Target vector optimization of composite box beam using real-coded genetic algorithm: a decomposition approach

This paper aims to obtain the optimal composite box-beam design for a helicopter rotor blade. The cross-sectional dimensions and the ply angles of the box beam are considered as design variables. The objective is to optimize the box beam to attain a target vector of stiffness values and maximum elastic coupling. The target vector is the optimal stiffness values of helicopter rotor blade obtained from a previous aeroelastic optimization study. The elastic couplings introduced by the box beam have beneficial effects on the aeroelastic stability of helicopter. The optimization problem is addressed by decomposing the optimization into two levels, a global level and a local level. The box-beam cross-sectional dimensions are optimized at the global level. The local-level optimization is a subproblem which finds optimal ply angles for each cross-sectional dimension considered in the global level. Real-coded genetic algorithm (RCGA) is used as the optimization tool in both the levels of optimization. Hybrid operators are developed for the RCGA, thereby enhancing the efficiency of the algorithm. Min–max method is used to scalarize the multiobjective functions used in this study. Optimal geometry and ply angles are obtained for composite box-beam designs with ply angle discretization of 1010, 1515, and 45^o45^o.     

区域极点约束下的具L2有界不确定性 系统鲁棒优化设计问题

研究了具L     

Reliability based design with a degradation model of laminated composite structures

Uncertainties in deviations of physical properties lead to a probabilistic failure analysis of the composite materials. The proposed optimization model for laminate composites is based on reliability analysis considering the ultimate failure state. To avoid difficulties associated with the complete analysis of the failure modes, bounds are established for the failure probability of the structural system. These bounds are related with theintact and degraded configurations of the structure. Using thefirst ply failure and thelast ply failure theories and a degradation model for the mechanical properties with load sharing rules we obtain the failure probabilities corresponding to the two above configurations. The failure probability of each configuration is obtained using level 2 reliability analysis and the Lind-Hasofer method.The optimization algorithm is developed based on the problem decomposition into three subproblems having as objectives the maximization of the structural efficiency atintact and degraded configurations of the structure and weight minimization subjected to allowable values for the structural reliability. Additionally, the search for the initial design is performed introducing a weight minimization level. It is expected to explore the remaining load capacity of the structures afterfirst ply failure as a function of the anisotropic properties of the composites. The design variables are the ply angles and the thicknesses of the laminates. The structural analysis for the model developed is performed through the finite element method mainly using the isoparametric degenerated shell finite element. The sensitivities are obtained using the discrete approach through the adjoint variable method. In order to show the performance of the analysis two examples are presented.     

Robust control design for best mean performance over an uncertain-parameters box

This paper deals with robust, polytopic, probabilistic H_∞ analysis and state-feedback synthesis of linear systems and focuses on the performance distribution over the uncertainty region (rather than on the performance bound). The proposed approach allows different disturbance attenuation levels (DALs) at the vertices of the uncertainty polytope. It is shown that the mean disturbance attenuation level (DAL) over an uncertain parameters-box is the average of the DALs at the vertices, if each parameter has an independent, symmetrical, centered probability density function. In such a (most common) case, the mean DAL over the uncertain parameters-box can be optimized by minimizing the sum of the DALs at the vertices. The standard deviation of the DAL over the uncertain parameters-box is also addressed, and a method to minimize this standard deviation is shown. A new robust H_∞ state-feedback synthesis theorem is given; it is based on a recent, most efficient analysis method and applies the proposed multiple-vertex-DALs approach. A state-feedback design example utilizing the latter theorem shows that a control design which minimizes the sum of the vertex-DALs leads to a better actual closed-loop performance than a similar design which minimizes only the bound of the DAL over the uncertainty polytope. The comparison is based on the statistics of a population of closed-loop ‘point-wise’ H_∞-norms created by a Monte-Carlo mechanism.     

