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A non-fragile robust model predictive control (RMPC) is designed in the uncertain systems under bounded control signals. To this aim, a class of the nonlinear systems with additive uncertainty is considered in its general form. The RMPC synthesis could lead to the proper selection of the controller's gains. Thus, the non-fragile RMPC design is translated into a minimization problem subjected to some constraints in terms of linear matrix inequality (LMI). Hence, the controller's gains are computed by solving such a minimization problem. In some numerical examples, the suggested non-fragile RMPC is compared with the other methods. The simulation results demonstrate the effectiveness of the proposed RMPC in comparison with similar techniques. • An uncertain system is described via the general form of the additive uncertainty. • The controller constraints and fragility are simultaneously concerned in RMPC design. • Non-fragile RMPC is translated into a minimization problem subjected to some LMIs. • The examples show effectiveness of the proposed method over the similar techniques. [ABSTRACT FROM AUTHOR]

• Systematically dealing with mismatch between a process model and the true plant. • Ensuring recursive feasibility and stability of SMPC when the process operating point is changed, for example, due to economic considerations. • Guaranteeing offset-free tracking for all operating points. This paper presents a stochastic-tube model predictive control (MPC) strategy that systematically handles plant-model mismatch, guarantees stability in the presence of changing operating conditions, and ensures offset-free tracking for all reachable operating conditions. The key notion of this work is to separate the system uncertainty into two distinct sources of additive bounded state error. The first source is a non-random uncertainty that represents mismatch between the linear model of the controller and the true plant (as well as other types of persistent disturbances). The second source represents random fluctuations due to either the intrinsic stochastic variability of the system, or exogenous disturbances. Recursive feasibility and stability of the stochastic-tube MPC strategy is guaranteed by defining the terminal invariant set to include the effect of changes in the steady-state operating conditions. Offset-free tracking is achieved with a disturbance estimator that can be tuned independently of the controller. To reduce the conservatism inherent to robust control performance, a new filter model for deterministic disturbances is proposed that predicts uncertainty in the future evolution of the disturbances based on a bound on how quickly the plant-model mismatch can vary. The stochastic-tube MPC strategy is demonstrated on two simulation case studies—a benchmark DC-DC converter and an industrially-motivated fluidized-bed catalytic cracking unit. [ABSTRACT FROM AUTHOR]

Abstract Robust constrained control of linear systems with parametric uncertainty and additive disturbance is addressed. The main contribution is the introduction of a mathematically rigorous and computationally tractable framework for stabilizing model predictive control with online parameter estimation to improve performance and reduce conservatism. Requirements for closed-loop stability and provable constraint satisfaction are considered separately, resulting in the use of online set-membership system identification combined with homothetic prediction tubes for robust constraint satisfaction, and an H ∞ optimal point estimate of the unknown parameters to achieve a finite closed-loop gain from the disturbance to the state. Extensions to time-varying parameters and persistently exciting inputs to guarantee parameter convergence are presented. A numerical example illustrates the proven properties and efficacy of the approach. [ABSTRACT FROM AUTHOR]

Abstract In this paper, we address the vibration abatement problem of a flexible riser system preceded by nonlinear input saturation characteristic and uncertainties of the system. By virtue of Lyapunov theory, auxiliary system and robust control strategy, a boundary robust adaptive anti-saturation control is developed to restrain the vibration, remove the nonlinear input saturation effects and compensate for the uncertainties of system parameters and boundary disturbance. Applying the rigorous analysis without simplifying or discretizing the partial differential equation dynamics, the controlled system is ensured to be uniformly bounded stable with the designed control law. In the end, simulation results are presented for control performance verification. Highlights • A boundary robust adaptive anti-saturation control is presented to suppress the riser's vibration. • The online updating laws are developed to compensate the uncertainties of system. • The auxiliary system is introduced to handle the input saturation. • The σ-modification is exploited to adjust the robustness of the system. • The stability of the closed-loop system is proved via rigorous Lyapunov analysis. [ABSTRACT FROM AUTHOR]

Abstract In this paper, the robust H ∞ filtering of polytopic uncertain stochastic systems is designed under quantized sampled outputs. An novel parameters-dependent time-scheduled Lyapunov functional is constructed using segmentation technology and linear interpolation. Based on this new Lyapunov functional and convex combination method, sufficient stochastic exponential stability criteria of the filtering error dynamics are proposed and a prescribed H ∞ performance level can be guaranteed by designing the stochastically stable filter. The better H ∞ performance can be obtained with a larger interval dividing parameter. A numerical example is provided to illustrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

Abstract This paper develops a robust gain-scheduled proportional–integral–derivative (PID) controller design method for a linear-parameter-varying (LPV) system with parametric uncertainty. It is recognized in the literature that the robust fixed-order controller design can be formulated as a feasibility problem of a bilinear matrix inequality (BMI) constraint. Unfortunately, the search for a feasible solution of a BMI constraint is an NP hard problem in general. Previous researchers have applied a linearization method, such as a variable change technique or a congruence transformation, to transform the BMI into a LMI. The applicability of the linearization method depends on the specific structure of the problem at hand and cannot be generalized. This paper instead formulates the gain-scheduled PID controller design as a feasibility problem of a quadratic matrix inequality (QMI) constraint, which covers the BMI constraint as a special case. An augmented sequential LMI optimization method is proposed to search for a feasible solution of the QMI constraint iteratively. As an illustrative application, a vehicle lateral control problem is presented to demonstrate the applicability of the proposed algorithm to a real-world output feedback control design system. [ABSTRACT FROM AUTHOR]

