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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]

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]

Dynamic optimization techniques for complex nonlinear systems can provide the process industry with sustainable and efficient operating regimes. The problem with these regimes is that they usually lie close to the limits of the process. It is therefore paramount that these operating conditions are robust with respect to the parameter uncertainties and to the process noise such that critical constraints are not violated. Besides the uncertainty in the constraints, also the uncertainty in the objective function needs to be taken into account. However, including robustness in an optimization problem typically leads to semi-infinite optimization problems that are challenging to solve in practice. In the current manuscript several computationally tractable methods are exploited to approximately solve the robust dynamic optimization problem. These methods allow the use of fast deterministic gradient based optimization techniques. The first type of methods are based on a linearization approach while the second method exploits the unscented transformation to construct an estimation of the uncertainty propagation. Both types provide the user with an approximation of the variance–covariance matrix of the critical constraints and of the objective function. This allows the user to easily take them into account in the dynamic optimization routine in a stochastic setting without the need of using computationally expensive Monte Carlo simulations in the optimization procedure. Moreover, an iterative scheme is mentioned to evaluate the approximate results and to improve them if necessary. Two illustrative case studies are discussed, a jacketed tubular reactor and the Williams-Otto reactor. [ABSTRACT FROM AUTHOR]

Abstract: Flexible air-breathing hypersonic vehicles feature significant uncertainties which pose huge challenges to robust controller designs. In this paper, four major categories of uncertainties are analyzed, that is, uncertainties associated with flexible effects, aerodynamic parameter variations, external environmental disturbances, and control-oriented modeling errors. A uniform nonlinear uncertainty model is explored for the first three uncertainties which lumps all uncertainties together and consequently is beneficial for controller synthesis. The fourth uncertainty is additionally considered in stability analysis. Based on these analyses, the starting point of the control design is to decompose the vehicle dynamics into five functional subsystems. Then a robust trajectory linearization control (TLC) scheme consisting of five robust subsystem controllers is proposed. In each subsystem controller, TLC is combined with the extended state observer (ESO) technique for uncertainty compensation. The stability of the overall closed-loop system with the four aforementioned uncertainties and additional singular perturbations is analyzed. Particularly, the stability of nonlinear ESO is also discussed from a Liénard system perspective. At last, simulations demonstrate the great control performance and the uncertainty rejection ability of the robust scheme. [Copyright &y& Elsevier]

Abstract: We present a method for determining optimal modes of operation for autonomously oscillating systems with uncertain parameters. In a typical application of the method, a nonlinear dynamical system is optimized with respect to an economic objective function with nonlinear programming methods, and stability is guaranteed for all points in a robustness region around the optimal point. The stability constraints are implemented by imposing a lower bound on the distance between the optimal point and all stability boundaries in its vicinity, where stability boundaries are described with notions from bifurcation theory. We derive the required constraints for a general class of periodically operated processes and show how these bounds can be integrated into standard nonlinear programming methods. We present results of the optimization of two chemical reaction systems for illustration. [Copyright &y& Elsevier]

Abstract: This paper focuses on robust fault residual generation for Uncertain Unknown Inputs Linear Parameter Varying ( ) systems. Firstly, the problem is addressed in standard LPV systems based on the adaptation of the parity-space approach. The main objective of this approach is to design a scheduled parity matrix according to the scheduling parameters. It results a perfectly decoupled parity matrix face to the system states. Then, the major contribution of this paper relies on the extension to systems. Since most of models which represent practical/real systems are subject to parameters variation, unmodeled dynamics and unknown inputs, the approach is clearly justified. The residual synthesis is rewritten in terms of a new optimization problem and solved using Linear Matrix Inequalities (LMIs) techniques. An applicative illustration is proposed and rests on a vehicle lateral dynamic system. [Copyright &y& Elsevier]

Highlights: [•] Is the ecological footprint of universities comparable? [•] How can model and parameter uncertainties affect the estimated ecological footprint? [•] Uncertainty analysis can help in assessing the relevancy of parameters and in making the distinction. [•] Results showed that model uncertainties have the largest impact on the estimates. [•] Conclusion is that uncertainty analysis provides a robust framework for inter-comparison of universities. [ABSTRACT FROM AUTHOR]

