered. The innovation of the proposed controller in this paper is the use of a hybrid intelligent combination of a decentralized CDM technique and optimization throughout its algebraic equations. In addition, a new algorithm namely grasshopper optimization algorithm (GOA) was used to find the key parameters of the proposed controller in solving the LFC problem for the first time. Furthermore, this study applied a powerful modified objective function by considering the integral of time multiplied squared error (ITSE) criteria for both controller input signal (ACE), to minimize the area control error and output signal (Δ u) to reduce the size of the actuator, settling time (Ts) to have a faster response and a function to increase the minimum damping ratio (MDR) among all eigen values. To demonstrate the effectiveness of the proposed scheme, the studied simulated power system was tested through different cases including a large step and sinusoidal load perturbations and wide uncertainty in dynamic parameters of a nonlinear power system. Comparative results have revealed the superiority of the optimal CDM technique, especially when it is equipped with RFB. In addition to graphical results, by taking into account the MDR of different control strategies, the preference of the proposed controller has become more validated. This newly developed strategy leads to a flexible and accurate controller with a powerful mathematical back up which can successfully cope with GRC, GDB and TD nonlinearities in perturbed uncertain power systems and provide fast, stable and robust dynamic responses. Thus, the proposed control strategy can be constructive and successfully applied to real world power system application. [ABSTRACT FROM AUTHOR]

The high penetrations of distributed energy resources (DERs) leads to severe problems such as reducing system inertia and increasing the frequency deviations from the nominal value. The main target of this study is to enable modern photovoltaics (PVs) with large penetration amounts to participate effectively in the load frequency control in the interconnected power systems, in which frequency and tie-line power sharing deviations exist. In this research, a model for the solar PV is developed to help study the heavy penetration of the solar PVs within interconnected power systems. Secondly, a time domain objective function based on the norm of the area control error is formulated. Thirdly, in order to tune the PI controllers, a combined meta-heuristic algorithm based on particle swarm optimization and whale optimization algorithm (PSO-WOA) is developed and compared with the individual PSO and WOA controllers. From the studied scenarios, the developed combined scheme outperforms the other algorithms in terms of system performance indices. Therefore, the developed PSO-WOA approach is plausible and straightforward to solve many engineering problems as it benefits from the exploitation characteristics of the conventional PSO and the exploration features of the WOA. [ABSTRACT FROM AUTHOR]

• Power System Stabilizer (PSS) is designed for a modified Heffron-Phillips model which is developed by taking transformer secondary bus voltage at generator side as reference, instead of infinite bus voltage. • Particle Swarm Optimization (PSO) algorithm is used to tune the parameters of PSS and gain settings of the PID controller. • Robustness of the proposed technique is tested by taking several operating conditions under two typical disturbance conditions. The efficacy of the proposed technique is demonstrated with Eigen value analysis. This paper presents a novel method for designing robust Power System Stabilizer (PSS) using Particle Swarm Optimization (PSO) technique to improve the dynamic stability of the power system. Modified Heffron-Phillip's model is developed by considering the generator side transformer voltage as the reference instead of considering the infinite bus voltage as the reference to reduce the complexity and computational time. Using this MHP model, a power system stabilizer called Modified Power System Stabilizer (MPSS) is developed and integrated with P-I-D controller using PSO (PSO-P-I-D-MPSS) on a Single Machine Infinite Bus System. PSO algorithm is used to determine the gain settings of the P-I-D-MPSS. The developed PSO-P-I-D-MPSS is simple to implement and will be a better alternative to the conventional or evolutionary based PSSs. The efficacy of the proposed PSO-P-I-D-MPSS is validated by the application of proposed stabilizer to a benchmark system for several operating conditions under various disturbances. The results clearly show that the proposed stabilizer improves the dynamic stability of the power system under wide range of operating conditions. [ABSTRACT FROM AUTHOR]

