Quadratic stabilizability of uncertain linear systems containing both constant and time-varying uncertain parameters

This paper is concerned with the problem of stabilizing an uncertain linear system using state feedback control. The uncertain systems under consideration are described by state equations containing unknown but bounded uncertain parameters. The uncertain parameters are classified into two types: either constant or time-varying. Indeed, the main feature of this paper is that it allows one to exploit the fact that some of the uncertain parameters are constant. In order to investigate the question of stabilizability, quadratic Lyapunov functions are used. Hence, the paper deals with the notion of quadratic stabilizability. The main result of the paper is a necessary and sufficient condition for the quadratic stabilizability of the uncertain systems under consideration.     

Decentralized robust control design for uncertain delay systems

We consider a class of large-scale uncertain delay systems. The uncertain parameter vector in the system is possibly fast time-varying. It may be nonlinear in the system dynamics. No statistical or fuzzy information of the uncertainty is known. Based on only the possible bound of the uncertain parameter, a decentralized linear robust control is proposed, which renders the system asymptotically stable.     

Limit Design in the Absense of a Given Layout: A Finite Element,Zero-One Programming Approach∗

Limit design in three dimensions is discussed and formulated as a constrained minimax problem in kinematic and geometric variables. A finite element discretization is proposed which, combined with piecewise linearization of the yield surfaces, reduces the minimum weight design to a pair of dual problems in linear mixed zero one programming. The relevant duality theory is shown to be useful for the theoretical frame of the mechanical problem. Various ways of reducing the number of variables and constraints are pointed out, in order to make available algorithms economically applicable to practical situations.     

Two non-probabilistic set-theoretical models to predict the transient vibrations of cross-ply plates with uncertainty

In practical engineering and scientific researches, all engineering analysis and design problems involve uncertainties to various degrees. Dynamic loads acting on a structure are usually with uncertain nature due to the difficulty of predicting the magnitudes of such loads. In this paper, a non-probabilistic and set-theoretical model named interval analysis method is developed to predict the transient vibrations of cross-ply plates with uncertain excitations. The dynamic loads involve deterministic and uncertain components of force function and initial conditions. Uncertainties in these functions are required to be bounded on the L₂ norm and expressed by finite eigenmodes. Analyzed by a numerical example, the width of the upper and lower bounds of the critical buckling loads that calculated by the interval analysis method is sharper than those are obtained by convex models. Moreover, the interval analysis has less computational cost than convex models. Considering specific cases, the effect of various parameters and the level of uncertainty on the response of the cross-ply plates are different.     

Modern tontine with bequest: Innovation in pooled annuity products

We introduce a new pension product that offers retirees the opportunity for a lifelong income and a bequest for their estate. Based on a tontine mechanism, the product divides pension savings between a tontine account and a bequest account. The tontine account is given up to a tontine pool upon death while the bequest account value is paid to the retiree’s estate. The values of these two accounts are continuously re-balanced to the same proportion, which is the key feature of our new product.Our main research question about the new product is what proportion of pension savings should a retiree allocate to the tontine account. Under a power utility function, we show that more risk averse retirees allocate a fairly stable proportion of their pension savings to the tontine account, regardless of the strength of their bequest motive. The proportion declines as the retiree becomes less risk averse for a while. However, for the least risk averse retirees, a high proportion of their pension savings is optimally allocated to the tontine account. This surprising result is explained by the least risk averse retirees seeking the potentially high value of the bequest account at very old ages.     

Worst-case robust Omega ratio

The Omega ratio is a recent performance measure proposed to overcome the known shortcomings of the Sharpe ratio. Until recently, the Omega ratio was thought to be computationally intractable, and research was focused on heuristic optimization procedures. We have shown elsewhere that the Omega ratio optimization is equivalent to a linear program and hence can be solved exactly in polynomial time. This permits the investigation of more complex and realistic variants of the problem. The standard formulation of the Omega ratio requires perfect information for the probability distribution of the asset returns. In this paper, we investigate the problem arising from the probability distribution of the asset returns being only partially known. We introduce the robust variant of the conventional Omega ratio that hedges against uncertainty in the probability distribution. We examine the worst-case Omega ratio optimization problem under three types of uncertainty – mixture distribution, box and ellipsoidal uncertainty – and show that the problem remains tractable.     

An interval uncertain optimization method for vehicle suspensions using Chebyshev metamodels

This paper proposes a new design optimization framework for suspension systems considering the kinematic characteristics, such as the camber angle, caster angle, kingpin inclination angle, and toe angle in the presence of uncertainties. The coordinates of rear inner hardpoints of upper control arm and lower control arm of double wishbone suspension are considered as the design variables, as well as the uncertain parameters. In this way, the actual values of the design variables will vary surrounding their nominal values. The variations result in uncertainties that are described as interval variables with lower and upper bounds. The kinematic model of the suspension is developed in software ADAMS. A high-order response surface model using the zeros of Chebyshev polynomials as sampling points is established, termed as Chebyshev metamodel, to approximate the kinematic model. The Chebyshev meta-model is expected to provide higher approximation accuracy. Interval uncertain optimization problems usually involve a nested computationally expensive double-loop optimization process, in which the inner loop optimization is to calculate the bounds of the interval design functions, while the outer loop is to search the optimum for the deterministic optimization problem. To reduce the computational cost, the interval arithmetic is introduced in the inner loop to improve computational efficiency without compromising numerical accuracy. The numerical results show the effectiveness of the proposed design method.     

Mean-chance model for portfolio selection based on uncertain measure

This paper discusses a portfolio selection problem in which security returns are given by experts’ evaluations instead of historical data. A factor method for evaluating security returns based on experts’ judgment is proposed and a mean-chance model for optimal portfolio selection is developed taking transaction costs and investors’ preference on diversification and investment limitations on certain securities into account. The factor method of evaluation can make good use of experts’ knowledge on the effects of economic environment and the companies’ unique characteristics on security returns and incorporate the contemporary relationship of security returns in the portfolio. The use of chance of portfolio return failing to reach the threshold can help investors easily tell their tolerance toward risk and thus facilitate a decision making. To solve the proposed nonlinear programming problem, a genetic algorithm is provided. To illustrate the application of the proposed method, a numerical example is also presented.     

A mean-field formulation for optimal multi-period mean–variance portfolio selection with an uncertain exit time

A multi-period mean–variance portfolio selection problem with an uncertain exit time is one of the nonseparable dynamic optimization problems as the principle of optimality of dynamic programming no longer applies. In this paper, we introduce a mean-field formulation to tackle this multi-period nonseparable problem directly without introducing an embedding scheme. Moreover, we shed light on the efficient feature of the mean-field formulation when dealing with the issue of dynamic nonseparability.