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In our study, we integrate the data uncertainty of real-world models into our regulatory systems and robustify them. We newly introduce and analyse robust time-discrete target–environment regulatory systems under polyhedral uncertainty through robust optimization. Robust optimization has reached a great importance as a modelling framework for immunizing against parametric uncertainties and the integration of uncertain data is of considerable importance for the model’s reliability of a highly interconnected system. Then, we present a numerical example to demonstrate the efficiency of our new robust regression method for regulatory networks. The results indicate that our approach can successfully approximate the target–environment interaction, based on the expression values of all targets and environmental factors. [ABSTRACT FROM AUTHOR]

In this paper, following the framework of robust optimization, we consider robust optimal solutions for a fractional optimization problem in the face of data uncertainty both in the objective and constraints. To this end, by using the properties of the subdifferential sum formulae, we first introduce some robust basic subdifferential constraint qualifications, and then obtain some completely characterizations of the robust optimal solutions of this uncertain fractional optimization problem. We show that our results encompass as special cases some optimization problems considered in the recent literature. Moreover, as applications, the proposed approach is applied to investigate weakly robust effcient solutions for multi-objective fractional optimization problems in the face of data uncertainty both in the objective and constraints. [ABSTRACT FROM AUTHOR]

A novel method to tune a Proportional–Integral (PI) compensator for an integrating plus dead time (IPDT) process, in presence of interval parametric uncertainty, is presented. The design is based on optimization of load disturbance rejection with constraints on the magnitude of the sensitivity and complementary sensitivity functions, that must be satisfied for any element belonging to a set of plants. Instead of solving this problem with a brute force approach (grid the uncertainty set), we prove that this problem can be solved by considering only two plants. That lets us to obtain a tuning rule, after using some approximations. To conclude, some examples will be given in order to elucidate the usefulness of the proposed tuning rule. [ABSTRACT FROM AUTHOR]

This paper investigates the problem of robust observer-based passive control for uncertain singular time-delay system subject to actuator saturation. A polytopic approach is used to describe the saturation behavior. First, by constructing Lyapunov-Krasovskii functional, a less conservative sufficient condition is obtained which guarantees that the closed-loop system is regular, impulse free, stable and robust strictly passive. Then, with this condition, the design method of state feedback controller and the observer are given by solving linear matrix inequalities. In addition, a domain of attraction in which the admissible initial states are ensured to converge asymptotically to the origin is solved as a convex optimization problem. Finally, some simulations are provided to demonstrate the effectiveness and superiority of the proposed method. [ABSTRACT FROM AUTHOR]

Consider the problem faced by a purchaser of solid waste management services, who needs to identify waste collection points, the assignment of waste generation points to waste collection points, and the type and number of receptacles utilized at each collection point. Receptacles whose collection schedule is specified in advance are charged a fixed fee according to the number of times the receptacle is serviced (emptied) per week. For other receptacles, the purchaser pays a fee comprised of a fixed service charge, plus a variable cost that is assessed on a per-ton-removed basis. We develop a mathematical programming model to minimize the costs that the purchaser pays to the waste management provider, subject to a level of service that is sufficient to collect all of the purchaser’s required waste. Examining historical data from the University of Missouri, we observed significant variability in the amount of waste serviced for nonscheduled receptacles. Because this variability has a significant impact on cost, we modified our model using robust optimization techniques to address the observed uncertainty. Our model’s highly robust solution, while slightly more expensive than the nonrobust solution in the most-optimistic scenario, significantly outperforms the nonrobust solution for all other potential scenarios. [ABSTRACT FROM AUTHOR]

In this paper, we develop a unified framework for studying constrained robust optimal control problems with adjustable uncertainty sets . In contrast to standard constrained robust optimal control problems with known uncertainty sets, we treat the uncertainty sets in our problems as additional decision variables. In particular, given a finite prediction horizon and a metric for adjusting the uncertainty sets, we address the question of determining the optimal size and shape of the uncertainty sets, while simultaneously ensuring the existence of a control policy that will keep the system within its constraints for all possible disturbance realizations inside the adjusted uncertainty set. Since our problem subsumes the classical constrained robust optimal control design problem, it is computationally intractable in general. Nevertheless, we demonstrate that by restricting the families of admissible uncertainty sets and control policies, the problem can be formulated as a tractable convex optimization problem. We show that our framework captures several families of (convex) uncertainty sets of practical interest, and illustrate our approach on a demand response problem of providing control reserves for a power system. [ABSTRACT FROM AUTHOR]