This paper presents a novel contribution of a low complexity control scheme for voltage control of a dynamic voltage restorer (DVR). The scheme proposed utilizes an error-driven proportional–integral–derivative (PID) controller to guarantee better power quality performance in terms of voltage enhancement and stabilization of the buses, energy efficient utilization, and harmonic distortion reduction in a distribution network. This method maintains the load voltage close to or equal to the nominal value in terms of various voltage disturbances such as balanced and unbalanced sag/swell, voltage imbalance, notching, different fault conditions as well as power system harmonic distortion. A grasshopper optimization algorithm (GOA) is used to tune the gain values of the PID controller. In order to validate the effectiveness of the proposed DVR controller, first, a fractional order PID controller was presented and compared with the proposed one. Further, a comparative performance evaluation of four optimization techniques, namely Cuckoo search (CSA), GOA, Flower pollination (FBA), and Grey wolf optimizer (GWO), is presented to compare between the PID and FOPID performance in terms of fault conditions in order to achieve a global minimum error and fast dynamic response of the proposed controller. Second, a comparative analysis of simulation results obtained using the proposed controller and those obtained using an active disturbance rejection controller (ADRC) is presented, and it was found that the performance of the optimal PID is better than the performance of the conventional ADRC. Finally, the effectiveness of the presented DVR with the controller proposed has been assessed by time-domain simulations in the MATLAB/Simulink platform. • We present a low complexity voltage control scheme for effective control of a DVR. • The control scheme utilizes an error-driven PID controller. • Various voltage disturbances are considered. • FOPID and ADRC controllers are presented and compared with the proposed controller. • Performance of the optimal PID outperforms performance of the other controllers. [ABSTRACT FROM AUTHOR]

Additive Manufacturing (AM) is catching increased attention in the recent past due to its critical contributions in the 4th Industry revolution, commonly known as Industry 4.0. AM has come a long way from manufacturing proto parts to functionally capable parts with various enhancements to suit variety of applications. AM is proven to be the effective way to manufacture parts faster and economical than conventionally manufactured parts especially in low volume productions. This agility makes AM the most suited manufacturing technique for better integration between different industries and domains as the need for better collaboration increases. It's increased flexibility to manufacture functional parts is pushing the industry to go for 3D printed parts. As the skill requirements to design the components for AM is different than conventional manufacturing, product designers are facing increased challenges to design for AM. Printing and post processing methodologies have close connection with quality of parts. This research article analyzes various aspects right from the importance of Design for AM (DfAM), material consumption and quality of the parts. This article also talks about the importance of print and part design optimization methodologies. [ABSTRACT FROM AUTHOR]

Summary: The loss of measurements used for controller scheduling or envelope protection in modern flight control systems due to sensor failures leads to a challenging fault‐tolerant control law design problem. In this article, an approach to design such a robust fault‐tolerant control system, including full envelope protections using multiobjective optimization techniques, is proposed. The generic controller design and controller verification problems are derived and solved using novel multiobjective hybrid genetic optimization algorithms. These algorithms combine the multiobjective genetic search strategy with local, single‐objective optimization to improve convergence speed. The proposed strategies are applied to the design of a fault‐tolerant flight control system for a modern civil aircraft. The results of an industrial controller verification and validation campaign using an industrial benchmark simulator are reported. [ABSTRACT FROM AUTHOR]

A step length adjustment (SLA) iterative algorithm was proposed for locating the minimum performance target point (MPTP) in the inverse reliability analysis. This paper elaborates SLA and two deliberately designed numerical examples are used to compare SLA with other algorithms appearing in recent literatures for locating MPTP. The results show that SLA is much more robust and efficient. Then SLA and sequential optimization and reliability assessment (SORA) are combined to solve reliability-based design optimization (RBDO) problems. In the reliability assessment of SORA, with the design obtained from the previous cycle, SLA is used to locate MPTP. Then in the deterministic optimization, the boundaries of violated constraints are shifted to the feasible direction according to the MPTP obtained in the reliability assessment. Several examples frequently cited in similar studies are used to compare SORA-SLA with other RBDO algorithms. The results indicate the effectiveness and robustness of SORA-SLA. [ABSTRACT FROM AUTHOR]