Abstract: This paper proposes a novel distributed estimation and control method for uncertain plants. It is of application in the case of large-scale systems, where each control unit is assumed to have access only to a subset of the plant outputs, and possibly controls a restricted subset of input channels. A constrained communication topology between nodes is considered so the units can benefit from estimates of neighboring nodes to build their own estimates. The paper proposes a methodology to design a distributed control structure so that the system is asymptotically driven to equilibrium with L 2-gain disturbance rejection capabilities. A difficulty that arises is that the separation principle does not hold, as every single unit ignores the control action that other units might be applying. To overcome this, a two-stage design is proposed: firstly, the distributed controllers are obtained to robustly stabilize the plant despite the observation errors in the controlled output. At the second stage, the distributed observers are designed aiming to minimize the effects of the communication noise in the observation error. Both stages are formulated in terms of linear matrix inequalities. The performance is shown on a level-control real plant. [Copyright &y& Elsevier]

Abstract: This paper analyzes the robustness of global exponential stability of delayed recurrent neural networks (DRNNs) subject to parameter uncertainty in connection weight matrices. Given a globally exponentially stable DRNNs, the problem to be addressed herein is how much parameter uncertainty in the connection weight matrices that the neural network can remain to be globally exponentially stable. We characterize the upper bounds of the parameter uncertainty for the DRNNs to sustain global exponential stability. The upper bounds of parameter uncertainty intensity are characterized by using transcendental equations. Moreover, we prove theoretically that, for globally exponentially stable DRNNs, if additive parameter uncertainties in connection weight matrices are smaller than the derived supper bounds arrived at here, then the perturbed DRNNs are guaranteed to also be globally exponentially stable. A numerical example is provided to illustrate the theoretical results. [Copyright &y& Elsevier]

Abstract: This paper investigates robust and global exponential synchronizations in an array of nonidentical neural networks with leakage delays and impulsive coupling subject to parametric uncertainties. Some simpler sufficient conditions for synchronization are obtained when uncertainties vanish. A numerical example is given to illustrate the effectiveness of the theoretical results. [Copyright &y& Elsevier]

Abstract: Antilock braking system (ABS) is a highly nonlinear system including variation and uncertainties in the parameters due to changes in vehicle loadings, road condition, etc. It is a difficult task to design an ideal controller for ABS. In this paper, a novel robust controller named fractional order sliding mode controller (FOSMC) is proposed for ABS to regulate the slip to a desired value. The proposed FOSMC combines sliding mode controller (SMC) with fractional order dynamics, in which fractional order proportional-derivative (FOPD) sliding surface is adopted. FOSMC can not only deal with the uncertainties in ABS system but also track the desired slip faster than conventional integer order SMC with proportional or proportional-derivative sliding surface. Experimental results demonstrate the effectiveness of the proposed method. [Copyright &y& Elsevier]

Abstract: This paper presents a robust optimization framework to improve the Managed Pressure Drilling (MPD) process for safer and superior economical and environmental operations while removing risk-prone conventional drilling limitations such as a need for constant monitoring of the system parameters. The nonlinear MPD process considers the mud pump flow rate and the differential flow rate of the backpressure pump and the choke as the two inputs while the process downhole pressure rate as the output. The MPD process unmodeled disturbances, uncertain geological parameters and related model nonlinearities are considered to be the corresponding system uncertainties in a closed loop robust control and optimization framework for real-time operations. Moreover, the MPD process inputs are formulated to remain within practical bounds by introducing performance weighting functions. The proposed framework numerical results demonstrate the efficiency of the closed loop robust control implementations for efficient drilling operations in operator guidance systems and provide a low-computational complexity design algorithm for safer drilling operations in regions with a-priori unknown geological properties. [Copyright &y& Elsevier]

Abstract: This paper concerns the design of a robust observer-based modified repetitive-control system for a class of strictly proper plants with periodic time-varying uncertainties. It exploits the inherent structure characteristics of repetitive control to convert the design problem to a robust stabilization problem for a continuous-discrete two-dimensional system. The singular-value decomposition and Lyapunov stability theory are used to derive a linear-matrix-inequality-based design algorithm for the parameters of control and state-observer gains. Two tuning parameters are introduced to perform the preferential adjustment of control and learning. A numerical example illustrates the adjusting procedure and demonstrates the validity of the method. [Copyright &y& Elsevier]

