Strict Robustness Research Articles

Strict robustness to incomplete information

We study a strict version of the notion of equilibrium robustness by Kajii and Morris (Econometrica 65:1283–1309, 1997) that allows for a larger class of incomplete information perturbations of a given complete information game, where with high probability, players believe that their payoffs are close to (but may be different from) those of the complete information game. We show that a strict monotone potential maximizer of a complete information game is strictly robust if either the game or the associated strict monotone potential is supermodular, and that the converse also holds in all binary-action supermodular games.

Strict Robustness to Incomplete Information

Strict Robustness to Incomplete Information

Robust Refinement of Built-in Network Information System Based on Nonparametric Density Estimation

In the research process of robustness refinement solution of built-in information systems for electronic networks, there are too many factors related to robustness in the current system robustness design, and different factors have different influences on robustness. In stochastic programming problems, uncertain variables usually obey a certain probability distribution, but in real decision-making, these determined distributions are often unknown or we only know part of the information of the distributions, and distributed robust refinement solution is just an effective solution to solve uncertain problems. The robustness measurement solution of information systems for electronic networks is analyzed. The robust refinement of information system is deeply studied by nonparametric density estimation solution, which is based on the strict robustness requirements put forward by users. Based on the research results of interdependent network theory and aiming at “improving the robustness of electronic information system,” this paper makes an in-depth study on the robustness refinement strategy of power information system. The comparison between the companies that adopted the robust refinement of built-in information systems for electronic networks based on nonparametric density estimation and the companies that did not adopt it shows that the refinement rate of the companies that adopted it in the first three years was 82%, while that of the companies that did not adopt it was only 57%, and the overall misjudgment rate was 43%. Therefore, it is proved that using the proposed reliability refinement solution to optimize, the embedded system can improve the service life, modeling accuracy, and availability of the system and has certain practicability.

Strictly and [formula omitted]-robust counterparts of electricity market models: Perfect competition and Nash–Cournot equilibria

This paper mainly studies two topics: linear complementarity problems for modeling electricity market equilibria and optimization under uncertainty. We consider both perfectly competitive and Nash–Cournot models of electricity markets and study their robustifications using strict robustness and the Γ-approach. For three out of the four combinations of economic competition and robustification, we derive algorithmically tractable convex optimization counterparts that have a clear-cut economic interpretation. In the case of perfect competition, this result corresponds to the two classic welfare theorems, which also apply in both considered robust cases that again yield convex robustified problems. Using the mentioned counterparts, we can also prove the existence and, in some cases, uniqueness of robust equilibria. Surprisingly, it turns out that there is no such economic sensible counterpart for the case of Γ-robustifications of Nash–Cournot models. Thus, an analog of the welfare theorems does not hold in this case. Finally, we provide a computational case study that illustrates the different effects of the combination of economic competition and uncertainty modeling.

Finite-Time Stability of MIMO Nonlinear Systems Based on Robust Adaptive Sliding Control: Methodology and Application to Stabilize Chaotic Motions

This paper introduces a robust adaptive sliding mode control to solve a finite-time stability of the uncertain nonlinear systems with multiple inputs and multiple outputs (MIMO). The proposed algorithm guarantees a strict robustness and fast convergence of the system trajectories to zero in a finite time under the negative effects of uncertainties and/or external disturbances. The fundamental methodology is based on an improved modification of the super-twisting sliding technique to alleviate an undesirable influence of the chattering phenomenon. In addition, a nonlinear adaptive law is constructed to ensure a strict stability of the control system even without prior awareness of the upper bounds of uncertainties and disturbances. A general stability of the closed-loop disturbed MIMO nonlinear system is achieved by the Lyapunov theorem. Lastly, the proposed algorithm is applied to stabilize the typical chaotic behaviors of Duffing - Holmes system and Lorenz system. The advantages and effectiveness of the proposed method are clearly demonstrated through the results of numerical simulations compared with other existent methods.