Semi-supervised classification is a hot topic in pattern recognition and machine learning. However, in presence of heavy noise and outliers, the unlabeled training data could be very challenging or even misleading for the semi-supervised classifier. In this paper, we propose a novel structure regularized self-paced learning method for semi-supervised classification problems, which can efficiently learn partially labeled training data sequentially from the simple to the complex ones. The proposed formulation consists of three components: a cost function defined by a mixture of losses, a functional complexity regularizer, and a self-paced regularizer; and the corresponding optimization algorithm involves three iterative steps: classifier updating, sample importance calculating, and pseudo-labeling. In the proposed method, the cost function for classifier updating and sample importance calculating is defined as a combination of the label fitting loss and manifold smoothness loss. Then, the importance of the pseudo-labeled and unlabeled samples is adaptively calculated by the novel cost. Unlabeled samples with high importance values are pseudo-labeled with their current predictions. In this way, labels are efficiently propagated from the labeled samples to the unlabeled ones in the robust self-paced manner. Experimental results on several benchmark data sets are provided to show the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

Objective: The goal of this paper was to optimize robust PID control for propofol anesthesia in children aged 5–10 years to improve performance, particularly to decrease the time of induction of anesthesia while maintaining robustness. Methods: We analyzed results of a previous study conducted by our group to identify opportunities for system improvement. Allometric scaling was introduced to reduce the interpatient variability and a new robust PID controller was designed using an optimization-based method. We evaluated this optimized design in a clinical study involving 16 new cases. Results: The optimized controller design achieved the performance predicted in simulation studies in the design stage. Time of induction of anesthesia was median [Q1, Q3] 3.7 [2.3, 4.1] min and the achieved global score was 13.4 [9.9, 16.8]. Conclusion: Allometric scaling reduces the interpatient variability in this age group and allows for improved closed-loop performance. The uncertainty described by the model set, the predicted closed-loop responses, and the predicted robustness margins are realistic. The system meets the design objectives of improved speed of induction of anesthesia while maintaining robustness and improving clinically relevant system behavior. Significance: Control system optimization and ongoing system improvements are essential to the development of a clinically relevant commercial device. This paper demonstrates the validity of our approach, including system modeling, controller optimization, and pre-clinical testing in simulation. [ABSTRACT FROM AUTHOR]

We propose an optimization for space-efficient implementations of explicit model-predictive controllers (MPC) for robust control of linear time-invariant (LTI) systems on embedded platforms. We obtain an explicitform robust model-predictive controller as a solution to a multi-parametric linear programming problem. The structure of the controller is a polyhedral decomposition of the control domain, with an affine map for each domain. While explicit MPC is suited for embedded devices with low computational power, the memory requirements for such controllers can be high. We provide an optimization algorithm for a mixed-precision implementation of the controller, where the deviation of the implemented controller from the original one is within the robustness margin of the robust control problem. The core of the mixed-precision optimization is an iterative static analysis that co-designs a robust controller and a low-bitwidth approximation that is statically guaranteed to always be within the robustness margin of the original controller. We have implemented our algorithm and show on a set of benchmarks that our optimization can reduce space requirements by up to 20.9% and on average by 12.6% compared to a minimal uniform precision implementation of the original controller. [ABSTRACT FROM AUTHOR]

• A novel concept of power-to-gas (P2G)-based virtual power plant (GVPP) is designed. • Power-gas-power effect of GVPP brought by P2G and gas storage tank is discussed. • A multi-objective flexible risk aversion model for GVPP operation is proposed. • Payoff table of optimization model is applied for multiple iterative weighting method. • Different operation cases for verifying the proposed operation strategy are defined. Power-to-gas (P2G) provides a new means for accommodating abandoned new energy that will support the optimal operation of virtual power plants (VPPs) in the future. In this study, a novel structure of a P2G-based virtual power plant (GVPP) is designed. A flexible risk aversion model for GVPP operation is proposed with two objectives—maximum operation profit and minimum operation risk. In the model, the conditional value at risk method and robust optimization theory are utilized to reflect uncertainty risks. To solve the multi-objective model, a solution algorithm was constructed for iteratively obtaining the optimal weight coefficient for transforming the multi-objective model into a single-objective model based on a payoff table and a rough set method. Four simulation cases were set for comparative analysis based on a nine-node energy hub system. The results show the following outcomes: (1) GVPP realizes the complementary utilization of distributed energy and forms a power-gas-power recycling mode, (2) the proposed model can provide an effective decision-making tool for different risk-attitude decision makers by setting a reasonable confidence level and robust coefficient, (3) P2G and price-based demand response (PBDR) improve the grid-connected space of clean energy, in particular, PBDR improves the flexibility of system operation and reduces operation risk, and (4) if the maximum emission trade allowance (META) is considered, P2G preferentially converts carbon dioxide into methane when the META is lower, while clean energy is preferentially used to satisfy load demand and the methane produced by P2G can be sold to the natural gas network when the META is higher. Overall, the proposed optimal decision model achieves the maximum utilization of clean energy to obtain higher economic benefits while rationally controlling operation risks; hence, providing reliable support for decision makers. [ABSTRACT FROM AUTHOR]