Abstract The augmented state robust regularized least-squares filter (ASRRLSF) and two-stage robust regularized least-squares filter (TSRRLSF) are proposed for discrete time-varying nonlinear systems with unknown inputs and norm-bounded uncertainties. Unknown inputs affect both state-space model and measurements equation of the system. Combining system states and unknown inputs as an augmented state, the ASRRLSF is developed by converting a deterministic min–max optimization problem to a robust regularized least-squares problem. If dimension of the augmented state increases, the performance of the proposed ASRRLSF will reduce and the computational cost will increase rapidly. Therefore, in the following, the TSRRLSF is proposed by decoupling the ASRRLSF to lower order filters as system states filter and unknown inputs filter using T transformation. Finally, two numerical examples are given in order to illustrate the performance of the proposed filtering approaches. [ABSTRACT FROM AUTHOR]

This paper establishes a general analytical framework for continuous-time stochastic control problems for an ambiguity-averse agent (AAA) with time-inconsistent preference, where the control problems do not satisfy Bellman’s principle of optimality. The AAA is concerned about model uncertainty in the sense that she is not completely confident in the reference model of the controlled Markov state process and rather considers some similar alternative models. The problems of interest are studied within a set of dominated models and the AAA seeks for an optimal decision that is robust with respect to model risks. We adopt a game-theoretic framework and the concept of subgame perfect Nash equilibrium to derive an extended dynamic programming equation and extended Hamilton–Jacobi–Bellman–Isaacs equations for characterizing the robust dynamically optimal control of the problem. We also prove a verification theorem to theoretically support our construction of robust control. To illustrate the tractability of the proposed framework, we study an example of robust dynamic mean–variance portfolio selection under two cases: 1. constant risk aversion; and 2. state-dependent risk aversion. [ABSTRACT FROM AUTHOR]

Many transportation systems for routing flows between several origin-destination pairs of demand nodes have been widely designed as hub-and-spoke networks. To improve the provided service level of these networks, service time requirements are here considered during modeling, giving rise to a multiple allocation incomplete hub location problem with service time requirements. The problem consists of designing a hub and spoke network by locating hubs, establishing inter-hub arcs, and routing origin-destination demand flows at minimal cost while meeting some service time requirements. As travel times are usually uncertain for most real cases, the problem is approached via a binary linear programming robust optimization model, which is solved by two specialized Benders decomposition algorithms. The devised Benders decomposition framework outperforms a general purpose optimization solver on solving benchmark instances of the hub location literature. The achieved results also show how the probability of violating the travel time requirements decreases with the prescribed protection level, at the expense of the higher costs of the optimal solution for the robust optimization model. [ABSTRACT FROM AUTHOR]

The problem of the attitude stabilization of a quadrotor unmanned aerial vehicle is considered in simulation. An uncertain-like Takagi–Sugeno model of the quadrotor, where the nonlinear entries which depend on the input motor voltages are reported in uncertainties, is proposed to avoid closed-loop algebraic loops. The design of a Parallel Distributed Compensation (PDC) control law is considered with D -stability constraints in order to improve the closed-loop transient response. In this context, new generic and relaxed Linear Matrix Inequality (LMI) conditions are proposed. These new PDC controller design conditions constitute an alternative to previously proposed D -stabilizing non-PDC controller ones. Indeed, non-PDC controllers require online inversions of time-varying matrices, which is a major drawback for embedded applications with low computational capabilities. The conservatism of the proposed LMI conditions with respect to previous results is illustrated through an academic example. Then, simulations of the quadrotor with usual prescribed LMI regions are proposed to show the effectiveness of the proposed conditions. [ABSTRACT FROM AUTHOR]

In this paper the following selection problem is discussed. A set of n items is given and we wish to choose a subset of exactly p items of the minimum total cost. This problem is a special case of 0–1 knapsack in which all the item weights are equal to 1. Its deterministic version has an O ( n ) -time algorithm, which consists in choosing p items of the smallest costs. In this paper it is assumed that the item costs are uncertain. Two robust models, namely two-stage and recoverable ones, under discrete and interval uncertainty representations, are discussed. Several positive and negative complexity results for both of them are provided. [ABSTRACT FROM AUTHOR]

Uncertainty is frequently present in logistics and transportation, where vehicle routing problems play a crucial role. However, due to the complexity inherent in dealing with uncertainty, most research has been devoted to deterministic problems. This paper considers a robust version of the vehicle routing problem with hard time windows, in which travel times are uncertain. A budget polytope uncertainty set describes the travel times, to limit the maximum number of sailing legs that can be delayed. This makes sure that improbable scenarios are not considered, while making sure that solutions are immune to delays on a given number of sailing legs. Existing exact methods are only able to solve small instances of the problem and can be computationally demanding. With the aim of solving large instances with reduced running times, this paper proposes an efficient heuristic based on adaptive large neighborhood search. The computational study performed on instances with different uncertainty levels compares and analyzes the performance of four versions of the heuristic and shows how good quality solutions can be obtained within short computational times. [ABSTRACT FROM AUTHOR]