Decentralized state-feedback stabilization and robust control of uncertain large-scale systems with integrally constrained interconnections

This paper is concerned with a problem of stabilization and robust control design for interconnected uncertain systems. A new class of uncertain large-scale systems is considered in which interconnections between subsystems as well as uncertainties in each subsystem are described by integral quadratic constraints. The problem is to design a set of local (decentralized) controllers which stabilize the overall system and guarantee robust disturbance attenuation in the presence of the uncertainty in interconnections between subsystems as well as in each subsystem. The paper presents necessary and sufficient conditions for the existence of such a controller. The proposed design is based on recent absolute stabilization and minimax optimal control results and employs solutions of a set of game-type Riccati algebraic equations arising in H_∞ control.     

Optimization under uncertainty with applications to design of truss structures

Many real-world engineering design problems are naturally cast in the form of optimization programs with uncertainty-contaminated data. In this context, a reliable design must be able to cope in some way with the presence of uncertainty. In this paper, we consider two standard philosophies for finding optimal solutions for uncertain convex optimization problems. In the first approach, classical in the stochastic optimization literature, the optimal design should minimize the expected value of the objective function with respect to uncertainty (average approach), while in the second one it should minimize the worst-case objective (worst-case or min–max approach). Both approaches are briefly reviewed in this paper and are shown to lead to exact and numerically efficient solution schemes when the uncertainty enters the data in simple form. For general uncertainty dependence however, the problems are numerically hard. In this paper, we present two techniques based on uncertainty randomization that permit to solve efficiently some suitable probabilistic relaxation of the indicated problems, with full generality with respect to the way in which the uncertainty enters the problem data. In the specific context of truss topology design, uncertainty in the problem arises, for instance, from imprecise knowledge of material characteristics and/or loading configurations. In this paper, we show how reliable structural design can be obtained using the proposed techniques based on the interplay of convex optimization and randomization.     

Robust output-feedback control of linear discrete-time systems

The problem of designing H_∞ dynamic output-feedback controllers for linear discrete-time systems with polytopic type parameter uncertainties is considered. Given a transfer function matrix of a system with uncertain real parameters that reside in some known ranges, an appropriate, not necessarily minimal, state-space model of the system is described which permits reconstruction of all its states via the delayed inputs and outputs of the plant. The resulting model incorporates the uncertain parameters of the transfer function matrix in the state-space matrices. A recently developed linear parameter-dependent LMI approach to state-feedback H_∞ control of uncertain polytopic systems is then used to design a robust output-feedback controllers that are of order comparable to the one of the plant. These controllers ensure the stability and guarantee a prescribed performance level within the uncertainty polytope.     

Quantitative non-linear compensation design for saturating unstable uncertain plants

Consider an unstable uncertain plant controlled by an element Np, which saturates when its input |x| ≥ M. The system can be stabilized by means of feedback, which, however, is absent during Np saturation. If the saturation interval is long enough, it is impossible to recover system stability via Np. This paper presents a synthesis technique for ensuring that Np does not saturate despite very large command inputs. The basic idea is to prevent |x|>M, via an added saturating element N with saturation level m, which in turn is determined by |x|. A systematic, quantitative design technique is presented for unstable plants with large uncertainty, to achieve (a) desired performance tolerances over the linear range (small command inputs) and (b)acceptable but unavoidably slower response for large command inputs. Both (a) and (b) are achieved over the specified extent of plant uncertainty. The design technique makes use of several previously developed quantitative synthesis theories for minimum- and non-minimum-phase uncertain plants in linear operation, and for uncertain minimum-phase stable plants subject to saturation.     