In this work, we consider the problem of daily production optimization in the upstream oil and gas domain. The objective is to find the optimal decision variables that utilize the production systems efficiently and maximize the revenue. Typically, mathematical models are used to find the optimal operation in such processes. However, such prediction models are subject to uncertainty that has been often overlooked, and the optimal solution based on nominal models can thus render the solution useless and may lead to infeasibility when implemented. To ensure robust feasibility, worst case optimization may be employed; however, the solution may be rather conservative. Alternatively, we propose the use of scenario-based optimization to reduce the conservativeness. The results of the nominal, worst case and scenario-based optimization are compared and discussed. [ABSTRACT FROM AUTHOR]

The problem of designing a globally optimal robust output feedback controller for time-varying polytopic uncertain systems is a well-known non-convex optimisation problem. In this paper, new sufficient conditions for both robustandswitching output-feedback control syntheses are proposed in terms of bilinear matrix inequalities (BMIs) under the multiple Lyapunov function framework. This set of synthesis conditions is further reduced to a special type of BMIs, which can be solved effectively using linear matrix inequality optimisation plus a line search. The associated robust output-feedback controller is constructed as a switching-type full-order dynamic output-feedback controller, consisting of a family of linear time-invariant subcontrollers and a min-switching logic. The proposed approach features the important property of computational efficiency with stringent performance. Its effectiveness and advantages have been demonstrated through extensive numerical studies. [ABSTRACT FROM PUBLISHER]

This paper considers minimum cost flow problem in dynamic networks with uncertain costs. First, we present a short introduction of dynamic minimum cost flow. Then, we survey discrete and continuous dynamic minimum cost flow problems, their properties and relationships between them. After that, the minimum cost flow problem in discrete dynamic network with uncertainty in the cost vector is considered such that the arc cost can be changed within an interval. Finally, we propose an algorithm to find the optimal solution of the proposed model. [ABSTRACT FROM AUTHOR]

To solve optimization problems with matrix uncertainty, a novel optimization approach is proposed based on chance-constrained and robust optimization, which focuses on constraints with continuous uncertainty, especially with matrix uncertainty. In chance-constrained approach, constraints with matrix uncertainty are always regarded as joint chance constraints, which can be simplified into individual chance constraints and can be further reformulated into algebraic constraints by robust methods. Motivated by reformulation of chance constraints with right-hand side uncertainty, a novel formulation of constraints with left-hand side uncertainty is proposed, where the uncertainty is described as intervals related to the confidence level of chance constraints. Through using kernel density estimation, confidence sets of uncertain parameters are built to approximate unknown true probability density functions. The approach is illustrated with a motivating and process industry scheduling example with energy consumption uncertainties. [ABSTRACT FROM AUTHOR]

This paper presents new results on linear transceiver designs in a multiple-input–multiple-output (MIMO) link. By considering the minimal total mean-square error (MSE) criterion, we prove that the robust optimal linear transceiver design has a channel-diagonalizing structure, which verifies the conjecture in the previous work. Based on this property, the original design problem can be transformed into a scalar problem, whose global optimal solution is first obtained in this work. Simulation results show the performance advantages of our solution over the existing schemes. [ABSTRACT FROM AUTHOR]

We propose an approach to the timing of markdowns in a continuous-time finite-horizon setting that does not require the precise knowledge of the underlying probabilities, instead relying on range forecasts for the arrival rates of the demand processes, and that captures the degree of the manager's risk aversion through intuitive budget of uncertainty functions. These budget functions bound the cumulative deviation of the arrival rates from their nominal values over the lengths of time for which a product is offered at a given price. A key issue is that using lengths of time as decision variables introduces non-convexities when budget functions are concave. In the single-product case, we describe a tractable and intuitive framework to incorporate uncertainty on customers' arrival rates, formulate the resulting robust optimization model, describe an efficient procedure to compute the optimal sale times, and provide theoretical insights. We then describe how to use the solution of the static robust optimization model to implement a dynamic markdown policy. We also extend the robust optimization approach to multiple products and suggest the idea of constraint aggregation to preserve performance for this type of problem structure. [ABSTRACT FROM AUTHOR]