This paper presents a new approach for control design of constrained linear systems affected by bounded additive disturbances and polytopic uncertainties. This method hinges on so-called convex liftings which emulate control Lyapunov function by providing a constructive framework for optimization based control implementation. It will be shown that this method can guarantee the recursive feasibility and robust stability. Finally, a numerical example will be presented to illustrate this method. [ABSTRACT FROM AUTHOR]

We present a method for robust input design for nonlinear state-space models. The method optimizes a scalar cost function of the Fisher information matrix over a set of marginal distributions of stationary processes. By using elements from graph theory we characterize such a set. Since the true system is unknown, the resulting optimization problem takes the uncertainty on the true value of the parameters into account. In addition, the required estimates of the information matrix are computed using particle methods, and the resulting problem is convex in the decision variables. Numerical examples illustrate the proposed technique by identifying models using the expectation–maximization algorithm. [ABSTRACT FROM AUTHOR]

Design of controllers in the form of a state-feedback coupled to a state observer is studied in the context of uncertain systems. The classical approach by Luenberger is revisited. Results provide a heuristic design procedure that mimics the independent state-feedback/observer gains design by minimizing the coupling of observation error dynamics on the ideal state-feedback dynamics. The proposed design and analysis conditions apply to linear systems rationally-dependent on uncertainties defined in the cross-product of polytopes. Convex linear matrix inequality results are given thanks to the combination of a descriptor multi-affine representations of systems and the S -variable approach. Stability and H ∞ performances are assessed by multi-affine parameter-dependent Lyapunov matrices. [ABSTRACT FROM AUTHOR]

A tracking controller is developed for a class of uncertain nonlinear systems subject to unknown time-varying input delay and additive disturbances. A novel filtered error signal is designed using the past states in a finite integral over a constant estimated delay interval. The maximum tolerable error between unknown time-varying delay and a constant estimate of the delay is determined to establish uniformly ultimately bounded convergence of the tracking error to the origin. The controller development is based on an approach which uses Lyapunov–Krasovskii functionals to analyze the effects of unknown sufficiently slowly time-varying input delays. A stability analysis is provided to prove ultimate boundedness of the tracking error signals. Numerical simulation results illustrate the performance of the developed robust controller. [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]

We provide adaptive controllers for curve tracking in the plane, under unknown curvatures and control uncertainty, which is a central problem in robotics. The system dynamics include a nonlinear dependence on the curvature, and are coupled with an estimator for the unknown curvature, to form the augmented error dynamics. We prove input-to-state stability of the augmented error dynamics with respect to an input that is represented by additive uncertainty on the control, under polygonal state constraints and under suitable known bounds on the curvature and on the control uncertainty. When the uncertainty is zero, this gives tracking of the curve and convergence of the curvature estimate to the unknown curvature. Our curvature identification result is a significant improvement over earlier results, which do not ensure parameter identification, or which identify the control gain but not the curvature. [ABSTRACT FROM AUTHOR]

In this paper, a robust actuator fault tolerant control (FTC) strategy for systems with polytopic uncertainty is proposed. Two types of model descriptions are investigated in this work: convex polytopic model uncertainty and linear-parameter-varying (LPV) convex polytopic model uncertainty; where, in the latter, the varying parameter is assumed to be measured. The proposed FTC strategy combines a robust fault detection and isolation (FDI) approach based on set separation with controller reconfiguration based on the use of a bank of virtual actuators (VA). Both, FDI and controller reconfiguration modules, use the same bank of VA. The robust FDI method is based on the separation of relevant sets defined for measurable residual signals, which are computed using the VA signals and taking into account system disturbances and model uncertainty. The closed-loop system is reconfigured by means of a VA which is adapted to the fault situation detected by the FDI unit. The performance of the resulting robust FTC scheme is analysed for the two types of model descriptions by means of a simulation example. [ABSTRACT FROM AUTHOR]

Ontology-based activity recognition is gaining interest due to its expressiveness and comprehensive reasoning mechanism. An obstacle to its wider use is that the imperfect observations result in failure of recognizing activities. This paper proposes a novel reasoning algorithm for activity recognition in smart environments. The algorithm integrates OWL ontological reasoning mechanism with Dempster–Shafer theory of evidence to provide support for handling uncertainty in activity recognition. It quantifies uncertainty while aggregating contextual information and provides a degree of belief that facilitates more robust decision making in activity recognition. The presented approach has been implemented and evaluated on an internal and public datasets and compared with a data-driven approach that is using hidden Markov model. Results have shown that the proposed reasoning approach can accommodate uncertainties and subsequently infer the activities more accurately in comparison with existing ontology-based recognition and perform comparably well to the data-driven approach. [ABSTRACT FROM AUTHOR]

The maximum capability of feedback control for discrete-time systems under a nonparametric Lipschitz uncertainty was first established in Xie and Guo (2000) for the simplest dynamical control system. It was shown that the necessary and sufficient condition for the adaptive stabilizability is of the form L < 3 2 + 2 , where L is the Lipschitz constant of the uncertainty. This result was extended in Huang and Guo (2012) to a basic class of scalar discrete-time minimum-phase control systems under an additional parametric uncertainty, and the adaptive stabilization was achieved with the use of an impracticable infinite memory feedback based on a brute-force search over a sufficiently fine grid in the prior set of unknown parameters. In the present paper, the adaptive stabilization problem is considered for a subclass of parameter-affine minimum-phase systems. The solution of the problem is based on new recurrent objective inequalities enabling to estimate and validate the closed loop system online and to formulate a simple projection-type parameter estimation algorithm instead of the brute-force search used in Huang and Guo (2012). The computational tractability of the proposed finite-memory stabilizing feedback is illustrated via simulations. [ABSTRACT FROM AUTHOR]

