Robust Design Problem Research Articles

H∞ Lower Order Controller for AC Servo System of Multiple Rockets

Design problem of a H∞ robust lower order controller of an AC servo system of multiple rockets is studied. It is pointed out that the problem is actually H∞ robust performance design problem, H∞ robust stability and performance requirements (enhance rapidity, shorten overshoot and static error). It is also recommended to represent the robust performance design as H∞ robust control problem and solve H∞ low-order controller, if the uncertainty weighting function and performance weighting function of system bandwidth and interference attenuation are properly modified. Solved the H∞ low-order controller. The simulation results show that the robust H∞ lower order control system has advantages of small overshoot and short setup time. It can also improve control system’s anti-disturbance ability. The simulation example of the H∞ lower order control is also provided to demonstrate the effectively of the proposed design method. The H∞ lower order controller is easy for engineering implementation.

Path-Based Approaches to Robust Network Design Problems Considering Boundedly Rational Network Users

Network users may choose non-shortest paths, when (1) they satisfice with sub-optimal routes, or (2) they have perception errors of the decision environment. The notion of generalized bounded rationality has been recently proposed to create a unified framework for these two sources of behavioral uncertainty in route choices. When the notion of generalized bounded rationality is used in robust network design problems, we obtain a bi-level optimization problem with the min–max objective function at the upper level, with three layers of optimization in total. In this paper, we derive equivalent single-level path-based formulations that are readily solvable by available optimization libraries. We show how to incorporate them into robust multi-commodity network design problems in hazardous materials transportation.

Robust Power- and Rate-Splitting-Based Transceiver Design in <inline-formula> <tex-math notation="LaTeX">$K$ </tex-math> </inline-formula>-User MISO SWIPT Interference Channel Under Imperfect CSIT

We investigate the rate-splitting (RS)-based robust transceiver design problem in a multi-antenna interference channel with simultaneous wireless information and power transfer under the norm-bounded errors of channel state information at transmitters. The beamforming vectors, power splitting ratios, and target common rates are jointly optimized via minimizing the total transmit power subject to the quality of service and energy harvesting requirements. The non-convex problem with infinite constraints is first transformed into finite-constraint convex one and then jointly solved by a gradient-based algorithm. The results demonstrate that the RS-based robust schemes outperform the conventional robust designs.

Stochastic back-off-based robust process design for continuous crystallization of ibuprofen

Robust model-based process design in continuous pharmaceutical manufacturing aims to implement quality by design principles under uncertainty. Notably, various studies have discussed the back-off concept to solve the underlying robust optimization problem; however, for the concept to have practical value, its efficiency and convergence must be improved. In this work, we introduce a novel, highly efficient stochastic back-off strategy. Instead of using statistical moments of limited validity, we incorporate the full statistical information of the constraints to solve the robust process design problem. To ensure manageable computational costs, we make use of polynomial chaos expansion for uncertainty quantification and propagation. The proposed concept is demonstrated with the design of a tubular crystallizer for ibuprofen crystallization. The results show that the novel stochastic back-off strategy is considerably faster compared with the standard back-off concept and provides more reliable quality by design results in general.

New approach to robust observer‐based control of one‐sided Lipschitz non‐linear systems

This study investigates the problem of robust observer design for a class of one-sided non-linear continuous-time systems with parameter uncertainties and $L_{2}$L2 bounded admissible external disturbance. The one-sided Lipschitz and quadratically inner-bounded conditions have been utilised to derive less conservative synthesis condition for the observer design. The corresponding design methodology is established, with the help some special derivations, bilinear matrix inequalities are successfully transformed into a set of linear matrix inequalities. Then, the robust controller and observer gains can be simultaneously found at one step. Finally, two numerical examples are given to illustrate the validity and the effectiveness of the proposed method.

Benders decomposition approach with heuristic improvements for the robust foodgrain supply network design problem

We investigate the problem of designing a supply chain for foodgrains distribution under uncertainty, which is motivated from the Indian public distribution system (PDS). Initially, a deterministic mixed-integer programming (MIP) model is formulated to determine the strategic decisions of storage and transportation capacity hiring and the tactical decisions of procurement, inventory, and transportation planning to minimise the total cost over a finite planning horizon. The storage capacity hiring decision is characterised by the options of hiring under long-term contract for the entire planning horizon and from spot market for individual period. Next, we extend the model to consider the uncertainties associated with supply, demand and procurement parameters, and propose a scenario-based robust optimisation model to minimum the total relative regret. An MIP-based fix-and-optimise heuristic is proposed to efficiently solve the deterministic equivalent problem of each scenario. To solve the robust model, we implement Benders decomposition algorithm (BDA) with several heuristic techniques including warm-start strategy to build an initial feasible solution, trust region for master problem, and logical inequalities to accelerate the performance of the BDA. Finally, the effectiveness of the solution approach is demonstrated through extensive computational experiments using the test instances simulating the Indian PDS.