Summary: We introduce a new robust stability measure for systems with multiple pointwise delays, which is called smoothed spectral abscissa, consistently with the existing measure for delay‐free systems. Its main characteristics are that it is smooth with respect to the system parameters and it provides a trade‐off between the decay rate of the system solution and the H2 norm of a transfer matrix related with the system. The smoothed spectral abscissa is implicitly defined in terms of the H2 norm of an auxiliary system, and its computation is based on the so‐called delay Lyapunov matrix. We show that these features make the smoothed spectral abscissa suitable for the design of robust controllers by using standard gradient‐based optimization techniques and exploiting a novel characterization of the derivatives of the delay Lyapunov matrix with respect to the system parameters. [ABSTRACT FROM AUTHOR]

The position control and vibration suppression problems of the flexible solar array drive system containing uncertainty are considered in this paper. The uncertainty in system may be due to unknown parameters and external disturbance. The uncertainty bound can be described via a fuzzy set. In addition, there exists the flexible vibration in the system. A new optimal robust control approach with input shaping is proposed for the flexible solar array drive system. By designing the position command trajectory, the input shaper is proposed to suppress the flexible vibration. To enhance the position control performance, the optimal robust control is proposed by fuzzy description of the uncertainty bound. Neither the system nor the control is fuzzy if–then rule based. The global solution to this optimal design problem is demonstrated to be always existent and unique. The resulting control is able to guarantee the uniform boundedness and uniform ultimate boundedness of the system in the presence of uncertainty, while minimizing a fuzzy-based performance index associated with both the fuzzy performance and the control cost. In addition, the flexible vibration can be effectively suppressed. The novelty of this research is a systematic control approach by blending input shaping technology, control theory, fuzzy set theory, and optimization theory into an integrated framework, for solving the position control and vibration suppression problems of flexible solar array drive system with mismatched conditions. [ABSTRACT FROM AUTHOR]

This paper presents a fixture configuration verification methodology that takes into account dynamic machining conditions--including the effect of dynamic gravitational forces--in the verification process. The fixture verification system is modelled as a linear optimization problem with respect to minimum clamping forces. The method provides a simple and effective means for (a) verifying whether a particular fixturing configuration is valid with respect to locating stability, deterministic workpiece location, clamping stability and total restraint; (b) identifying which locator loses contact with the part for an invalid fixture configuration; (c) identifying which clamp needs to be replaced; and (d) determining the minimum clamping forces to restrain the piece during the entire machining process. Since a fixture configuration design is validated not only under a given cutting direction, but also under an inverse cutting direction, this allows designers to understand thoroughly whether the fixture configuration is valid and what the sufficient dynamic clamping forces are for the fixture system to withstand unpredicted machining forces over the entire machining time. Hence, it makes the verification system more robust and reliable. Two case studies are included to demonstrate the effectiveness and the capabilities of the methodology. [ABSTRACT FROM AUTHOR]

This paper is focused on a dual-loop current control method (grid current loop and fundamental current loop) for digitally controlled LCL-type shunt active power filters (APFs). Normally, a proportional-resonant (PR) unit is used as the fundamental current controller, where the proportional part of PR unit actually serves as the proportional feedback of inverter-side current and provides a certain degree of damping for LCL resonance. However, its valid damping region is only up to one-sixth of the sampling frequency (fs/6), which leads to less robustness to the grid impedance. To address this issue, a delay-compensation control link is proposed in this paper to replace the proportional part of the PR fundamental current controller and widen the effective damping region. As a result, the system robustness is improved without adding extra sensors or introducing an extra active damping loop. Theoretical analysis proves that it can obtain a wider damping region of (0, fs/4). Moreover, a systematic controller parameter design criterion is studied. In particular, a numerical optimization algorithm is developed to optimize damping property, and a design method based on root locus plot and Bode diagram is presented to enhance harmonic compensation accuracy. Finally, experimental results implemented on a 30 kVA APF prototype have validated the feasibility of the proposed current controller and parameter design criterion. [ABSTRACT FROM AUTHOR]