Solving optimization problems under hybrid uncertainty bears a heavy computational burden. In this study, we propose a unified structured optimization approach, termed robust granular optimization (RGO), to tackle the optimization problems under hybrid manifold uncertainties in a computationally tractable manner. Essentially, the RGO can be regarded as a complementary fusion of granular computing and robust optimization techniques. The paradigm of RGO consists of three core phases: 1) uncertainty identification, 2) information granulation in which basic granular units (BGUs) are formed, and 3) robust optimization realized over the BGUs. Following the proposed paradigm, we develop two classes of RGO models for general single-stage and two-stage optimization problems with separable and higher order hybrid uncertainties, respectively. It is shown that both types RGO models can be equivalently transformed into linear programs or mixed integer linear programs that can be handled efficiently by off-the-shelf solvers. Furthermore, a target-based tradeoff model is developed to enhance the flexibility of the RGO models in balancing the granularity level (or robustness level) and the solution conservativeness. The tradeoff model can also be efficiently solved by a binary search algorithm. Finally, sufficient computational studies are presented, and comparisons with the existing approaches show that the RGO models can bring much higher computational efficiency and scalability without losing much optimality, and the RGO solutions exhibit a stronger resistance to the uncertainty. [ABSTRACT FROM PUBLISHER]

A robust congestion pricing (ROPRICE) of signal-controlled road network is considered for equilibrium network flow with uncertain travel demand. A min–max bi-level program is presented to mitigate vulnerability of area traffic control road network against growing travel demand and reduce traffic congestion. A cutting plane projection approach (CPP) is proposed to effectively solve the ROPRICE problem with global convergence. Numerical computations are performed using various test road networks and comparisons are made with recently proposed heuristics. Computational results indicate that the proposed solution scheme can substantially achieve greater system performance as compared to other alternatives. [ABSTRACT FROM AUTHOR]

Flooding is one of the leading causes of loss due to natural catastrophes, and at least one third of all losses due to natural forces can be attributed to flooding. Flood management systems involve a variety of complexities, such as multiple uncertainties, dynamic variations, and policy implications. This paper presents an inexact probabilistic–possibilistic programming with fuzzy random coefficients (IPP-FRC) model for flood management in a hybrid uncertain environment. IPP-FRC is capable not only of tackling multiple uncertainties in the form of intervals with fuzzy random boundaries but of addressing the dynamic complexity through capacity expansion planning within a multi-region, multi-flood-level, and multi-option context. The possibility and necessity measures used in IPP-FRC are suitable for risk-seeking and risk-averse decision making, respectively. A case study is used to demonstrate the applicability of the proposed methodology for facilitating flood management. The results indicate that the inexact degrees of possibility and necessity would decrease with increased probabilities of occurrence, implying a potential tradeoff between fulfillment of objectives and associated risks. A number of decision alternatives can be obtained under different policy scenarios. They are helpful for decision makers to formulate the appropriate flood management policy according to practical situations. The performance of IPP-FRC is analyzed and compared with a possibility-based fractile model. [ABSTRACT FROM AUTHOR]

We formulated a solution procedure for vehicle routing problems with uncertainty (VRPU for short) with regard to future demand and transportation cost. Unlike E-SDROA (expectation semideviation robust optimisation approach) for solving the proposed problem, the formulation focuses on robust optimisation considering situations possibly related to bidding and capital budgets. Besides, numerical experiments showed significant increments in the robustness of the solutions without much loss in solution quality. The differences and similarities of the robust optimisation model and existing robust optimisation approaches were also compared. [ABSTRACT FROM AUTHOR]

In this paper we provide a systematic way to construct the robust counterpart of a nonlinear uncertain inequality that is concave in the uncertain parameters. We use convex analysis (support functions, conjugate functions, Fenchel duality) and conic duality in order to convert the robust counterpart into an explicit and computationally tractable set of constraints. It turns out that to do so one has to calculate the support function of the uncertainty set and the concave conjugate of the nonlinear constraint function. Conveniently, these two computations are completely independent. This approach has several advantages. First, it provides an easy structured way to construct the robust counterpart both for linear and nonlinear inequalities. Second, it shows that for new classes of uncertainty regions and for new classes of nonlinear optimization problems tractable counterparts can be derived. We also study some cases where the inequality is nonconcave in the uncertain parameters. [ABSTRACT FROM AUTHOR]

Current naval shipowners are being forced to extend the service lives of their aging vessels from budgetary and political constraints. This is causing them to incur significant costs due to maintaining the structure of these older ships to keep the ships in operation. These increasing costs make it desirable to design new naval structures with their minimization in mind, as well as ensuring that such vessels are robust to changes in expected service life with respect to their total lifetime cost. However, such structures will necessarily have higher production costs, therefore, an optimization framework is presented to estimate both production and maintenance costs for a naval vessel's internal structure and develop trade-spaces between these two competing objectives in order to find designs that represent a balance of both. [ABSTRACT FROM AUTHOR]