Abstract: This paper analyzes the robustness of global exponential stability of recurrent neural networks subject to parameter uncertainty in connection weight matrix. Given a globally exponentially stable recurrent neural network, the problem to be addressed herein is how much parameter uncertainty in the connection weight matrix that the neural network can remain to be globally exponentially stable. We characterize the upper bounds of the parameter uncertainty for the recurrent neural networks to sustain global exponential stability. A numerical example is provided to illustrate the theoretical result. [Copyright &y& Elsevier]

Abstract: In this study, an adaptive robust tracking control scheme for a nanomechanical beam is proposed. The mathematical nanobeam model takes into consideration the presence of parametric uncertainties, and external disturbances, and fringing field effects and intermolecular forces, are also incorporated. The proposed backstepping controller is enhanced with an adaptive dynamic surface technique and an control scheme. The overall effectiveness of the designed controller is checked and illustrated with the presented results. These results show that the desired transient output tracking performance is achieved, and that the closed loop system exhibits good robustness to system uncertainties. Particular attention has been paid, so as to identify any relevance between the variations in the controller''s design parameter and the system''s output response and performance. [Copyright &y& Elsevier]

Abstract: In this paper, a discrete time sliding mode controller (DSMC) is proposed for higher order plus delay time (HOPDT) processes. A sliding mode surface is selected as a function of system states and error and the tuning parameters of sliding mode controller are determined using dominant pole placement strategy. The condition for the existence of stable sliding mode is obtained by using Lyapunov function. The proposed method is applicable to HOPDT processes with oscillatory and integrating behavior, open loop instability or non-minimum phase characteristics and works satisfactory under the effect of parametric uncertainty. The method does not require reduced order model and provides simple way to design the controllers. The simulation and experimentation results show that the proposed method ensures desired tracking dynamics. [Copyright &y& Elsevier]

Abstract: This paper investigates the robust decentralized attitude control problem for spacecraft formations under uncertain communication topologies. Based on modified Rodrigues parameters representation and a Lagrange-like model, a class of decentralized attitude control schemes designed by the use of sliding mode control approach is proposed to steer the attitude of the spacecraft formation to a time-varying reference states with no assumption on the information exchange graph. By taking into account the model uncertainties and external disturbances simultaneously, the proposed robust control strategies are proven effective to overcome these unexpected phenomena. Finally, numerical examples are included to demonstrate the effectiveness and robustness of the developed control schemes. [Copyright &y& Elsevier]

Abstract: In this paper, a robust adaptive fuzzy decentralized backstepping output feedback control approach is proposed for a class of uncertain large-scale stochastic nonlinear systems with unknown nonlinear functions, dynamical uncertainties and without the measurements of the states. The fuzzy logic systems are used to approximate the unknown nonlinear functions, and a fuzzy state observer is designed for estimating the unmeasured states. To solve the problem of the dynamical uncertainties, the changing supply function technique is incorporated into the backstepping recursive design technique, and a new robust adaptive fuzzy decentralized output feedback control approach is constructed. It is proved that the proposed control approach can guarantee that all the signals of the resulting closed-loop system are semi-globally uniformly ultimately bounded (SGUUB) in probability, and the observer errors and the output of the system converge to a small neighborhood of the origin by choosing design parameters appropriately. A simulation example is provided to show the effectiveness of the proposed approach. [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]

Abstract: In this paper, a generalized robust nonlinear filtering method is proposed for a class of Lipschitz descriptor systems, in which the nonlinearities appear both in the state and measured output equations. The system is assumed to have norm-bounded uncertainties in the realization matrices as well as nonlinear uncertainties. We synthesize the filter through semidefinite programming and strict LMIs. The admissible Lipschitz constants of the nonlinear functions are maximized through LMI optimization. The resulting filter guarantees asymptotic stability of the estimation error dynamics with prespecified disturbance attenuation level and is robust against time-varying parametric uncertainties as well as Lipschitz nonlinear additive uncertainty. Explicit bound on the tolerable nonlinear uncertainty is derived based on a norm-wise robustness analysis. [Copyright &y& Elsevier]