Projection Modification Based Robust Adaptive Backstepping Control for Multipurpose Quadcopter UAV

In this paper, the robust adaptive control scheme based on backstepping technique is presented that improves the trajectory tracking performance of the quadrotor unmanned aerial vehicles (UAVs), specially tasked for supply, rescue and combat missions. The proposed control scheme is designed to estimate all the system parameters that may posses uncertainties and effectively rejects the completely unknown time varying external disturbances. The adaptive laws, derived through Lyapunov stability theorem are robustified by merging with derivative-integral (DI) term, resulting in rapid and accurate adaptation. In addition, to avoid parametric drift phenomenon, we introduce the projection modification (PM) in the designed DI-adaptive laws that ensures the closed-loop system signals bounded. The trajectory tracking and parameter estimation performance of the UAV in the presence of external disturbances, the payload pick up/drop off effect on altitude and recoil effect on attitude is analyzed by means of numerical simulations. The results validate strict robustness with extended applicability of proposed control scheme.

Robust Multi-Objective Optimization for EE-SE Tradeoff in D2D Communications Underlaying Heterogeneous Networks

In this paper, we concentrate on the robust multi-objective optimization (MOO) for the tradeoff between energy efficiency (EE) and spectral efficiency (SE) in device-to-device (D2D) communications underlaying heterogeneous networks (HetNets). Different from traditional resource optimization, we focus on finding robust Pareto optimal solutions for spectrum allocation and power coordination in D2D communications underlaying HetNets with the consideration of interference channel uncertainties. The problem is formulated as an uncertain MOO problem to maximize EE and SE of cellular users (CUs) simultaneously while guaranteeing the minimum rate requirements of both CUs and D2D pairs. With the aid of ε-constraint method and strict robustness, we propose a general framework to transform the uncertain MOO problem into a deterministic single-objective optimization problem. As exponential computational complexity is required to solve this highly non-convex problem, the power coordination and the spectrum allocation problems are solved separately, and an effective two-stage iterative algorithm is developed. Finally, simulation results validate that our proposed robust scheme converges fast and significantly outperforms the non-robust scheme in terms of the effective EE-SE tradeoff and the quality of service satisfying probability of D2D pairs.

Robust combinatorial optimization under convex and discrete cost uncertainty

In this survey, we discuss the state of the art of robust combinatorial optimization under uncertain cost functions. We summarize complexity results presented in the literature for various underlying problems, with the aim of pointing out the connections between the different results and approaches, and with a special emphasis on the role of the chosen uncertainty sets. Moreover, we give an overview over exact solution methods for NP-hard cases. While mostly concentrating on the classical concept of strict robustness, we also cover more recent two-stage optimization paradigms.

From buzz to bucks: The impact of social media opinions on the locus of innovation

Abstract Social media influences business practices such as innovation activities. This study is anchored in the theoretical paradigm of strategic information technology (IT) alignment and the literature on social media and its business value. We examine how the valence and volume of user-generated content (UGC) from social media influence firm-level innovation strategies. Based on an analysis of five years of panel data for 886 listed firms and their 6.2 million relevant microblogs, we observed three interesting results. First, the valence of social media UGC has a U-shaped relationship with firms’ innovation investments; and compared with neutral UGC, both negative and positive content lead to more innovation investment. Second, we found that this curvilinear relationship is mitigated as the volume of UGC increases. Third, we verified that increasing innovation investment improves firm performance. We then examined these findings using a series of strict robustness checks and discussed our study’s contribution to theory and practice.