PFOSM: An efficient algorithm for aerodynamic robust design based on continuous adjoint and matrix-vector products

This article proposes a novel robust design tool based on the Method of Moments (MoM), demonstrated in problems governed by laminar flows of incompressible fluids. The objective function of the robust design problem consists of the weighted sum of the mean value and standard deviation of the Quantity of Interest (QoI), computed based on the value and gradient of the latter with respect to the uncertain variables. First-order derivatives with respect to the uncertain and design variables are computed using the continuous adjoint method. Using a first-order MoM to compute the objective function and by minimizing it with a gradient-based approach leads to the need of computing up to second-order derivatives of the QoI with respect to the design and uncertain variables. This can lead to a high computational cost in problems with a great number of uncertain variables. The proposed robust design algorithm avoids computing second-order derivatives by computing matrix-vector products instead, using a combination of adjoint and direct differentiation. This makes the cost per gradient computation independent of the numbers of both the design and uncertain variables. The proposed method is demonstrated through the constrained shape optimization of an isolated 2D airfoil under uncertain farfield flow conditions.

Legitimate Monitoring via Cooperative Relay and Proactive Jamming

With the development of communication technologies, many suspicious communication technologies have also been greatly improved. Therefore, one single monitor may not be able to afford in a monitoring process. In this paper, we propose a wireless communication system using two legitimate monitors for cooperative monitoring program, in which the signals sent by two monitors are respectively designed. One monitor is used as the cooperative relay, which is mainly used to improve the overall information transmission rate. The other monitor, which simultaneously receiving suspicious information and sending jamming signals, is used to ensure the successful eavesdropping process. Our purpose is to obtain the maximum eavesdropping rate by jointly design the transmit beamforming of two monitors. Two cases that the channel state information (CSI) is perfectly and imperfectly known by the monitors are considered. For the perfect CSI, several cases corresponding to the different conditions about the CSI from the suspicious transmitter to two monitors are discussed. In each case, a closed-form solution of the appropriate sending strategy is obtained, in which the physical meaning is also proposed. Then, for the imperfect CSI case, by employing the S-procedure method, we reformulate the robust beamforming design problem and solve it optimally. Finally, in the simulation results, the comparison between the cooperative monitoring scheme and the single monitoring scheme demonstrates that the proposed scheme is better in terms of eavesdropping rate.

A Globalized Robust Optimization Approach of Dynamic Network Design Problem With Demand Uncertainty

This paper presents a globalized robust optimization approach for a network design problem explicit incorporating traffic dynamics and demand uncertainty. In particular, a non-holding back cell transmission model (CTM) based network design problem of linear programming type is considered to describe dynamic traffic flows, and the normal range of the uncertain demand is assumed to be a box set, i.e., the uncertain demand outside box set is allowed. The major contribution of this paper is to formulate such a globalized robust network design problem as a tractable linear programming model and demonstrate the model robustness and flexibility by comparing its solution performance with the robust solution from the usual robust model and the adjustable robust solution from the adjustable robust model, respectively. A numerical experiment is conducted to demonstrate that the modeling advantage of the globalized robust optimization in terms of solution quality. The proposed globalized robust optimization approach may provide useful insights and have broader applicability in traffic management and traffic planning problems under uncertainty.

Offset-Based Beamforming: A New Approach to Robust Downlink Transmission

The design of beamformers for the multi-user multiple-input single-output downlink that provide prespecified levels of quality-of-service can be quite challenging when the channel state information is not perfectly known at the base station. The constraint of having the signal-to-interference-and-noise ratio (SINR) satisfy a given threshold with high probability is intractable in general, which results in problems that are fundamentally hard to solve. We develop a high-quality approximation of the SINR outage constraint that, along with a semidefinite relaxation, enables us to formulate the robust beamformer design problem for Gaussian channel estimation errors as a convex optimization problem that can be efficiently solved. For systems with small uncertainties, further approximations yield design algorithms based on iterative evaluations of closed-form expressions that have substantially lower computational cost. Since finding the beamforming directions incurs most of that cost, analogous power loading algorithms for predefined beamforming directions are developed and their performance is shown to be close to optimal. When the system contains a large number of antennas, the proposed power loading can be obtained at a computational cost that grows only linearly in the number of antennas. The proposed power loading algorithm provides an explicit relationship between the outage probability required and the power consumed, which allows us to precisely control the power consumption, and automatically identifies users who are consuming most of the power resources. The flexibility of the proposed approach is illustrated by developing a power loading technique that minimizes an average notion of outage.