This paper presents a novel robust control for electrically driven robot manipulators by designing an adaptive uncertainty estimator based on the first order Taylor series. The estimator is simple and model-free in a decentralized structure. The uncertainty is then efficiently compensated in the control system. The controller does not require the bounding functions as an advantage over the conventional robust controller. Therefore, it is simpler, less computational, and more efficient. It is verified by stability analysis and its effectiveness is shown through comparisons with a terminal sliding mode control approach and a Legendre polynomials uncertainty bound estimator simulated on a SCARA robot driven by permanent magnet dc motors. [ABSTRACT FROM AUTHOR]

In network analysis, a community can be defined as a group of nodes of a network (or clusters) that are densely interconnected with each other but only sparsely connected with the rest of the network. Several algorithms have been used to obtain a convenient partition allowing extracting the communities in a given network, based on their topology and, possibly, the weights of links. These weights usually represent specific characteristics for example: distance, reactance, reliability. Even if the optimum partitions could be derived, there are uncertainties associated to the network parameters that affect the network partition. In this paper, the authors extend a previous approach for assessing the effects of weight uncertainties on community structures and propose a global approach for (a) understanding the global similarity among the partitions; (b) analyzing the robustness of the communities derived without uncertainty; and (c) quantifying the robustness of the inter-community links. To this aim an uncertainty propagation analysis, based on the Monte Carlo technique is proposed. The approach is illustrated through analyzing the topology of an electric power system. [ABSTRACT FROM AUTHOR]

This paper addresses a design method of controller networks, i.e., networked controllers which cooperatively determine the control inputs by exchanging the information with their neighbors. The problem considered here is to design the controllers stabilizing the resulting feedback system for an unknown network topology. As a solution to the problem, we propose controllers such that the entire network acts as a state feedback controller through a consensus protocol, and derive gain conditions to stabilize the resulting feedback system. This enables us to obtain a controller network that is robust against uncertainties of the network topology. [ABSTRACT FROM AUTHOR]

• A cooperative robust non-fragile fault tolerant strategy for safety of the intended functionality of CACC with complex uncertainties. • An intermediate based cooperative robust estimation method is proposed to estimate the motion information and performance limitations of the platoon vehicles, simultaneously. • A distributed robust non-fragile fault tolerant H∞ control method is proposed to compensate the effects of performance limitations and uncertainties. • This research opens a path towards SOTIF of connected and autonomous vehicles by designing fault tolerant strategies. Safety of the intended functionality (SOTIF) of connected and autonomous vehicles (CAVs) is very challenging due to heterogeneous performance limitations and complex uncertainties in real road environments. In this paper, a cooperative robust non-fragile fault tolerant control (CRNFTC) strategy is presented to reduce the risks caused by multi-vehicle performance limitations of perception and actuation systems for ensuring SOTIF of cooperative adaptive cruise control (CACC). First, an intermediate based cooperative robust estimation method is proposed, by combining ego and cooperative information, system states, matched disturbances, performance limitations of perception and actuation of the vehicles in the platoon are simultaneously estimated. Existence conditions of estimators are given with respect to predecessor following (PF) and bi-directional (BD) communication network topologies. Then, based on the estimation, a distributed robust non-fragile fault tolerant H∞ control method is proposed, such that compensation of the effects of heterogeneous performance limitations and matched disturbances, and suppression of the remaining unmatched disturbances can be achieved. The sufficient condition and optimal solution of the proposed CRNFTC are obtained by using Lyapunov theory with explicit consideration of the system uncertainty and controller perturbation. The efficacy and superiority of the proposed CRNFTC for ensuring SOTIF of the CACC of PF and BD communication network topologies with complex uncertainties are substantiated via a series of simulations and quantitative comparisons. [ABSTRACT FROM AUTHOR]

This paper studies the fixed-time composite robust tracking control problem of a class of marine surface vessel (MSV) systems with uncertainty items and external disturbances. First, the tracking error is restricted within the bounded range by the tan-type barrier Lyapunov function (TT-BLF). Second, a fixed-time disturbance observer (FTDO) is designed to offset the lumped disturbances caused by system uncertainty items and external disturbances. Then, relying on the characteristics of H ∞ control, the error is limited within the L 2 norm bounded by suppressing the interference of the observation error. Furthermore, considering the importance of saving network resources, an event-triggered controller based on relative thresholds is proposed, which guarantees excellent robustness while greatly reducing the communication bandwidth. Finally, it is shown by Lyapunov stability analysis that all error signals of the nonlinear system converge to a small region close to zero in fixed time under the guidance of the robust control law. The effectiveness of the proposed composite robust controller is verified by numerical simulation results. • A fixed-time observer is employed to offset the lumped disturbances caused by system uncertainty items and external disturbances. • An H∞ control strategy is proposed to improve robustness, which has L 2 gain less than or equal to given γ. • A composite robust controller is proposed to ensure the error signal converge to a small range near zero within a predetermined time and robustness. • A ETS based on relative threshold is developed to greatly reduce the communication bandwidth of the controller. [ABSTRACT FROM AUTHOR]