LMI optimization approach to robust H∞ observer design and static output feedback stabilization for discrete‐time nonlinear uncertain systems

A new approach for the design of robust H_∞ observers for a class of Lipschitz nonlinear systems with time‐varying uncertainties is proposed based on linear matrix inequalities (LMIs). The admissible Lipschitz constant of the system and the disturbance attenuation level are maximized simultaneously through convex multiobjective optimization. The resulting H_∞ observer guarantees asymptotic stability of the estimation error dynamics and is robust against nonlinear additive uncertainty and time‐varying parametric uncertainties. Explicit norm‐wise and element‐wise bounds on the tolerable nonlinear uncertainty are derived. Also, a new method for the robust output feedback stabilization with H_∞ performance for a class of uncertain nonlinear systems is proposed. Our solution is based on a noniterative LMI optimization and is less restrictive than the existing solutions. The bounds on the nonlinear uncertainty and multiobjective optimization obtained for the observer are also applicable to the proposed static output feedback stabilizing controller. Copyright © 2008 John Wiley & Sons, Ltd.     

Resilient H∞ Control Design for Discrete‐Time Uncertain Linear Systems: An Auxiliary System Transformation Approach

This paper studies the resilient (non‐fragile) H∞ output‐feedback control design for discrete‐time uncertain linear systems with controller uncertainty. The design considers parametric norm‐bounded uncertainty in all state‐space matrices of the system, output and controller equations. The paper shows that the resilient H∞ output‐feedback control problem is equivalent to a scaled H∞ output‐feedback control problem of an auxiliary system without any system or controller uncertainty. Using the existing optimal H∞ design to solve the auxiliary system, the design guarantees that the resultant closed‐loop systems are quadratically stable with disturbance attenuation γ for all admissible system and controller uncertainties. A numerical example is given to illustrate the design method and its benefits.     

Robust H2 and H∞ Filter Design for Continuous‐time Uncertain Linear Fractional Transformation Systems via LMI

This paper considers the problem of robust H₂ and H_∞ filter design for uncertain continuous‐time linear systems. Linear fractional transformation (LFT) representation is considered for the uncertainty modeling and by definition of large number of slack variables, extra free dimensions are provided to the H₂ and H_∞ filter design optimization problem, so method presented in this paper expected to be less conservative than the existing methods for the polytopic uncertain systems and its efficiency for filter design is illustrated by means of numerical comparisons with some benchmark examples from the literature.     

Robust H∞ Filtering For Uncertain Stochastic Time‐Delay Systems

This paper deals with the problem of robust H_∞ filtering for uncertain stochastic systems. The system under consideration is subject to time‐varying norm‐bounded parameter uncertainties and unknown time delays in both the state and measurement equations. The problem we address is the design of a stable filter that ensures the robust stochastic stability and a prescribed H_∞ performance level for the filtering error system irrespective of all admissible uncertainties and time delays. A suffient condition for the solvability of this problem is proposed and a linear matrix inequality approach is developed for the design of the robust H_∞ filters. An illustrative example is provided to demonstrate the effctiveness of the proposed approach.     

Quadratic guaranteed cost control for uncertain dissipative models: A Riccati equation approach

The problem of H₂ guaranteed cost control and dynamic output-feedback for linear uncertain systems with dissipative uncertainty is addressed. The problem of robust H₂ synthesis has been open for the last two decades. In this paper, a problem of H₂ quadratic guaranteed cost control is defined for uncertain systems affected by LTI quadratic dissipative model uncertainty. A necessary and sufficient condition of quadratic stabilizability via output-feedback is derived in terms of two coupled parameter-dependent Riccati equations. Then, a method is given to design controllers which minimize an upper bound for the worst-case H₂ norm of the uncertain system. It therefore assesses a guaranteed level of robust performance where in literature, only nominal performance is ensured in most cases. A reliable numerical iterative procedure based on Riccati solvers and one-dimensional convex parameter search is provided. With this uncertainty modelling and the developed numerical procedure, we hope to reduce the usual conservatism of quadratic designs.     