Quadcopter Robust Adaptive Second Order Sliding Mode Control Based on PID Sliding Surface

We present a robust adaptive second-order sliding mode controller that rejects external disturbances and uncertainties to improve the tracking performance of attitude and altitude in a quadcopter based on a Proportional–Integral–Derivative sliding surface. The algorithm provides a rapid adaptation and strict robustness of the flight control for the vehicle under the effect of perturbations. The proposed controller design is based on the theory of second order sliding mode technique that eliminates the chattering phenomenon present in first-order sliding mode controllers. In addition, we derive an adaptive law from the Lyapunov stability to ensure the robust control for the quadcopter even without knowing the upper bound for disturbances. Applying the same external disturbances, we use a numerical simulation to compare our algorithm to recent alternatives, such as normal adaptive sliding mode control, super-twisting sliding mode control, modified super-twisting sliding mode control, and nonsingular terminal sliding mode control. The results demonstrate the effectiveness of our proposed algorithm.

Robust goal programming using different robustness echelons via norm-based and ellipsoidal uncertainty sets

The notion of robust goal programming (RGP) using cardinality-constrained robustness via interval-based uncertainty was first examined over a decade ago. Since then, the RGP methodology has not been widely researched, specifically when considering different uncertainty sets to implement. Within this context, this paper compares interval-based and norm-based uncertainty sets using cardinality-constrained robustness. Strict robustness using ellipsoidal uncertainty sets is also examined in the RGP realm. The aforementioned methods are demonstrated for a simple instance from the literature, and the results are summarized. Conclusions are made regarding the proposed RGP models when likened to a similar RGP model seen in the literature. Further, the suitability of each RGP model is offered when a decision maker's risk preference or computing availability are taken into consideration. Inferences are made regarding the effectiveness of each uncertainty set in the context of solutions that are relatively unaffected by data uncertainty – that is, robust solutions.

Robust storage loading problems with stacking and payload constraints

We consider storage loading problems where items with uncertain weights have to be loaded into a storage area, taking into account stacking and payload constraints. Following the robust optimization paradigm, we propose strict and adjustable optimization models for finite and interval-based uncertainties. To solve these problems, exact decomposition and heuristic solution algorithms are developed. For strict robustness, we also propose a compact formulation based on a characterization of worst-case scenarios. Computational results for randomly generated data with up to 300 items are presented showing that the robustness concepts have different potential depending on the type of data being used.

The robust knapsack problem with queries

We consider robust knapsack problems where item weights are uncertain. We are allowed to query an item to find its exact weight,where the number of such queries is bounded by a given parameter Q. After these queries are made, we need to pack the items robustly, i.e., so that the choice of items is feasible for every remaining possible scenario of item weights.The central question that we consider is: Which items should be queried in order to gain maximum profit? We introduce the notion of query competitiveness for strict robustness to evaluate the quality of an algorithm for this problem, and obtain lower and upper bounds on this competitiveness for interval-based uncertainty. Similar to the study of online algorithms, we study the competitiveness under different frameworks, namely we analyze the worst-case query competitiveness for deterministic algorithms, the expected query competitiveness for randomized algorithms and the average case competitiveness for known distributions of the uncertain input data. We derive theoretical bounds for these different frameworks and evaluate them experimentally. We also extend this approach to Γ-restricted uncertainties introduced by Bertsimas and Sim.Furthermore, we present heuristic algorithms for the problem. In computational experiments considering both the interval-based and the Γ-restricted uncertainty, we evaluate their empirical performance. While the usage of a Γ-restricted uncertainty improves the nominal performance of a solution (as expected), we find that the query competitiveness gets worse.

Generalized light robustness and the trade-off between robustness and nominal quality