In this paper a robust and optimal attitude control design that uses the minimal kinematic parameters and angular velocities feedback is presented for the three-axis attitude stabilization of spacecraft with inertia uncertainties. After proposing a new class of robust attitude control laws for the three-axis attitude stabilization of spacecraft with inertia uncertainties, it is shown that the proposed robust attitude control laws are optimal with respect to performance indices. A numerical example is given to illustrate the theoretical results presented in this paper. [ABSTRACT FROM AUTHOR]

Mathematical models of biochemical reaction networks are important tools in systems biology and systems medicine, e.g., to analyze disease causes or to make predictions for the development of effective treatments. Models are also used in synthetic biology for the design of circuits that perform specialized tasks. Prediction, analysis and design require plausible and reliable models, that is, models must reflect the properties of interest of the considered biochemical networks. One remarkable property of biochemical networks is robust functioning over a wide range of perturbations and environmental conditions. The intrinsic robustness of a network should be reflected into its associated mathematical model. The description and analysis of robustness in biochemical reaction networks are challenging, however, because accounting explicitly for the various types of structural, parametric and data uncertainty in the description of the models is not straightforward. Furthermore, system properties are typically inherently uncertain and often only given by qualitative or verbal descriptions that impede a straightforward and comprehensive mathematical analysis. In the first part of this overview article, network functions and behaviors of interest are formally defined, and different classes of uncertainties and perturbations are consistently described. The second part reviews frequently used mathematical formulations and presents the authors’ recent developments for robustness analysis, estimation, and model-based prediction. One biochemical network model is used to illustrate the capabilities of various methods to deal with the different types of uncertainties and robustness requirements. [ABSTRACT FROM AUTHOR]

In this paper, we focus on the robustness and fragility problem for piecewise affine (PWA) control laws for discrete-time linear system dynamics in the presence of parametric uncertainty of the state space model. A generic geometrical approach will be used to obtain robustness/fragility margins with respect to the positive invariance properties. For PWA control laws defined over a bounded region in the state space, it is shown that these margins can be described in terms of polyhedral sets in parameter space. The methodology is further extended to the fragility problem with respect to the partition defining the controller. Finally, several computational aspects are presented regarding the transformation from the theoretical formulations to explicit representations (vertex/halfspace representation of polytopes) of these sets. [ABSTRACT FROM AUTHOR]

This paper investigates 2D mixed continuous–discrete-time systems whose coefficients are polynomial functions of an uncertain vector constrained into a semialgebraic set. It is shown that a nonconservative linear matrix inequality (LMI) condition for ensuring robust stability can be obtained by introducing complex Lyapunov functions depending polynomially on the uncertain vector and a frequency. Moreover, it is shown that nonconservative LMI conditions for establishing upper bounds of the robust H ∞ and H 2 norms can be obtained by introducing analogous Lyapunov functions depending rationally on the frequency. Some numerical examples illustrate the proposed methodology. [ABSTRACT FROM AUTHOR]

This paper deals with the development of a robust model predictive control strategy with guarantee of stability, applicable to the stable and unstable processes. The model uncertainty is assumed to be described by a discrete set of linear models (multi-plant uncertainty), and the robustness is achieved by assembling cost-contracting constraints for all the possible models in the uncertainty domain. On the basis of a suitable state-space model description, an offset free control law is obtained by means of a one-step optimization formulation. The usefulness of the method proposed here is illustrated with control simulations of an unstable reactor system taken from the literature. [ABSTRACT FROM AUTHOR]

The problems of stationary robust L ∞ -induced filtering and deconvolution are addressed for discrete-time linear systems with deterministic and stochastic uncertainties in the state–space model. Stochastic uncertainties are in the form of state- and input-dependent multiplicative white noises which appear in both state and the measurement equations. The deterministic part of the system matrices and covariance matrices of the stochastic parameters is unknown and resides in a given polytopic-type domain. For this system a new lemma is derived which characterizes the induced L ∞ norm disturbance attenuation performance by linear matrix inequalities (LMIs). According to this lemma, the problem of estimator design is solved for stochastic uncertain systems based on the notion of quadratic stability. To further reduce the overdesign in the quadratic framework, this paper also proposes a parameter-dependent design procedure, which is much less conservative than the quadratic approach. The proposed estimators guarantee the mean-square exponential stability of estimation error dynamics and satisfy the prescribed induced L ∞ performance index. Two examples are used to demonstrate the proposed methods and their effectiveness. [ABSTRACT FROM AUTHOR]

This paper investigates the non-fragile and robust finite-time H ∞ control problem for a class of uncertain Markovian jump nonlinear systems with bounded parametric uncertainties and norm-bounded disturbance. By employing stochastic analysis and linear matrix inequality techniques, sufficient criteria of stochastic finite-time boundedness and stochastic H ∞ finite-time boundedness are first provided for the class of stochastic jump systems. Then, a controller is designed such that the class of stochastic nonlinear dynamics are stochastically finite-time bounded and have an H ∞ attention performance level by utilizing matrix decomposition approach. Furthermore, the analysis and design of non-fragile and robust finite-time controller are provided to guarantee that the class of uncertain stochastic systems are stochastically finite-time boundeded with a prescribed attention index by using non-fragile control technique. In addition, we also deal with the analysis and design of stochastic finite-time stability and stochastic finite-time stabilization. All criterions can be characterized in terms of linear matrix inequalities. Finally, two examples are also given to illustrate the effectiveness of obtained results. [ABSTRACT FROM AUTHOR]