Robust multiple model adaptive control: Modified using ν‐gap metric

A new robust adaptive control method is proposed, which removes the deficiencies of the classic robust multiple model adaptive control (RMMAC) using benefits of the ν‐gap metric. First, the classic RMMAC design procedure cannot be used for systematic design for unstable plants because it uses the Baram Proximity Measure, which cannot be calculated for open‐loop unstable plants. Next, the %FNARC method which is used as a systematic approach for subdividing the uncertainty set makes the RMMAC structure being always companion with the µ‐synthesis design method. Then in case of two or more uncertain parameters, the model set definition in the classic RMMAC is based on cumbersome ad hoc methods. Several methods based on ν‐gap metric for working out the mentioned problems are presented in this paper. To demonstrate the benefits of the proposed RMMAC method, two benchmark problems subject to unmodeled dynamics, stochastic disturbance input and sensor noise are considered as case studies. The first case‐study is a non‐minimum‐phase (NMP) system, which has an uncertain NMP zero; the second case‐study is a mass‐spring‐dashpot system that has three uncertain real parameters. In the first case‐study, five robust controller design methods (H₂, H_∞, QFT, H_∞ loop‐shaping and µ‐synthesis) are implemented and it is shown via extensive simulations that RMMAC/ν/QFT method improves disturbance‐rejection, when compared with the classic RMMAC. In the second case‐study, two robust controller design methods (QFT and mixed µ‐synthesis) are applied and it is shown that the RMMAC/ν/QFT method improves disturbance‐rejection, when compared with RMMAC/ν/mixed?µ. Copyright © 2010 John Wiley & Sons, Ltd.     

Robust fault estimation of uncertain systems using an LMI‐based approach

General recent techniques in fault detection and isolation (FDI) are based on H_∞ optimization methods to address the issue of robustness in the presence of disturbances, uncertainties and modeling errors. Recently developed linear matrix inequality (LMI) optimization methods are currently used to design controllers and filters, which present several advantages over the Riccati equation‐based design methods. This article presents an LMI formulation to design full‐order and reduced‐order robust H_∞ FDI filters to estimate the faulty input signals in the presence of uncertainty and model errors. Several cases are examined for nominal and uncertain plants, which consider a weight function for the disturbance and a reference model for the faults. The FDI LMI synthesis conditions are obtained based on the bounded real lemma for the nominal case and on a sufficient extension for the uncertain case. The conditions for the existence of a feasible solution form a convex problem for the full‐order filter, which may be solved via recently developed LMI optimization techniques. For the reduced‐order FDI filter, the inequalities include a non‐convex constraint, and an alternating projections method is presented to address this case. The examples presented in this paper compare the simulated results of a structural model for the nominal and uncertain cases and show that a degree of conservatism exists in the robust fault estimation; however, more reliable solutions are achieved than the nominal design. Copyright © 2008 John Wiley & Sons, Ltd.     

Robust Reliable H∞ Control for Discrete‐Time Systems with Actuator Delays

This article focuses on the robust state feedback reliable H_∞ control problem for discrete‐time systems. Discrete‐time systems with time‐varying delayed control input are formulated. Based on the Lyapunov–Krasovskii method and linear matrix inequality (LMI) approach, delay‐dependent sufficient conditions are developed for synthesizing the state feedback controller for an uncertain discrete‐time system. The parameter uncertainty is assumed to be norm bounded. A design scheme for the state feedback reliable H_∞ controller is proposed in terms of LMIs, which can guarantee the global asymptotic stability and the minimum disturbance attenuation level. Finally, numerical examples are provided to illustrate the effectiveness and reduced conservatism of the proposed methods.     

Unstable uncertain plants with rate and amplitude saturations

A previous paper presented a synthesis technique for highly uncertain unstable plants subject to a single saturating element. The design philosophy was to use an inserted element N with adjustable saturating value m to control the plant input so as to prevent plant saturations. This paper extends the design technique to plants with both rate and amplitude saturations. The design philosophy is the same, but design of the m control is more subtle. The design also guarantees that the linear response satisfies specified tolerances over the range of plant uncertainty. The design theory is based upon previously developed quantitative synthesis techniques for unstable and for non-minimum-phase plants.