Robust optimization considers optimization problems with uncertainty in the data. The common data model assumes that the uncertainty can be represented by an uncertainty set. Classic robust optimization considers the solution under the worst case scenario. The resulting solutions are often too conservative, e.g. they have high costs compared to non-robust solutions. This is a reason for the development of less conservative robust models. In this paper we extract the basic idea of the concept of light robustness originally developed in Fischetti and Monaci (Robust and online large-scale optimization, volume 5868 of lecture note on computer science. Springer, Berlin, pp 61–84, 2009) for interval-based uncertainty sets and linear programs: fix a quality standard for the nominal solution and among all solutions satisfying this standard choose the most reliable one. We then use this idea in order to formulate the concept of light robustness for arbitrary optimization problems and arbitrary uncertainty sets. We call the resulting concept generalized light robustness. We analyze the concept and discuss its relation to other well-known robustness concepts such as strict robustness (Ben-Tal et al. in Robust optimization. Princeton University Press, Princeton, 2009), reliability (Ben-Tal and Nemirovski in Math Program A 88:411–424, 2000) or the approach of Bertsimas and Sim (Oper Res 52(1):35–53, 2004). We show that the light robust counterpart is computationally tractable for many different types of uncertainty sets, among them polyhedral or ellipsoidal uncertainty sets. We furthermore discuss the trade-off between robustness and nominal quality and show that non-dominated solutions with respect to nominal quality and robustness can be computed by the generalized light robustness approach.

The Price of Strict and Light Robustness in Timetable Information

In timetable information in public transport the goal is to search for a good path between an origin and a destination. Usually, the travel time and the number of transfers will be minimized. In this paper, we consider robust timetable information; i.e., we want to identify a path that will bring the passenger to the planned destination even in the case of delays. The classic notion of strict robustness leads to the problem of identifying those transfer activities that will never break in any of the expected delay scenarios. We show that this is, in general, a strongly NP-hard problem. Therefore, we propose a conservative heuristic which identifies a large subset of these strictly robust transfer activities in polynomial time by dynamic programming and so allows us to efficiently find strictly robust paths. We also transfer the notion of light robustness, originally introduced for timetabling, to timetable information. In computational experiments we then study the price of strict and light robustness: how much longer is the travel time of a robust path than of a shortest one, according to the published schedule? Based on the 2011 train schedule within Germany, we quantitatively explore the trade-off between the level of guaranteed robustness and the increase in travel time. Strict robustness turns out to be too conservative, whereas light robustness is promising: a modest level of guarantees is achievable at a reasonable price for the majority of passengers.

Managing uncertainty and discontinuous condition numbers in geometric computation

We consider operations on subdivision surfaces under the strict robustness requirement that these floating-point computations return an object with the same topological form as the true solution. The problems involved may however be ill-conditioned, and defined in terms of uncertain data, and even supplementary interval arithmetic may not ensure robustness. Trapping mechanisms are therefore proposed to resolve this difficulty.

Controller performance assessment by frequency domain techniques

Abstract A system identification based method for assessing the performance of closed-loop systems is proposed, utilizing measures which coincide naturally with classical and modern frequency domain design specifications. Standard robust control system design methodologies seek to maximize closed-loop performance, subject to strict robustness requirements and include specifications for bandwidth and peak magnitude of the sensitivity and complementary sensitivity functions. Estimates of these transfer functions can be obtained by exciting the reference input with a zero mean, pseudo random binary sequence, observing the process output and error response, and developing a closed-loop model. Performance assessment is based on the comparison between the observed frequency response characteristics and the design specifications. Selection of appropriate model structures, experiment design, and model validation which will ensure reasonable estimates of the closed-loop transfer functions are considered in this paper. A case study involving the performance assessment of a packed bed tubular reactor control system is presented.

Robust strict positive real stabilization and asymptotic hyperstability robustness

Abstract This paper is devoted to the study of robust strict positive real stabilization of SISO uncertain systems, i.e. finding a single controller that not only robustly stabilizes a plant with uncertainties under unity-feedback but also makes the closed-loop system robustly strictly positive real. It is proved that there must exist a stable controller achieving robust strict positive real stabilization of uncertain systems with both parameter variations and unstructured uncertainties under some reasonable assumptions. The propemess of the controller is guaranteed when the largest relative degree of an uncertain system is retricted. By applying these results to nonlinear systems, some significant conclusions on asymptotic hyperstability robustness are given.