Uncertainty is ubiquitous in practical engineering design applications. Recent years have witnessed a growing research interest in the study of structural topology optimization problems considering uncertainties. Most of these works, however, are focused on the optimization of macro-scale structures. In the present paper, robust concurrent optimization of material and structure under unknown-but-bounded load uncertainties is investigated in a multi-scale framework. Problem formulation that can allow for the effect of worst-case scenario in a confidence way and the corresponding numerical solution procedure are proposed. It is found that when load uncertainties are considered, optimal material distributions in microstructures tend to be isotropic and Kagome structure seems to be superior to other forms of microstructures. The conclusions drawn from the present work are helpful for manufacturing hierarchical structures with Additive Manufacturing technologies. [ABSTRACT FROM AUTHOR]

Info-Gap Decision Theory is adopted to assess the robustness of a technique aimed at identifying the optimal excitation signal to be used for active sensing approaches to damage detection. Here the term "active sensing" refers to procedures where a known input is applied to the structure to enhance the damage detection process. Given limited system response measurements and ever-present physical limits on the level of excitation, the ultimate goal of the mentioned technique is to improve the detectability of damage by increasing the difference between measured outputs of the undamaged and damaged systems. In particular, a two degree-of-freedom mass-spring-damper system characterized by the presence of a nonlinear stiffness is considered. Uncertainty is introduced to the system in the form of deviations of its parameters (mass, stiffness, damping ratio) from their nominal values. Variations in the performance of the mentioned technique are then evaluated both in terms of changes in the estimated difference between the responses of the damaged and undamaged systems and in terms of deviations of the identified optimal input signal from its nominal estimation. Finally, plots of the performances of the analyzed algorithm for different levels of uncertainty are obtained, enabling a clear evaluation of the risks connected with designing excitation signals for damage detection, when the parameters that dictate system behavior (e.g. stiffness, mass) are poorly characterized or improperly modeled. [ABSTRACT FROM AUTHOR]

A new approach to solving the robust topology optimization problem considering random field loading uncertainty was developed. The Karhunen-Loeve expansion was employed to characterize the random field as a reduced set of random variables. Efficient method of sensitivity analysis was developed and integrated into the density based topology optimization approach. The numerical example demonstrated the efficiency of the proposed approach and the effect of loading uncertainty on the robust design results. [ABSTRACT FROM AUTHOR]

In this paper, we consider the multi-facility Weber location problem (MFWP) with uncertain location of demand points and transportation cost parameters. Equivalent formulations of its robust counterparts for both the Euclidean and block norms and interval and ellipsoidal uncertainty sets are given as conic linear optimization problems. [ABSTRACT FROM AUTHOR]

Despite studies that consider service level rates of individual factories in a supply chain system, the interactions between connected factories and the impact of these interactions on the overall supply chain service level rate have been rarely studied. Moreover, due to uncertainties induced by various sources such as transportation delay and manufacturing processes variability, ensuring the robustness of system service level rate while considering these uncertainties in individual factories is a highly complex task. This paper studies uncertainty effect introduced by factory service level rates on the robustness of overall supply chain network performance, and presents a novel robust design optimization methodology to derive designs of factory service level rates in order to satisfy the service level rate requirement of the system and ensure its robustness. A case study with a multi-level multiple factories supply chain network is used to demonstrate the efficacy of the proposed methodology. [ABSTRACT FROM AUTHOR]

This paper investigates the problem of the sampled-data extended dissipative control for uncertain Markov jump systems. The systems considered are transformed into Markov jump systems with polytopic uncertainties and sawtooth delays by using an input delay approach. The focus is on the design of a mode-independent sampled-data controller such that the resulting closed-loop system is mean-square exponentially stable with a given decay rate and extended dissipative. A novel exponential stability criterion and an extended dissipativty condition are established by proposing a new integral inequality. The reduced conservatism of the criteria is demonstrated by two numerical examples. Furthermore, a sufficient condition for the existence of a desired mode-independent sampled-data controller is obtained by solving a convex optimisation problem. Finally, a resistance, inductance and capacitance (RLC) series circuit is employed to illustrate the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

Highlights: [•] We develop an approach to robust topology optimization under loading uncertainty. [•] We model loading uncertainty by the distribution of their magnitude and direction. [•] The effects of loading uncertainty on optimization results are demonstrated. [ABSTRACT FROM AUTHOR]

In this paper, we present a duality theory for fractional programming problems in the face of data uncertainty via robust optimization. By employing conjugate analysis, we establish robust strong duality for an uncertain fractional programming problem and its uncertain Wolfe dual programming problem by showing strong duality between the deterministic counterparts: robust counterpart of the primal model and the optimistic counterpart of its dual problem. We show that our results encompass as special cases some programming problems considered in the recent literature. Moreover, we also show that robust strong duality always holds for linear fractional programming problems under scenario data uncertainty or constraint-wise interval uncertainty, and that the optimistic counterpart of the dual is tractable computationally. [ABSTRACT FROM AUTHOR]