This paper proposes a new robustification strategy of a primary H ∞ controller based on a systematic selection of adequate fractional weights. Its robust performance (RP) margin is well enhanced with respect to unstructured multiplicative uncertainties presented in linear feedback systems. The proposed robustification strategy provides a robustified H ∞ controller when following proposed hierarchical control is well respected. First, the primary H ∞ controller is synthesized from solving a weighted-mixed sensitivity H ∞ problem using initial integer weights. Thus, an initial RP margin is obtained. Second, an automatic selection of adjustable fractional weights is performed by the particle swarm optimization algorithm, in which some proposed tuning rules are accordingly well satisfied. Third, frequency response data of these weights are computed and then fitted by corresponding approximated integer weights using a frequency identification technique. Finally, these weights reformulate a new weighted-mixed sensitivity problem. The optimal solution to this problem updates the previous initial RP margin. These last three steps are repeated as the updated RP margin is diminished. Otherwise, the proposed hierarchical control is achieved by selecting the best adjustable fractional weights, providing, therefore, the best approximated integer weights and leading, therefore, to the robustified H ∞ controller. In order to confirm the effectiveness of our proposed hierarchical control, primary and robustified H ∞ controllers are applied on a permanent magnet synchronous motor where its actual behavior is modeled by an unstructured multiplicative uncertain model. The results obtained are compared in frequency domains using the singular value plots of their sensitivity functions. Otherwise, the same results are compared in time domains using the Powersim ® software. [ABSTRACT FROM AUTHOR]

PID controller is the most popular controller in many applications because of many advantages such as its high efficiency, low cost, and simple structure. But the main challenge is how the user can find the optimal values for its parameters. There are many intelligent methods are proposed to find the optimal values for the PID parameters, like neural networks, genetic algorithm, Ant colony and so on. In this work, the PID controllers are used in three different layers for generating suitable control signals for controlling the position of the UAV (x,y and z), the orientation of UAV (θ, Ø and ψ) and for the motors of the quadrotor to make it more stable and efficient for doing its mission. The particle swarm optimization (PSO) algorithm is proposed in this work. The PSO algorithm is applied to tune the parameters of proposed PID controllers for the three layers to optimize the performances of the controlled system with and without existences of disturbance to show how the designed controller will be robust. The proposed controllers are used to control UAV, and the MATLAB 2018b is used to simulate the controlled system. The simulation results show that, the proposed controllers structure for the quadrotor improve the performance of the UAV and enhance its stability. [ABSTRACT FROM AUTHOR]

To achieve the state estimation of uncertain nonlinear systems, this paper proposes a novel optimal robust observer via the fuzzy bound information of the uncertainty. A robust observer scheme is first proposed to guarantee the uniform boundedness and uniform ultimate boundedness of the state estimation system regardless of the actual value of the uncertainty. To optimize the observer gain, a fuzzy set-theoretic-based optimal approach is then proposed by utilizing the fuzzy information of the uncertainty bound. The optimization problem is completely solved in analytic form. The resulting observer is able to guarantee the robustness of the state estimation system to the uncertainty, while minimizing an optimization index related to the state estimation performance and the observer cost. The novelty of this research is a creative optimal robust observer design by blending state estimation theory, fuzzy set theory, and optimization theory into an integrated framework. [ABSTRACT FROM AUTHOR]

• Studying service network design considering multiple types of services. • Proposing both deterministic and two-stage robust optimization formulations. • Implementing a column-and-constraint generation approach to solve the robust model. • The proposed algorithm outperforms the Benders decomposition method. • The diversification of service types reduces total cost and the number of vehicles. Integrated transportation systems providing multiple types of services are attracting increasing attention due to the diversification of demands. In this paper, we propose both deterministic and two-stage robust optimization formulations for the service network design problem considering multiple types of services. A probability-free uncertainty set is employed to deal with demand uncertainty in the proposed robust model. We implement a column-and-constraint generation approach to solve the robust model, which outperforms the Benders decomposition method. Comparative results indicate that it helps reduce the total cost and the number of vehicles to consider multiple service types in the network. [ABSTRACT FROM AUTHOR]