This paper studies a numerical optimization-based extremum seeking scheme for systems with unmodeled dynamics and unknown disturbances without using dither signals. The robust extremum seeking scheme is composed of a numerical gradient estimator, a numerical optimizer and an extended-state observer based state regulator. A conjugate gradient method is adopted to achieve extremum seeking. A nonlinear extended-state observer based state regulator is proposed to regulate the states. The robust extremum seeker is based on the numerical optimization based extremum seeking framework. Sufficient conditions are derived to ensure the convergence of the overall extremum seeking scheme. The ultimate convergence bound is quantified for a class of strongly convex functions. A numerical example is presented to verify the proposed method. [ABSTRACT FROM AUTHOR]

Accurate measurement of the convective heat transfer coefficient h c at external surfaces, e.g. at building facades and roofs, is of fundamental importance for heat transfer studies of the built environment. There are two basic methods for measurement of h c , the Loveday and Ito methods, which use one and two heated sensor units, respectively. To guide in selection of method and operating conditions, and in design of the sensor, we performed an error analysis. This included estimation of systematic errors, comparison between methods, and to established Nusselt number correlations, sensitivity analysis, and an evaluation of the measurement uncertainty. The main conclusion was that both methods, at forced convection, yielded measurement uncertainties at the 4% level, provided that the Ito method was operated under the new condition, where one of its sensors remained unheated. However, at natural convection conditions, the Ito method cannot be operated with one of its sensors unheated, since h c is then zero at that sensor surface, which violates the method assumption that h c is the same at both sensors. Sensitivity analysis showed that systematic errors will be reduced by decreasing the sensor surface emissivity. The major source of measurement uncertainty was the conductive heat flux estimate. [ABSTRACT FROM AUTHOR]

In this study, we consider the robust uncapacitated multiple allocation p -hub median problem under polyhedral demand uncertainty. We model the demand uncertainty in two different ways. The hose model assumes that the only available information is the upper limit on the total flow adjacent at each node, while the hybrid model additionally imposes lower and upper bounds on each pairwise demand. We propose linear mixed integer programming formulations using a minmax criteria and devise two Benders decomposition based exact solution algorithms in order to solve large-scale problems. We report the results of our computational experiments on the effect of incorporating uncertainty and on the performance of our exact approaches. [ABSTRACT FROM AUTHOR]

Uncertainty quantification has recently been receiving much attention from aerospace engineering community. With ever-increasing requirements for robustness and reliability, it is crucial to quantify multidisciplinary uncertainty in satellite system design which dominates overall design direction and cost. However, coupled multi-disciplines and cross propagation hamper the efficiency and accuracy of high-dimensional uncertainty analysis. In this study, an uncertainty quantification methodology based on active subspaces is established for satellite conceptual design. The active subspace effectively reduces the dimension and measures the contributions of input uncertainties. A comprehensive characterization of associated uncertain factors is made and all subsystem models are built for uncertainty propagation. By integrating a system decoupling strategy, the multidisciplinary uncertainty effect is efficiently represented by a one-dimensional active subspace for each design. The identified active subspace is checked by bootstrap resampling for confidence intervals and verified by Monte Carlo propagation for the accuracy. To show the performance of active subspaces, 18 uncertainty parameters of an Earth observation small satellite are exemplified and then another 5 design uncertainties are incorporated. The uncertainties that contribute the most to satellite mass and total cost are ranked, and the quantification of high-dimensional uncertainty is achieved by a relatively small number of support samples. The methodology with considerably less cost exhibits high accuracy and strong adaptability, which provides a potential template to tackle multidisciplinary uncertainty in practical satellite systems. [ABSTRACT FROM AUTHOR]

The problem of robust adaptive predictive control for a class of discrete-time nonlinear systems is considered. First, a parameter estimation technique, based on an uncertainty set estimation, is formulated. This technique is able to provide robust performance for nonlinear systems subject to exogenous variables. Second, an adaptive MPC is developed to use the uncertainty estimation in a framework of min–max robust control. A Lipschitz-based approach, which provides a conservative approximation for the min–max problem, is used to solve the control problem, retaining the computational complexity of nominal MPC formulations and the robustness of the min–max approach. Finally, the set-based estimation algorithm and the robust predictive controller are successfully applied in two case studies. The first one is the control of anonisothermal CSTR governed by the van de Vusse reaction. Concentration and temperature regulation is considered with the simultaneous estimation of the frequency (or pre-exponential) factors of the Arrhenius equation. In the second example, a biomedical model for chemotherapy control is simulated using control actions provided by the proposed algorithm. The methods for estimation and control were tested using different disturbances scenarios. [ABSTRACT FROM AUTHOR]