Methodology of Robust Optimal Design of the Multistage Axial Compressor on the Basis of Discrete Analogue-Related Data

Consideration was given to the formulation and methodology of the direct nonlinear design problem of structural dimensional circuits in conditions of a priori parametric uncertainty. It was shown that the solution of the direct nonlinear design problem of structural dimensional circuits can be reduced to the multicriteria problems of stochastic optimization with mixed conditions. Mathematical models and methods of the solution of multicriteria problems of stochastic optimization with mixed conditions were analyzed. A.N. Tikhonov method of the regulation of solution of incorrectly formulated problems was used as a computation method for the synthesis of quasi-solutions of incorrectly formulated problems. An effective memetic algorithm for the synthesis of the solutions of MV-problems was suggested. It is based on the genetic algorithm combined with the randomized path tracing method. The suggested methodology allows us to search for rational solutions of the multicriteria problems of system modification through the creation of hierarchic two-level scheme for the synthesis of solutions that includes the construction of robust surrogate models of the systems and processes with subsequent robust estimation of sought values for the parametric data uncertainty. As an example, we obtained the solution data for the problem of robust optimal design of two-stage axial compressor in conditions of a stochastic nature of the input data obtained using the interactive decision support computer system «Concept_Pro_St ® ».

Robust fault estimation observer design for switched systems with unknown input

In this paper, the problem of robust fault estimation observer design for continuous-time switched systems subject to unknown input is investigated. Firstly, based on the average dwell-time method and the switched Lyapunov function technique, an unknown input observer is designed for the augmented switched system by eliminating the unknown input, which can guarantee that the error system is globally uniformly asymptotically stable with a prescribed H∞ performance index. Next, the method is extended to the measurement disturbances case. Finally, an example is presented to illustrate the design and efficiency of the proposed fault estimation observer technique.

Discrete-time robust controller and observer for a ball and beam system

This paper deals with a digital controller and observer design problem for the ball and beam system which is extended version of the previous investigated result. The controller is an extension of robust integral tracking controller. In the discrete-time system, it cannot perform integration and differentiation operation, so we introduce a difference system to design controller for the distance subsystem between reference and output. The observer is designed using dual system LQ design method. The observer gain is able to obtain as the result of robust control design problem of dual system. Each design problem is solved by the guaranteed cost control method. Through the numerical result, we validity and effectiveness of our proposed method.

On robust Kalman filter for two-dimensional uncertain linear discrete time-varying systems: A least squares method

The robust Kalman filter design problem for two-dimensional uncertain linear discrete time-varying systems with stochastic noises is investigated in this study. First, we prove that the solution to a certain deterministic regularized least squares problem constrained by the nominal two-dimensional system model is equivalent to the generalized two-dimensional Kalman filter. Then, based on this relationship, the robust state estimation problem for two-dimensional uncertain systems with stochastic noises is interpreted as a deterministic robust regularized least squares problem subject to two-dimensional dynamic constraint. Finally, by solving the robust regularized least squares problem and using a simple approximation, a recursive robust two-dimensional Kalman filter is determined. A heat transfer process serves as an example to show the properties and efficacy of the proposed filter.

An input–output approach to H∞ reduced filter design for polytopic time-varying delay systems

ABSTRACTThis paper discusses the problem of delay-dependent robust filtering design for polytopic systems with a time-varying delay. A new model transformation is firstly applied by employing a three-term approximation for the delayed state, which leads to a smaller approximation error than the two-term approximation. Then, based on the scaled small-gain Theorem combined with an appropriate Lyapunov–Krasovskii Functional, the performance analysis of the filtering error system is examined and then the full- and reduced-order filters are designed in terms of linear matrix inequalities via a simple linearisation technique. Before the end, a sufficient condition is presented to solve the problem of filtering design for a time-delay system without polytopic uncertainties. Finally, illustrative examples are presented to demonstrate the validity of the proposed methods.