Highlights • A robust structured sparse sensing matrix consisting of a sparse matrix with a few non-zero entries per row and a base matrix with fast implementation. • Designed a robust structured sparse sensing matrix by minimizing the mutual coherence and a surrogate function for the sparse representation error. • Proposed an alternating minimization algorithm for solving the corresponding optimization problem. • Provided global sequence convergence analysis for the proposed algorithm. Abstract We consider designing a robust structured sparse sensing matrix consisting of a sparse matrix with a few non-zero entries per row and a dense base matrix for capturing signals efficiently. We design the robust structured sparse sensing matrix through minimizing the distance between the Gram matrix of the equivalent dictionary and the target Gram of matrix holding small mutual coherence. Moreover, a regularization is added to enforce the robustness of the optimized structured sparse sensing matrix to the sparse representation error (SRE) of signals of interests. An alternating minimization algorithm with global sequence convergence is proposed for solving the corresponding optimization problem. Numerical experiments on synthetic data and natural images show that the obtained structured sensing matrix results in a higher signal reconstruction than a random dense sensing matrix. [ABSTRACT FROM AUTHOR]

Highlights • We introduced an additional objective function of the ability of peak load regulation to deal with the reverse peak load regulation characteristic of wind power; • The novelty of the paper is to propose a novel multi-objective robust optimization model for unit commitment considering peak load regulation ability and temporal correlation of wind powers. • This paper combined Constraint-and-Column Generation and Normalized Normal Constraint to deal with the proposed multi-objective robust optimization problem. • The widely-used IEEE 118-bus test system is used to verify the proposed robust optimization model. Abstract With the increasing applications of wind energy & power technologies, the stochastic fluctuation and reverse peak load regulation characteristic of wind power brings great challenges to unit commitment of power systems. It is difficult to meet the demand of the peak load regulation with the wind power integration for the existing robust unit commitment models when only considering the cost. In order to solve this problem, an additional objective function of the ability of peak load regulation is constructed for unit commitment solutions. As a result, a novel multi-objective robust unit commitment model considering both the cost and peak load regulation is proposed. Moreover, probabilistic scenario analysis is applied to constraint the model of the fluctuant wind power, and temporal correlation of wind powers is also considered to further improve the economy in the long run. In order to deal with multi-objective problem for the robust optimization solutions, the above-mentioned problem is decomposed into two stages, i.e., a main problem and a subproblem. The main problem is to determine unit commitment and the subproblem is a "min–max optimization" one to obtain the unit outputs. Finally, the simulation analysis based on IEEE118 node system verified the robustness and the validity of the proposed model. [ABSTRACT FROM AUTHOR]

We develop search algorithms based on local search, and a matheuristic that solves a set of mixed integer programming models to improve the robustness of a set of solutions for an academic timetabling problem. The matheuristic uses the solution pool feature of CPLEX while solving two related MIP models iteratively. The solutions form a network (Akkan et al. in Eur J Oper Res 249(2):560-576, 2016. doi:10.1016/j.ejor.2015.08.047), in which edges are defined by the Hamming distance between pairs of solutions. This network is used to calculate a robustness measure, where disruption of a solution is assumed to occur when the time slot to which a team had been assigned is no longer feasible for that team and the heuristic response to this disruption is choosing one of the neighbors of the disrupted solution. Considering the objective function of the timetabling problem and this robustness measure results in a bi-criteria optimization problem where the goal is to improve the Pareto front by enlarging the network. We compare the performance of the heuristics on a set of random instances and seven semesters' actual data. These results show that some of the proposed local search algorithms and the matheuristic find high quality approximate Pareto fronts. Besides being one of the few timetabling algorithms in the literature addressing robustness, a key contribution of this research is the demonstration of the effectiveness of the matheuristic approach. By using this matheuristic approach, for any discrete optimization model that can be solved optimally or near-optimally in an acceptable time, researchers can develop a robustness improvement algorithm. [ABSTRACT FROM AUTHOR]