SUMMARY We show how to introduce the Value at Risk (VaR) concept in optimization algorithms with emphasis in calculation complexity issues. To do so, we assume known the PDF of the uncertainties. Our aim is to quantify our confidence on the optimal solution at low complexity without sampling of the control space. The notion of over-solving appears naturally where it becomes useless to solve accurately near an optimum when the variations in control parameters fall below the uncertainties. Examples show the behavior of this VaR-based correction and link the approach to momentum-based optimization where the mean and variance of a functional are considered. The approach is then applied to an inverse problem with fluids with uncertainties in the definition of the injection devices. It is shown that an optimization problem with an admissible solution in the control space in the deterministic case can lose its solution in the presence of uncertainties on the control parameters, which suggests that the control space itself should be redefined in such a situation to recover an admissible problem. This permits to evaluate the cost of making reliable a system that has been deterministically designed but has uncertain parameters. A shape optimization problem closes the paper showing the importance of including VaR information during the design iterations and not only at the end of the procedure. Copyright © 2013 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Highlights: [•] We explored dynamic-optimization for managing goose harvests in western Europe. [•] We considered nine alternative population models. [•] A strategy robust to model uncertainty assumed all models were equally likely. [•] Reducing model uncertainty would produce a marginal gain in management performance. [Copyright &y& Elsevier]

Abstract: The paper presents a bi-objective robust program to design a cost-responsiveness efficient emergency medical services (EMS) system under uncertainty. The proposed model simultaneously determines the location of EMS stations, the assignment of demand areas to EMS stations, and the number of EMS vehicles at each station to balance cost and responsiveness. We develop a robust counterpart approach to cope with the uncertain parameters in the EMS system. Extensive numerical studies are performed to demonstrate the benefits of our robust optimization approach. [Copyright &y& Elsevier]

Abstract: The data of real-world optimization problems are usually uncertain, that is especially true for early stages of system design. Data uncertainty can significantly affect the quality of the nominal solution. Robust Optimization (RO) methodology uses chance and robust constraints to generate a robust solution immunized against the effect of data uncertainty. RO methodology can be applied to any generic optimization problem where one can separate uncertain numerical data from the problem's structure. Since 2000, the RO area is witnessing a burst of research activity in both theory and applications. However, RO could lead to over-conservative requirements, resulting in typical-case bad solutions or even empty solution spaces. This drawback of the classical RO methodology can be overcome by distinguishing between real decision variables and so-called state variables. While the first type should satisfy the chance or robust constraints and their value cannot depend on a specific realization of the uncertain data, the state variables are adjustable (i.e., their value can depend on the specific realization of the uncertain data), since most of the constraints defining state variables merely “calculate” their exact value, and hence are always satisfied. In this paper we summarize how adjustable RO approach can be applied to a general uncertain linear optimization problem. Then, using an allocation example we demonstrate how this approach can be integrated in the design optimization process and its impact on the optimal system design. [Copyright &y& Elsevier]

As amajor energy-saving industry, power industry has implemented energy-saving generation dispatching. Apart from security and economy, low carbon will be the most important target in power dispatch mechanisms. In this paper, considering a power system with many thermal power generators which use different petrochemical fuels (such as coal, petroleum, and natural gas) to produce electricity, respectively, we establish a self-scheduling model based on the forecasted locational marginal prices, particularly taking into account CO2 emission constraint, CO2 emission cost, and unit heat value of fuels. Then, we propose a distributionally robust self-scheduling optimizationmodel under uncertainty in both the distribution formand moments of the locational marginal prices, where the knowledge of the prices is solely derived from historical data. We prove that the proposed robust self-scheduling model can be solved to any precision in polynomial time. These arguments are confirmed in a practical example on the IEEE 30 bus test system. [ABSTRACT FROM AUTHOR]

Under a genal affine data perturbation uncertainty set, we propose a computationally tractable robust optimization method for minimizing the CVaR of a portfolio. Using L1 norm, the robust counterpart problem can be a linear programming problem. Moreover, it is less conservative than the Quaranta and Zaffaroni's method which is under box uncertainty set. We present some numerical experiments with real market data to illustrate the behavior of robust optimization model. [ABSTRACT FROM AUTHOR]

Grain transportation plays an important role in many relief and emergency supply chains. In this paper, we take the grain emergency vehicle scheduling model between multiware houses as the research object. Under the emergency environment, the aim of the problem is to maximize the utilization of vehicles and minimize the delay time. The randomness of the key parameters in grain emergency vehicle scheduling, such as time and demand, is determined through statistical analysis and the model is solved through robust optimization method. Besides, we apply the numerical examples for experimental analysis. We compare the robust optimization model with classic model to illustrate the differences and similarities between them. The results show that the uncertainty of both time and demand has great influence on the efficiency of grain emergency vehicle scheduling problem. [ABSTRACT FROM AUTHOR]