A realistic control paradigm should concurrently account for different sources of uncertainty such as those in modeling parameters, external disturbances and noise, as well as operational cost. Yet, this is a daunting task for which many current control approaches lack in one aspect or the other. In particular, the consumed control energy is an important aspect of controller design that is often ignored. In this paper, we propose a stable robust adaptive interval type-2 fuzzy H 2 /H ∞ controller (RAIT2FH 2 H ∞ C) for a class of uncertain nonlinear systems that aims to address the above concerns through its hybrid robust/adaptive structure. In particular, the H 2 energy and tracking cost function is minimized with respect to a H ∞ disturbance attenuation constraint, while the adaptive interval fuzzy logic system (IT2FLS) handles the uncertainties in approximating the unknown nonlinear dynamics of the system. In principle, the interval fuzzy logic approach aims to manage portions of uncertainty that could not be precisiated, leading to improved error performance. Several simulation studies, with or without disturbance and noisy measurements, as well as actual experimental implementation on a 3-PSP (prismatic-spherical-prismatic) parallel robot confirm this assessment. More specifically, in comparison with a competing methodology as well as its type-1 counterpart, the proposed interval type-2 strategy expends better or comparative control effort while reaching considerably better tracking performance. [ABSTRACT FROM AUTHOR]

This paper is concerned with the problem of robust stability analysis for discrete-time neural networks with time-varying coupling delays, random parameter uncertainties and time-varying leakage delays. The uncertainties enter into the system parameters in a random way and such randomly occurring uncertainties obey certain mutually uncorrelated Bernoulli-distributed white noise sequences. The important feature of the results reported here is that the probability of occurrence of the parameter uncertainties are known a priori. Constructing suitable Lyapunov–Krasovskii functional (LKF) terms, sufficient conditions ensuring the stability of the discrete-time neural networks are derived in terms of linear matrix inequalities (LMIs). Finally, numerical examples are rendered to exemplify the effectiveness of the proposed results. [ABSTRACT FROM AUTHOR]

GPS/INS integrated system is very subject to uncertainties due to exogenous disturbances, device damage, and inaccurate sensor noise statistics. Conventional Kalman filer has no robustness to address system uncertainties which may corrupt filter performance and even cause filter divergence. Based on the INS error dynamic equation, a robust Kalman filter is analyzed and applied in loosely coupled GPS/INS integration system. The norm bounded robust Kalman filter, with recursive form by solving two Riccati equations, guarantees a estimation variance bound for all the admissible uncertainties, and can evolve into the conventional Kalman filter if no uncertainties are considered. This paper will analyze the suitable case for the robust Kalman filter in GPS/INS system, the filter characteristics including parameter setting, parameter meaning, and filter convergence condition are discussed simutaneously. The robust filter performance will be compared with conventional Kalman filter through simulation results. [ABSTRACT FROM AUTHOR]

We address a stochastic dynamic distribution problem where a family of products needs to be shipped from a warehouse to a distribution center (DC). Uncertainty is on carriers' availability and demand at the DC. Internal, external and spot carriers must be optimally selected to minimize the expected discounted cost of transportation, inventories and shortages. We numerically prove that an optimal selection policy, SDMBSP, is based on three thresholds of the available inventory in the DC. A simulation model is proposed and proves the robustness of the SDMBSP and its outperformance over two other carrier selection policies. [ABSTRACT FROM AUTHOR]

The fixed-time master–slave synchronization of Cohen–Grossberg neural networks with parameter uncertainties and time-varying delays is investigated. Compared with finite-time synchronization where the convergence time relies on the initial synchronization errors, the settling time of fixed-time synchronization can be adjusted to desired values regardless of initial conditions. Novel synchronization control strategy for the slave neural network is proposed. By utilizing the Filippov discontinuous theory and Lyapunov stability theory, some sufficient schemes are provided for selecting the control parameters to ensure synchronization with required convergence time and in the presence of parameter uncertainties. Corresponding criteria for tuning control inputs are also derived for the finite-time synchronization. Finally, two numerical examples are given to illustrate the validity of the theoretical results. [ABSTRACT FROM AUTHOR]

Azimuthal angles and Doppler frequencies of radar targets usually suffer from estimation uncertainty in practice, which poses a big challenge in target detection. In this work, we consider the problem of target detection in the presence of uncertainty in the azimuthal angle and Doppler frequency. This uncertainty is characterized by a subspace model. Precisely, the spatial and temporal steering vectors of the target are assumed to lie in certain known subspaces but with unknown coordinates. Two detectors are devised in the framework of generalized likelihood ratio test. Moreover, the properties of the proposed detectors are derived for the case of sufficiently large training data. It is shown by numerical examples that the detector derived according to the one-step design procedure has higher probability of detection than its counterparts in the absence of signal mismatch, while the detector devised according to the two-step design procedure is most robust to the signal mismatch. [ABSTRACT FROM AUTHOR]

This paper presents a method which combines the bilinear control technique with a set-point reset technique to control the space temperature when its cooling is provided by a GSHP equipped with an on/off capacity control, aiming to (i) improve the robustness of the space temperature control by taking account of load uncertainty; and (ii) to reduce the frequency of the GSHP on/off cycling by using the indoor space temperature set-point reset. When the GSHP is on, a smaller space temperature set point is used; while the GSHP is off, a larger set point is used. The proposed control was tested on a simulation platform, which consists of a ground source heat exchanger, a GSHP, an air-handling unit (AHU) and a middle-sized room. The test results show that the proposed control method is able to achieve a good control performance and has the potential to be applied to a real GSHP integrated air conditioning system to improve the robustness of space temperature control and simultaneously reduce the on/off frequency of the GSHP. [ABSTRACT FROM AUTHOR]