Abstract An extension of the well-known delayed resonator concept is proposed with the objective to enhance its robustness in vibration suppression under guaranteeing stability of the overall set up. The novel resonator feedback is based on an acceleration measurements passing through a delay of polynomial distribution. The feedback design is formulated as an optimization problem over the parameter set formed by the polynomial coefficients and the gain of the delay free part. The first objective is to minimize the sensitivity of the resonator performance with respect to variations of the excitation frequency, i.e. to widen its frequency stop-band centered at the nominal excitation frequency. The second, equally significant objective is to guarantee that this does not lead to instability of the overall mechanical system coupled with the absorber and to ensure sufficient stability margin. The arising non-convex and non-smooth optimization problem is widely discussed and a penalty method is developed, where the unconstrained problem in every iteration step is solved using available software tools for optimization and spectral design of time delay systems. The proposed design technique is validated by simulations for two case study examples. [ABSTRACT FROM AUTHOR]

Abstract In this paper, a novel fault detection method is developed based on robust characteristic dimensionality reduction (RCDR). The time-constrained sparse representation (TCSR) method is firstly introduced by considering the space and time characteristics of industrial process monitoring data simultaneously. It can remove space-related outliers, time-related outliers and noises by solving an optimization problem. Then, a new RCDR method is proposed, which fully utilizes the constructed robust adjacency graph and considers the data characteristics. Its scatter matrices are specially designed by consideration of the data characteristics of fault detection. The within-class scatter matrix only characterizes normal data set with a classic covariance matrix, while the inter-class scatter matrix characterizes the separability between normal data and fault data through a pre-defined scatter matrix. It is worth mentioning that our method does not make Gaussian assumptions about the distribution of the fault data, and the number of projection directions is not limited as well. The TCSR is also embedded into our proposed dimensionality reduction method, enabling it to handle the fault detection problem under strong disturbances. Simulations on Tennessee Eastman process (TEP) and a case study of electric multiple unit (EMU) braking system of high-speed trains fully demonstrate the effectiveness and applicability of our proposed fault detection method. Highlights • New time-constrained sparse representation method is put forward. • Novel robust characteristic dimensionality reduction method is proposed. • Online fault detection algorithm is developed and fault detectability is analyzed. • Experimental studies on TEP and EMU braking system validate the proposed methods. [ABSTRACT FROM AUTHOR]

This paper proposes to apply probabilistic classification technique to stochastic robust flight control design. Stochastic robust control design is an approach to optimize a flight controller based on Monte Carlo Evaluation. The region in the parameter space satisfying design requirements with high probability is estimated using Bayesian inference and is used to search the optimal design parameters. The approach has the potential to reduce computational load in stochastic optimization. It is applied to a simple example problem of flight control design and the result is promising. [ABSTRACT FROM AUTHOR]

Highlights • A robust PTC RD model based on equilibrium stage was developed for the first time. • Optimization of RD systems using the RD PTC model was robust and fast. • An RDWC was optimized using equation-oriented algorithm for the first time. • The bypass efficiency method was applied to optimize RD systems for the first time. • Three intrinsic properties of bypass efficiency method were introduced in this work. Abstract Reactive distillation has significant economic and environmental advantages compared to conventional processes. However, the optimal design of a reactive distillation system is far from mature. This work proposed a novel equation-oriented optimization framework based on a rigorous equilibrium stage model for the optimization of reactive distillation systems. A pseudo-transient continuation (PTC) reactive distillation model was developed to solve the convergence problem of simulations. The bypass efficiency method was incorporated into the PTC model to avoid the intractable mixed integer optimization. The developed model can be integrated well with a steady-state optimization algorithm assisted by PTC models. Two cases demonstrated that the proposed model and optimization framework were robust and fast. However, the bypass efficiency method caused physically meaningless solutions, but they were found to be convertible to physically meaningful solutions without influencing the accurate optimization of number of stages according to the intrinsic properties of the bypass efficiency method introduced in the current work. [ABSTRACT FROM AUTHOR]