Abstract: Constructing a reliable model for process monitoring, control and optimization requires accurate data satisfying balance equations of absolute validity, such as mass and energy balances. Under normal circumstances, process data are inaccurate since they are affected by random errors and possibly gross errors. A robust estimator for data reconciliation is needed to reduce the effect of gross errors and to yield less biased estimates, but most of the estimators are not robust enough to deal with gross errors. A novel robust estimator using correntropy, an information theoretic alternative to the traditional mean square error criterion, is proposed. As correntropy measures both the uncertainty and dispersion, it can be used as an optimality criterion in the estimation problems. By properly adjusting its kernel width, the effectiveness of this correntropy estimator can be tuned. The optimal kernel width value is chosen by minimizing Aikake information criterion. The results of two case studies demonstrate the advantages of using the correntropy estimator. The effectiveness of the proposed estimator is compared to several conventional methods, especially the quasi-weight least squares estimator, which does not have much computation load. [Copyright &y& Elsevier]

Abstract: In this paper, 1 [1] Part of the algorithm in this paper has been presented in IEEE ISIT’2008 [1]. we examine the problem of robust power control in a downlink beamforming environment under uncertain channel state information (CSI). We suggest that the method of power control using the lower bounds of signal-to-interference-and-noise ratio (SINR) is too pessimistic and will require significantly higher power in transmission than is necessary in practice. Here, a new robust downlink power control solution based on worst-case performance optimization is developed. Our approach employs the explicit modeling of uncertainties in the downlink channel correlation (DCC) matrices and optimizes the amount of transmission power while guaranteeing the worst-case performance to satisfy the quality of service (QoS) constraints for all users. This optimization problem is non-convex and intractable. In order to arrive at an optimal solution to the problem, we propose an iterative algorithm to find the optimum power allocation and worst-case uncertainty matrices. The iterative algorithm is based on the efficient solving of the worst-case uncertainty matrices once the transmission power is given. This can be done by finding the solutions for two cases: (a) when the uncertainty on the DCC matrices is small, for which a closed-form optimum solution can be obtained and (b) when the uncertainty is substantial, for which the intractable problem is transformed into a convex optimization problem readily solvable by an interior point method. Simulation results show that the proposed robust downlink power control using the approach of worst-case performance optimization converges in a few iterations and reduces the transmission power effectively under imperfect knowledge of the channel condition. [Copyright &y& Elsevier]

In this paper, we propose a duality theory for semi-infinite linear programming problems under uncertainty in the constraint functions, the objective function, or both, within the framework of robust optimization. We present robust duality by establishing strong duality between the robust counterpart of an uncertain semi-infinite linear program and the optimistic counterpart of its uncertain Lagrangian dual. We show that robust duality holds whenever a robust moment cone is closed and convex. We then establish that the closed-convex robust moment cone condition in the case of constraint-wise uncertainty is in fact necessary and sufficient for robust duality. In other words, the robust moment cone is closed and convex if and only if robust duality holds for every linear objective function of the program. In the case of uncertain problems with affinely parameterized data uncertainty, we establish that robust duality is easily satisfied under a Slater type constraint qualification. Consequently, we derive robust forms of the Farkas lemma for systems of uncertain semi-infinite linear inequalities. [ABSTRACT FROM AUTHOR]

Abstract: One of the problems encountered in the design of manufacturing systems is how to arrange the machines on the surface of the workshop, which is commonly referred to as a layout problem. Such a problem has been widely investigated in the literature. Most approaches use optimization technique to determine the position of each facility, assuming that the required data is available. Unfortunately, this assumption is often unrealistic, since the study design of a workshop is obviously conducted much before it is operating, so that data related to customer demands, for example, is generally not known with enough precision. Indeed, if good forecasts about what is to be produced in the next weeks can be available, they will obviously become more and more unreliable as the considered period of time will increase, so that layout found using classical approaches can turn out not to be relevant on the medium or long term. We propose an approach to design a robust layout in a context where the certainty of the information available decreases over time, which is usually the case for real applications. We propose a resolution approach based on a fuzzy evolutionary algorithm, which includes uncertain customer demands for each product. We show how this problem can be stated as a fuzzy dynamic layout problem with growing uncertainty over time. We suggest an evolutionary algorithm with adapted operators. Their performances are first tested using 2crisp layout problems already published. Then the impact of increasing uncertainty is studied using a suggested benchmark. The results of our experiments show the importance of considering the degradation of the information for designing robust layouts. [Copyright &y& Elsevier]