As an example of one-class classification methods, support vector data description (SVDD) offers an opportunity to improve the performance of outlier detection and reduce the loss caused by outlier occurrence in many real-world applications. However, due to limited outliers, the SVDD model is built only by using the normal data. In this situation, SVDD may easily lead to over fitting when the normal data contain noise or uncertainty. This paper presents two types of new SVDD methods, named R-SVDD and ε NR-SVDD, which are constructed by introducing cutoff distance-based local density of each data sample and the ε -insensitive loss function with negative samples. We have demonstrated that the proposed methods can improve the robustness of SVDD for data with noise or uncertainty by extensive experiments on ten UCI datasets. The experimental results have shown that the proposed ε NR-SVDD is superior to other existing outlier detection methods in terms of the detection rate and the false alarm rate. Meanwhile, the proposed R-SVDD can also achieve a better outlier detection performance with only normal data. Finally, the proposed methods are successfully used to detect the image-based conveyor belt fault. [ABSTRACT FROM AUTHOR]

This paper provides a solution for the position tracking and attitude synchronization problem of the close proximity phase in spacecraft rendezvous and docking. The chaser spacecraft must be driven to a certain fixed position along the docking port direction of the target spacecraft, while the attitude of the two spacecraft must be synchronized for subsequent docking operations. The kinematics and dynamics for relative position and relative attitude are modeled considering dynamic coupling, parametric uncertainties and external disturbances. The relative motion model has a new form with a novel definition of the unknown parameters. An original robust adaptive control method is developed for the concerned problem, and a proof of the asymptotic stability is given for the six degrees of freedom closed-loop system. A numerical example is displayed in simulation to verify the theoretical results. [ABSTRACT FROM AUTHOR]

This paper analyzes the influence of urban development density on transit network design with stochastic demand by considering two types of services, rapid transit services, such as rail, and flexible services, such as dial-a-ride shuttles. Rapid transit services operate on fixed routes and dedicated lanes, and with fixed schedules, whereas dial-a-ride services can make use of the existing road network, hence are much more economical to implement. It is obvious that the urban development densities to financially sustain these two service types are different. This study integrates these two service networks into one multi-modal network and then determines the optimal combination of these two service types under user equilibrium (UE) flows for a given urban density. Then we investigate the minimum or critical urban density required to financially sustain the rapid transit line(s). The approach of robust optimization is used to address the stochastic demands as captured in a polyhedral uncertainty set, which is then reformulated by its dual problem and incorporated accordingly. The UE principle is represented by a set of variational inequality (VI) constraints. Eventually, the whole problem is linearized and formulated as a mixed-integer linear program. A cutting constraint algorithm is adopted to address the computational difficulty arising from the VI constraints. The paper studies the implications of three different population distribution patterns, two CBD locations, and produces the resultant sequences of adding more rapid transit services as the population density increases. [ABSTRACT FROM AUTHOR]

In this paper, we study the transit itinerary planning problem with incorporation of randomness that arises in transit vehicle arrival/departure and passenger transfer. We investigate two approaches to address the uncertainty: a minmax robust approach and an expectation-based probabilistic approach. We adapt a two-phase framework to mitigate computational challenges in large-scale planning problems. In phase I, we compute candidate route connections offline and store them into a database. Although expensive computation is required in phase I, it is typically performed only once over a period of time (e.g., half a year). Phase II takes place whenever a request is received, for which we query candidate route connections from the database, build a stochastic shortest-path model based on either approach listed above, and solve the model in real time. With phase I, computational requirement in phase II is substantially reduced so as to ensure real-time itinerary planning. To demonstrate the practical feasibility of our two-phase approach, we conduct extensive case studies and sensitivity analyses based on a large real-world transit network. [ABSTRACT FROM AUTHOR]

Context Model-based data-interpretation techniques are increasingly used to improve the knowledge of complex system behavior. Physics-based models that are identified using measurement data are generally used for extrapolation to predict system behavior under other actions. In order to obtain accurate and reliable extrapolations, model-parameter identification needs to be robust in terms of variations of systematic modeling uncertainty introduced when modeling complex systems. Approaches such as Bayesian inference are widely used for system identification. More recently, error-domain model falsification (EDMF) has been shown to be useful for situations where little information is available to define the probability density function (PDF) of modeling errors. Model falsification is a discrete population methodology that is particularly suited to knowledge intensive tasks in open worlds, where uncertainty cannot be precisely defined. Objective This paper compares conventional uses of approaches such as Bayesian inference and EDMF in terms of parameter-identification robustness and extrapolation accuracy. Method Using Bayesian inference, three scenarios of conventional assumptions related to inclusion of modeling errors are evaluated for several model classes of a simple beam. These scenarios are compared with results obtained using EDMF. Bayesian model class selection is used to study the benefit of posterior model averaging on the accuracy of extrapolations. Finally, ease of representation and modification of knowledge is illustrated using an example of a full-scale bridge. Results This study shows that EDMF leads to robust identification and more accurate predictions than conventional applications of Bayesian inference in the presence of systematic uncertainty. These results are illustrated with a full-scale bridge. This example shows that the engineering knowledge necessary to perform parameter identification and remaining-fatigue-life predictions of a complex civil structure is easily represented by the EDMF methodology. Conclusion Model classes describing complex systems should include two components: (1) unknown physical parameters that are identified using measurements; (2) conservative modeling error estimations that cannot be represented only as uncertainties related to physical parameters. In order to obtain accurate predictions, both components need to be included in the model-class definition. This study indicates that Bayesian model class selection may lead to over-confidence in certain model classes, resulting in biased extrapolation. [ABSTRACT FROM AUTHOR]