Nature is rife with networks that are functionally optimized to propagate inputs to perform specific tasks. Whether via genetic evolution or dynamic adaptation, many networks create functionality by locally tuning interactions between nodes. Here we explore this behavior in two contexts: strain propagation in mechanical networks and pressure redistribution in flow networks. By adding and removing links, we are able to optimize both types of networks to perform specific functions. We define a single function as a tuned response of a single "target" link when another, predetermined part of the network is activated. Using network structures generated via such optimization, we investigate how many simultaneous functions such networks can be programed to fulfill. We find that both flow and mechanical networks display qualitatively similar phase transitions in the number of targets that can be tuned, along with the same robust finite-size scaling behavior. We discuss how these properties can be understood in the context of constraint-satisfaction problems. [ABSTRACT FROM AUTHOR]

Graphical abstract Highlights • A preventive crude oil scheduling method to handle ±10% demand fluctuation is developed. • The scheduling is performed to maximize the profit in single objective optimization. • Inter-period fluctuations in feed rate of crude distillation unit is additionally minimized in multi-objective optimization. • Four industrial-scale examples with time horizon of 3, 7, 14 and 20 days are solved. Abstract Crude oil supply about 33% of the total energy consumption worldwide and is predominantly (>50%) processed in marine access refineries. Therefore, crude oil scheduling which enables the efficient processing of the crude to increase the profitability is an important problem. It often becomes challenging due to the presence of combinatorial constraints, discrete variables and uncertainties. This study addresses the crude oil scheduling under commonly present demand uncertainty. A proactive two-stage approach has been developed to solve such optimization problems. A discrete-time model is used with structure adapted genetic algorithm (SAGA) for solving single- and multi-objective scheduling optimizations. In the first stage, an initial schedule is generated with the nominal parameters provided a priory. The same schedule is then checked and accepted in the second stage only if it is robust with respect to demand uncertainty. This method is applied to four different industrial size problems with scheduling horizon of 3, 7, 14 and 20 days. The objective function in the single objective formulation is the maximization of profit. However, in multi-objective optimization, an additional objective of minimization of fluctuation in crude oil supply to crude distillation units is used as it provides a better control and operability of the plant. The proposed method is successfully implemented for the above four different crude oil scheduling problems to generate the robust schedule. [ABSTRACT FROM AUTHOR]

Abstract A new model-reference data-driven approach is presented which uses the frequency response data of a system in order to avoid the problem of unmodeled dynamics associated with low-order parametric models. It is shown that a convex optimization problem can be formulated (in either the H ∞ , H 2 or H 1 sense) to shape the closed-loop sensitivity functions while guaranteeing the closed-loop stability. The effectiveness of the method is illustrated by considering several case studies where the proposed design scheme is applied in both simulation and to a power converter control system for a specific accelerator requirement at CERN. [ABSTRACT FROM AUTHOR]

This paper considers the dynamic output feedback robust model predictive control (MPC) for a system with both polytopic model parametric uncertainty and bounded disturbance. For this topic, the techniques for handling the unknown true state are crucial, and the strict guarantee of the input/output/state constraints requires replacing the true state by its bounds in the optimisation problems. Previously, in the separate works, we (i) gave the general polyhedral bound; (ii) proposed the general ellipsoidal bound; (iii) applied some special polyhedral bounds to tighten the ellipsoidal bound since the latter is crucial for guaranteeing recursive feasibility. In this paper, (i)-(iii) are unified, and the up-to-date least conservative treatment of the true state bound is given, so the control performance can be greatly improved. The contribution mainly lies in overcoming the difficulties in developing technical details for the unification. A numerical example is given to illustrate the effectiveness of the new method. [ABSTRACT FROM AUTHOR]

Many global optimization (GO) algorithms have been introduced in recent decades to deal with the Computationally Expensive Black-Box (CEBB) optimization problems. The high number of objective function evaluations, required by conventional GO methods, is prohibitive or at least inconvenient for practical design applications. In this work, a new Kriging-Bat algorithm (K-BA) is introduced for solving CEBB problems with further improved search efficiency and robustness. A Kriging surrogate model (SM) is integrated with the Bat Algorithm (BA) to find the global optimum using substantially reduced number of evaluations of the computationally expensive objective function. The new K-BA algorithm is tested and compared with other well-known GO algorithms, using a set of standard benchmark problems with 2 to 16 design variables, as well as a real-life engineering optimization application, to determine its search capability, efficiency and robustness. Results of the comprehensive tests demonstrated the suitability and superior capability of the new K-BA. [ABSTRACT FROM AUTHOR]