Considering the load frequency control (LFC) of large-scale power system, a robust distributed model predictive control (RDMPC) is presented. The system uncertainty according to power system parameter variation alone with the generation rate constraints (GRC) is included in the synthesis procedure. The entire power system is composed of several control areas, and the problem is formulated as convex optimization problem with linear matrix inequalities (LMI) that can be solved efficiently. It minimizes an upper bound on a robust performance objective for each subsystem. Simulation results showgood dynamic response and robustness in the presence of power system dynamic uncertainties. [ABSTRACT FROM AUTHOR]

Abstract: This paper presents a novel model for designing a reliable network of facilities in closed-loop supply chain under uncertainty. For this purpose, a bi-objective mathematical programming formulation is developed which minimizes the total costs and the expected transportation costs after failures of facilities of a logistics network. To solve the model, a new hybrid solution methodology is introduced by combining robust optimization approach, queuing theory and fuzzy multi-objective programming. Computational experiments are provided for a number of test problems using a realistic network instance. [Copyright &y& Elsevier]

Abstract: The robust delay-dependent control for an uncertain switched system with sampled-data input is investigated in this paper. The design of the sampled-data state feedback control technique is based on a computer digital control theory and used instead of analog elements. Hence designing a practical and useful feedback control strategy is a very important work in implementation. The time-varying delay approach is used to deal the sampled-data state feedback input problem. The upper bound for the sampled time of state is estimated from the proposed LMI optimization approach. A numerical example is illustrated to show the use of the main results. [Copyright &y& Elsevier]

Abstract: In this paper, we present the synthesis of a robust controller for Linear Time Invariant (LTI) uncertain systems. A linear parametric uncertainties model is used to describe the system dynamic behavior. The main purpose of this controller is to guarantee some step response performances such as the settling time and the overshoot. The controller synthesis is formulated as a min–max optimization problem which takes in account the desired closed-loop performances and the uncertainties on the model parameters. Then the controller parameters represent the best solution for the worst case of all possible models. In order to emphasize its performances and its efficiency, a real time implementation of the proposed controller on a laboratory pilot plant has been presented. [Copyright &y& Elsevier]

This correspondence addresses the analysis of the steady states of uncertain genetic regulatory networks (GRNs). The uncertainty is represented as a vector constrained in a given set that affects the coefficients of the mathematical model of the GRN. It is shown how regions containing all possible steady states can be estimated via an iterative strategy that progressively splits the concentration space into smaller sets, discarding those that are guaranteed not to contain equilibrium points of the considered model. This strategy is based on worst case evaluations of some appropriate functions of the uncertainty via linear matrix inequality optimization. [ABSTRACT FROM PUBLISHER]

Abstract: This paper investigates the problem of robust finite frequency (FF) filtering for two-dimensional (2-D) Roesser models with polytopic uncertainties. Our attention is focused on designing filters guaranteeing the robustly asymptotic stability and FF disturbance attenuation level of the filtering error system. By the parameter-dependent idea and the generalized Kalman–Yakubovich–Popov lemma for 2-D Roesser models, the existence conditions of robust FF filters are obtained in terms of solving an optimization problem, which is more general than the existing results. An example is given to validate the proposed methods. The contribution of the paper is twofold: (1) systematic methods are proposed for designing FF filters for Roesser models; (2) an improved strategy has been presented to deal with the robust filter design for Roesser models. [Copyright &y& Elsevier]

Abstract: In this paper, we investigate the problem of synthesizing performance weights and a controller that maximize the level of robust performance for a plant subject to both complex and real uncertainties. In particular, in this work the formulation proposed in and is manipulated in order to include the possibility to handle both real and complex uncertainties. Additionally, we introduce a novel solution algorithm that presents performance and computational advantages with respect to those described in and . [Copyright &y& Elsevier]

Estimation errors in both the expected returns and the covariance matrix hamper the construction of reliable portfolios within the Markowitz framework. Robust techniques that incorporate the uncertainty about the unknown parameters are suggested in the literature. We propose a modification as well as an extension of such a technique and compare both with another robust approach. In order to eliminate oversimplifications of Markowitz' portfolio theory, we generalize the optimization framework to better emulate a more realistic investment environment. Because the adjusted optimization problem is no longer solvable with standard algorithms, we employ a hybrid heuristic to tackle this problem. Our empirical analysis is conducted with a moving time window for returns of the German stock index DAX100. The results of all three robust approaches yield more stable portfolio compositions than those of the original Markowitz framework. Moreover, the out-of-sample risk of the robust approaches is lower and less volatile while their returns are not necessarily smaller. [ABSTRACT FROM AUTHOR]