New Designs on MVDR Robust Adaptive Beamforming Based on Optimal Steering Vector Estimation

The robust adaptive beamforming design problem based on estimation of the signal of interest steering vector is considered in the paper. In this case, the optimal beamformer is obtained by computing the sample matrix inverse and an optimal estimate of the signal of interest steering vector. The common criteria to find the best estimate of the steering vector are the beamformer output SINR and output power, while the constraints assume as little as possible prior inaccurate knowledge about the signal of interest, the propagation media, and the antenna array. Herein, a new beamformer output power maximization problem is formulated and solved subject to a double-sided norm perturbation constraint, a similarity constraint, and a quadratic constraint that guarantees that the direction-of-arrival (DOA) of the signal of interest is away from the DOA region of all linear combinations of the interference steering vectors. In the new robust design, the prior information required consists of some allowable error norm bounds, the approximate knowledge of the antenna array geometry, and the angular sector of the signal of interest. It turns out that the array output power maximization problem is a non-convex QCQP problem with inhomogeneous constraints. However, we show that the problem is still solvable, and develop efficient algorithms for finding globally optimal estimate of the signal of interest steering vector. The results are generalized to the case where an ellipsoidal constraint is considered, and sufficient conditions for the global optimality are derived. In addition, a new quadratic constraint on the actual signal steering vector is proposed in order to improve the array performance. To validate our results, simulation examples are presented, and they demonstrate the improved performance of the new robust beamformers in terms of the output SINR as well as the output power.

A sliding mode observer design for uncertain fractional Ito stochastic systems with state delay

ABSTRACTThis paper addresses the robust observer design problem for uncertain time-delay fractional Ito stochastic systems. A sliding surface is proposed and it is shown that state estimates converge towards it and remain there for the subsequent time. Additionally, by constructing a novel Lyapunov functional, a sufficient condition for the stability of the sliding motion of the estimated states is given in the form of Linear Matrix Inequalities (LMIs). It is demonstrated that the state estimates are stabilizable in probability provided that the LMI is feasible. Moreover, a finite-time sliding mode control law based on the estimated states is proposed. Simulation examples are given to show the validity and effectiveness of the results.

Robust and Optimal Output-Feedback Control for Interval State-Space Model: Application to a Two-Degrees-of-Freedom Piezoelectric Tube Actuator

The problem of robust and optimal output feedback design for interval state-space systems is addressed in this paper. Indeed, an algorithm based on set inversion via interval analysis (SIVIA) combined with interval eigenvalues computation and eigenvalues clustering techniques is proposed to seek for a set of robust gains. This recursive SIVIA-based algorithm allows to approximate with subpaving the set solutions [K] that satisfy the inclusion of the eigenvalues of the closed-loop system in a desired region in the complex plane. Moreover, the LQ tracker design is employed to find from the set solutions [K] the optimal solution that minimizes the inputs/outputs energy and ensures the best behaviors of the closed-loop system. Finally, the effectiveness of the algorithm is illustrated by a real experimentation on a piezoelectric tube actuator.

Robust Fuzzy Control with Transient and Steady-State Performance Constraints for Ship Fin Stabilizing Systems

This paper studies the robust fuzzy controller design problem for the nonlinear ship fin stabilizing systems. By considering the perturbations, the nonlinear ship fin stabilizing system is represented by the perturbed Takagi–Sugeno fuzzy model. According to the perturbed Takagi–Sugeno fuzzy model, the parallel distributed compensation technique is used to design a model-based robust fuzzy controller. The purpose of the parallel distributed compensation fuzzy controller is to derive linear controllers such that each fuzzy rule of the Takagi–Sugeno fuzzy model can be compensated. In addition to the robust stability performance, the variance constraint and transient performance constraint are also considered in this paper. According to these performance constraints, the linear matrix inequality technique is employed to solve the sufficient conditions developed in this paper. At last, some simulations for the control of nonlinear ship fin stabilizing systems are made to show the usefulness and effectiveness of the proposed design method.

A quadratic boundedness approach to a neural network-based simultaneous estimation of actuator and sensor faults

The paper is devoted to the problem of a neural network-based robust simultaneous actuator and sensor faults estimator design for the purpose of the fault diagnosis of nonlinear systems. In particular, the methodology of designing a neural network-based fault estimator is developed. The main novelty of the approach is associated with possibly simultaneous sensor and actuator faults under imprecise measurements. For this purpose, a linear parameter-varying description of a recurrent neural network is exploited. The proposed approach guaranties a predefined disturbance attenuation level and convergence of the estimator. In particular, it uses the quadratic boundedness approach to provide uncertainty intervals of the achieved estimates. The final part of the paper presents an illustrative example concerning the application of the proposed approach to the multitank system fault diagnosis.