Abstract: A novel design of a robust decentralized load frequency control (LFC) algorithm is proposed for an inter-connected three-area power system, for the purpose of regulating area control error (ACE) in the presence of system uncertainties and external disturbances. The design is based on the concept of active disturbance rejection control (ADRC). Estimating and mitigating the total effect of various uncertainties in real time, ADRC is particularly effective against a wide range of parameter variations, model uncertainties, and large disturbances. Furthermore, with only two tuning parameters, the controller provides a simple and easy-to-use solution to complex engineering problems in practice. Here, an ADRC-based LFC solution is developed for systems with turbines of various types, such as non-reheat, reheat, and hydraulic. The simulation results verified the effectiveness of the ADRC, in comparison with an existing PI-type controller tuned via genetic algorithm linear matrix inequalities (GALMIs). The comparison results show the superiority of the proposed solution. Moreover, the stability and robustness of the closed-loop system is studied using frequency-domain analysis. [Copyright &y& Elsevier]

Abstract: In this article, a robust control scheme for trajectory tracking of very lightweight single-link flexible arms is discussed. Since the payload is one of the most variable parameters in a manipulator, the control is designed to achieve an accurate tracking of the desired tip trajectory for any value of the robot tip mass, or even for a tip mass changing during the maneuver. The proposed controller also guarantees stability for small uncertainties in parameters such as stiffness or motor friction. In addition, the effect of spillover on the performance of the controlled system is analyzed, and it is proven that stability and a good performance are preserved independently from the non-modeled high-order dynamics. The control scheme is based on a two nested loops structure. Each of these loops implements a Generalized Proportional Integral (GPI) controller. Moreover, the outer loop includes a disturbance compensation term based on a disturbance observer, which achieves the required insensitivity to payload changes. The theoretical analysis is supported by an extensive set of numerical simulations which shows controlled system response when variations in the robot payload, or dynamics neglected in the controller design, are considered. Finally, some experiments have been carried out in order to test the performance of the tip trajectory tracking of the proposed control system. [Copyright &y& Elsevier]

Abstract: Parameter perturbations in dynamical models of biochemical networks affect the qualitative dynamical behaviour observed in the model. Since this qualitative behaviour is in many cases the key model output used to explain biological function, the robustness analysis of the model’s behaviour with respect to parametric uncertainty is a crucial step in systems biology research. In this paper, we develop a new method for robustness analysis of the dynamical behaviour. As a first step, we provide a characterization of non-robust perturbations as a system of polynomial equalities and inequalities. In the second step, we apply the Positivstellensatz and Handelman representation of polynomials to check for the non-existence of solutions to this system, which can be relaxed to solving a linear program. Thereby, a solution to the linear program yields a robustness certificate for the considered dynamical behaviour. With these robustness certificates, we propose an algorithm to compute a lower robustness bound corresponding to a level of parametric uncertainty up to which no local bifurcations can occur. The applicability of the proposed method to biochemical network models is illustrated by analysing the robustness of oscillations in a model of the NF-B signalling pathway. The results may be used to define a level of confidence in the observed model behaviour under parametric uncertainty, making them valuable for evaluating dynamical models of biological networks. [Copyright &y& Elsevier]

We develop a new adaptive gain-scheduling control scheme for continuous-time linear systems with polytopic uncertainties. The gain-scheduled control law is proposed as a convex sum of a fixed set of controller gains, exploiting the polytopic representation of the system uncertainty, which is not possible with classical robust control results in the literature. To realize this scheme, an adaptation law is proposed to adaptively provide the tuning parameter for the gain-scheduling implementation. The admissible domain of the stabilizing control feedback gains, defined by the fixed set of controller gains, can be determined offline by solving a set of linear matrix inequality constraints over a scalar line search. Using Lyapunov-based arguments, the proposed design conditions and the adaptation law ensure that all closed-loop signals are bounded. In particular, if the uncertain parameters are not time-varying, then the system states asymptotically converge to the origin. Theoretical arguments and appropriate numerical illustrations are provided to demonstrate the effectiveness of the proposed control scheme. [ABSTRACT FROM AUTHOR]

Abstract: SIPAR_ID is a software based on a robust multiobjective inverse modeling technique for estimating field values of infiltration and roughness parameters of a surface irrigation event under both steady and variable inflow conditions. Its simulation engine is quite flexible and accurate thanks to a hybrid model that combines a volume-balance model with artificial neural networks. SIPAR_ID also provides an estimate of the uncertainty and sensitivity of the identified parameters. [Copyright &y& Elsevier]