This study investigates the robust quantised H∞ control problem for active suspension systems. First, based on the half-vehicle suspension model, the dynamical system with polytopic parameter uncertainties, which are caused by vehicle load variation, is established. In the meanwhile, the active suspension system performance, namely ride comfort, road holding and suspension deflection, are taken into account for the control design aim. Secondly, an input delay approach is utilised to transform the resulting active vehicle suspension system with sampling and quantisation measurements into a continuous-time system with a delay in the input sector bound uncertainty. Thirdly, robust quantised H∞ performance analysis and controller synthesis criteria are presented in the form of convex optimisation problem by exploiting the Lyapunov functional approach. The existing robust quantised H∞ controller condition not only guarantees the robust asymptotical stability of the closed-loop system, but also satisfies the output constrained performance. Finally, the effectiveness and application of the proposed method can be demonstrated by providing a design example. [ABSTRACT FROM AUTHOR]

Abstract: Since the yield condition for frame structures is non-linear, piecewise linear approximations are needed in order to apply linear optimization methods. Four approaches are presented and compared. After the theoretical consideration and comparison of the different approximation methods, they are applied to the robust design of an 18-bar frame in case of uncertainty. Here, the less restrictive methods yield the cheapest design, as expected. It will be shown, that the approximation from inside of first level does not cause much higher costs than the other methods. But since its constraints are sufficient in contrast to other approximations, it is recommended. [Copyright &y& Elsevier]

Abstract: Conventional super-efficiency data envelopment analysis (DEA) models require the exact information of inputs or outputs. However, in many real world applications this simple assumption does not hold. Stochastic super-efficiency is one of recent methods which could handle uncertainty in data. Stochastic super-efficiency DEA models are normally formulated based on chance constraint programming. The method is used to estimate the efficiency of various decision making units (DMUs). In stochastic chance constraint super-efficiency DEA, the distinction of probability distribution function for input/output data is difficult and also, in several cases, there is not enough data for estimating of distribution function. We present a new method which incorporates the robust counterpart of super-efficiency DEA. The perturbation and uncertainty in data is assumed as ellipsoidal set and the robust super-efficiency DEA model is extended. The implementation of the proposed method of this paper is applied for ranking different gas companies in Iran. [Copyright &y& Elsevier]

Abstract: In this paper, we present a new robust iterative learning control (ILC) design for a class of linear systems in the presence of time-varying parametric uncertainties and additive input/output disturbances. The system model is described by the Markov matrix as an affine function of parametric uncertainties. The robust ILC design is formulated as a min–max problem using a quadratic performance criterion subject to constraints of the control input update. Then, we propose a novel methodology to find a suboptimal solution of the min–max optimization problem. First, we derive an upper bound of the worst-case performance. As a result, the min–max problem is relaxed to become a minimization problem in the form of a quadratic program. Next, the robust ILC design is cast into a convex optimization over linear matrix inequalities (LMIs) which can be easily solved using off-the-shelf optimization solvers. The convergences of the control input and the error are proved. Finally, the robust ILC algorithm is applied to a physical model of a flexible link. The simulation results reveal the effectiveness of the proposed algorithm. [Copyright &y& Elsevier]

Abstract: In this work the input amplitude saturation problem is analysed in the Quantitative Feedback Theory (QFT) framework. This paper reviews previous works in the literature dealing with the input amplitude saturation problem in the presence of an uncertain plant in the frequency domain using QFT. The objective of this paper is to compare the different available approaches and summarize the design process for each case so that this paper can be used as a tutorial; there are six main approaches to this problem. Two of these approaches use the classical two degrees of freedom control scheme for QFT; in both of these, the design constraints of a linear QFT compensator are added in the loop shaping stage: they are added in the first approach to avoid excitation of the actuator saturation and in the second one to guarantee global stability. The other three techniques are considered as anti-windup (AW) approaches. Starting from a base design in QFT with two degrees of freedom, the first AW approach introduces a third degree of freedom that guarantees the stability of the system, allowing for base designs for high performance. The other two AW approaches also introduce a third degree of freedom, but they take simple stability considerations into account and focus on the performance of the system. The last solution consists of using a reference governor technique, which guarantees the computation of a reference signal for an inner control loop that is shaped using QFT in such a way that robust stability will be guaranteed. The reference governor technique is a time domain approach that implies the resolution of an optimization problem. The rest of the approaches are frequency domain techniques based on a loop shaping method in the traditional QFT sense. [Copyright &y& Elsevier]