Control of Stochastic Systems with Time-Varying Multiple Time Delays: LMI Approach

This paper deals with the class of continuous-time linear systems with Markovian jumps and multiple time delays. The systems that we are treating are assumed to have time-varying delays in their dynamics which can be different and also have uncertainties in the system parameters. The time-varying structure of the bounded uncertainties is considered. Delay-dependent conditions for stochastic stability and stochastic stabilizability and their robustness are considered. A design algorithm for a stabilizing memoryless controller is proposed. All the results are given in the LMI formalism.     

Robust stabilization of uncertain linear dynamical systems with time-varying delay

In this paper, the problem of the robust stabilization for a class of uncertain linear dynamical systems with time-varying delay is considered. By making use of an algebraic Riccati equation, we derive some sufficient conditions for robust stability of time-varying delay dynamical systems with unstructured or structured uncertainties. In our approach, the only restriction on the delay functionh(t) is the knowledge of its upper boundh ^–. Some analytical methods are employed to investigate these stability conditions. Since these conditions are independent of the delay, our results are also applicable to systems with perturbed time delay. Finally, a numerical example is given to illustrate the use of the sufficient conditions developed in this paper.     

Hard uncertainties in multiobjective layout optimization of photovoltaic power plants

This paper describes how to treat hard uncertainties defined by so-called uncertainty maps in multiobjective optimization problems. For the uncertainty map being set-valued, a Taylor formula is shown under appropriate assumptions. The hard uncertainties are modeled using parametric set optimization problems for which a scalarization result is given. The presented new approach for the solution of multiobjective optimization problems with hard uncertainties is then applied to the layout optimization of photovoltaic power plants. Since good weather forecasts are difficult to obtain for future years, weather data are really hard uncertainties arising in the planning process. Numerical results are presented for a real-world problem on the Galapagos island Isabela.     

参数不确定统一混沌系统的鲁棒分数阶比例-微分控制

针对含参数不确定的整数阶统一混沌系统, 提出一种鲁棒分数阶比例-微分(PD^μ)控制. 通过变换将受控统一混沌系统转换成等效被控对象及其等效控制器. 针对等效被控对象, 基于一种改进Monje-Vinagre方法并考虑到求解性能约束方程组的复杂度, 设计了鲁棒PD^μ控制器. 通过基于最小相角边界传递函数和最大增益边界传递函数的设计约束来保证受控统一混沌系统对参数不确定性的鲁棒性能. 数值仿真验证了所提出方法的有效性.     

Observer-based passive control for uncertain linear systems with delay in state and control input

This paper deals with the robust passivity synthesis problem for a class of uncertain linear systems with time-varying delay in state and control input. The parameter uncertainties are norm-bounded and allowed to appear in all matrices of the model. The problem aims at designing an observer-based dynamic output-feedback controller that robustly stabilizes the uncertain systems and achieves the strict passivity of closed-loop systems for all admissible uncertainties. By converting the problem at hand into a class of strictly passive control problem for a parameterized system, the explicit solution is established and expressed in terms of a linear matrix inequality. A numerical example is provided to demonstrate the validity of the proposed approach.     

Finite attraction for nonlinear uncertain mechanical systems

This paper deals with the robust control problem for uncertainnonlinear mechanical systems with ideal and holonomic constraints.A robust control law having the form of state feedback is obtained.The control law consists of two parts: the first one is a nominalcontrol law which affects the behaviour of the nominal dynamicsfor the considered mechanical system; the second one is a learningcontrol law which reduces the influence of uncertainties onthe stability of the mechanical system. Under the action ofthe robust control law, the closed-loop system for the uncertainmechanical system reaches a region specified a short time inadvance.     

Decentralized robust control for a class of uncertain large-scale interconnected nonlinear dynamical systems

The problem of the decentralized robust control for a class of large-scale interconnected nonlinear dynamical systems with input interconnection and external interconnection perturbations is considered. Based on the stabilizability of each nominal isolated subsystem (i.e., the isolated subsystem in the absence of interconnection perturbations), a class of decentralized local state feedback controllers is proposed, and some sufficient conditions are derived by making use of the Lyapunov stability criterion such that uncertain large-scale interconnected systems can be stabilized asymptotically by these decentralized state feedback controllers. For large-scale systems with only input interconnection perturbations, such decentralized controllers become a class of decentralized stabilizing state feedback controllers. That is, the decentralized stability of such large-scale systems can be guaranteed always by using the decentralized state feedback controllers proposed in the paper. Finally, a numerical example is given to demonstrate the validity of the results.     

基于前景理论的混合不确定情景下在线多属性反向拍卖的赢者确定方法

在线反向拍卖在当今的经济社会发展中扮演越来越重要的角色,其主要应用于采购招标领域。而在实际的采购拍卖中有关商品属性和供应商信息等方面常会存在一定程度的不确定性,且这些不确定性的刻画又存在着多种模糊表述形式,这些都将增加采购方的风险预期和竞标供应商赢者确定的难度。为此,本文基于前景理论及模糊集理论,研究了同时存在精确数、区间数、三角模糊数、梯形模糊数和语义模糊术语五种属性描述方式的在线多属性反向拍卖的赢者确定问题,提出了一种更具一般性的混合不确定情景下的在线多属性反向拍卖赢者(中标者)确定方法。最后,通过数值算例和比较分析验证了本文所提方法的合理性与有效性,并通过稳健性分析进一步说明方法的稳定性和适用性。     

An application of the Kriging method in global sensitivity analysis with parameter uncertainty

For structural systems with both epistemic and aleatory uncertainties, the effect of epistemic uncertainty on failure probability is measured by the variance based sensitivity analysis, which generally needs a “triple-loop” crude sampling procedure to solve and is time consuming. Thus, the Kriging method is employed to avoid the complex sampling procedure and improve the computational efficiency. By utilizing the Kriging predictor model, the conditional expectation of failure probability on the given epistemic uncertainty can be calculated efficiently. Compared with the Sobol’s method, the proposed one can ensure reasonable accuracy of results but with lower computational cost. Three examples are employed to demonstrate the reasonability and efficiency of the proposed method.     

LMI‐based criterion for the robust guaranteed cost control of uncertain switched neutral systems with time‐varying mixed delays and nonlinear perturbations by dynamic output feedback

This article reports on an investigation into robust guaranteed cost control (GCC) for uncertain switched neutral systems (USNSs) with interval time‐varying mixed delays and nonlinear perturbations via dynamic output feedback. Delay‐dependent sufficient conditions are suggested to guarantee the robust exponential stability and to obtain robust GCC for USNSs using the average dwell time approach and the piecewise Lyapunov function technique in terms of a set of linear matrix inequalities. The problem of uncertainty in the system model is solved by deploying the Yakubovich lemma. Lastly, two examples (i.e., a numerical example and the water‐quality dynamic model for the Nile River) are given to verify the efficiency of the propounded theories. © 2016 Wiley Periodicals, Inc. Complexity 21: 555–578, 2016