An efficient methodology for robust control of dynamic systems with interval matrix uncertainties

Interval models are frequently used for dealing with uncertainties of control systems. However, it is well known that direct analysis and synthesis of a controlled dynamic system with interval matrix uncertainties may be a NP-hard problem. In this work, an efficient methodology for robustness analysis and robust control design of dynamic systems with interval matrix uncertainties is presented systematically, in which the uncertainties appearing in the controlled plant and controller realisation are taken into account simultaneously in an integrated framework. The fundamental problems, such as quadratic stability, guaranteed cost control and H_∞ control of uncertain systems are taken as examples to show the methodology. Necessary and sufficient conditions for linear dynamic systems with interval matrices are derived by transforming all the interval matrices into some more tractable forms. The whole reasoning process is logical and rigorous, and NP-hard problem is successfully avoided. The presented formulations are within the framework of linear matrix inequality and can be implemented conveniently. In contrast to existing vertex-set methods, in which the vertices of interval matrices need to be constructed and checked, the presented methods are more efficient. Three numerical examples are investigated to demonstrate the effectiveness and feasibility of the presented method.     

Modeling Multibody Systems with Uncertainties. Part I: Theoretical and Computational Aspects

This study explores the use of generalized polynomial chaos theory for modeling complex nonlinear multibody dynamic systems in the presence of parametric and external uncertainty. The polynomial chaos framework has been chosen because it offers an efficient computational approach for the large, nonlinear multibody models of engineering systems of interest, where the number of uncertain parameters is relatively small, while the magnitude of uncertainties can be very large (e.g., vehicle-soil interaction). The proposed methodology allows the quantification of uncertainty distributions in both time and frequency domains, and enables the simulations of multibody systems to produce results with “error bars”. The first part of this study presents the theoretical and computational aspects of the polynomial chaos methodology. Both unconstrained and constrained formulations of multibody dynamics are considered. Direct stochastic collocation is proposed as less expensive alternative to the traditional Galerkin approach. It is established that stochastic collocation is equivalent to a stochastic response surface approach. We show that multi-dimensional basis functions are constructed as tensor products of one-dimensional basis functions and discuss the treatment of polynomial and trigonometric nonlinearities. Parametric uncertainties are modeled by finite-support probability densities. Stochastic forcings are discretized using truncated Karhunen-Loeve expansions. The companion paper “Modeling Multibody Dynamic Systems With Uncertainties. Part II: Numerical Applications” illustrates the use of the proposed methodology on a selected set of test problems. The overall conclusion is that despite its limitations, polynomial chaos is a powerful approach for the simulation of multibody systems with uncertainties.     

Robust stabilization of switched positive linear systems with uncertainties

This paper investigates the robust stabilization of a class of switched positive linear systems. The uncertainties of system models refer to the interval and polytopic uncertainty. By using the multiple linear copositive Lyapunov functions approach and linear programming approache, the robust stabilization of those systems in the autonomous form with uncertainties is studied. Further, the control synthesis of those systems in the non-autonomous form with uncertainties is addressed. Finally, a simulating example illustrates the validity of the design.     

Sliding-mode control of uncertain systems in the presence of unmatched disturbances with applications

This article considers the development of constructive sliding-mode control strategies based on measured output information only for linear, time-delay systems with bounded disturbances that are not necessarily matched. The novel feature of the method is that linear matrix inequalities are derived to compute solutions to both the existence problem and the finite time reachability problem that minimise the ultimate bound of the reduced-order sliding-mode dynamics in the presence of state time-varying delay and unmatched disturbances. The methodology provides guarantees on the level of closed-loop performance that will be achieved by uncertain systems which experience delay. The methodology is also shown to facilitate sliding-mode controller design for systems with polytopic uncertainties, where the uncertainty may appear in all blocks of the system matrices. A time-delay model with polytopic uncertainties from the literature provides a tutorial example of the proposed method. A case study involving the practical application of the design methodology in the area of autonomous vehicle control is also presented.     

Robust design optimization of electro-thermal microactuator using probabilistic methods

Micromachining of microelectromechanical systems which is similar to other fabrication processes has inherent variation that leads to uncertain dimensional and material properties. Methods for optimization under uncertainty analysis can be used to reduce microdevice sensitivity to these uncertainties in order to create a more robust design, thereby increasing reliability and yield. In this paper, approaches for uncertainty and sensitivity analysis, and robust optimization of an electro-thermal microactuator are applied to take into account the influence of dimensional and material property uncertainties on microactuator tip deflection. These uncertainties include variation of thickness, length and width of cold and hot arms, gap, Young modulus and thermal expansion coefficient. A simple and efficient uncertainty analysis method is performed by creating second-order metamodel through Box-Behnken design and Monte Carlo simulation. Also, the influence of uncertainties has been examined using direct Monte Carlo Simulation method. The results show that the standard deviations of tip deflection generated by these uncertainty analysis methods are very close to each other. Simulation results of tip deflection have been validated by a comparison with experimental results in literature. The analysis is performed at multiple input voltages to estimate uncertainty bands around the deflection curve. Experimental data fall within 95 % confidence boundary obtained by simulation results. Also, the sensitivity analysis results demonstrate that microactuator performance has been affected more by thermal expansion coefficient and microactuator gap uncertainties. Finally, approaches for robust optimization to achieve the optimal designs for microactuator are used. The proposed robust microactuators are less sensitive to uncertainties. For this goal, two methods including Genetic Algorithm and Non-dominated Sorting Genetic Algorithm are employed to find the robust designs for microactuator.     

Robust stability considerations in optimal design of dynamic systems under uncertainty

This paper presents a method for the incorporation of robust stability criteria in the design of dynamic systems under uncertainty. Process systems are modelled via dynamic mathematical models, variations include both uncertain parameters and time-varying disturbances, while control structure selection and controller design is considered as part of the design optimization problem. Stability criteria are included, based on the concept of the measure of a matrix, to maintain desired dynamic characteristics, in a multiperiod design formulation. A combined flexibility-stabiluty analysis step is also introduced to ensure feasible and stable operation of the dynamic system in the presence of parametric uncertainties and process disturbances. The potential of the proposed approach is illustrated with a ternary distillation column design and control problem (featuring a rigorous tray-by-tray model).     

Synchronization of uncertain complex dynamical networks via adaptive control

In this paper, synchronization of an uncertain dynamical network with time‐varying delay is investigated by means of adaptive control schemes. Time delays and uncertainties exist universally in real‐world complex networks. Especially, parameters of nodes in these complex networks are usually partially or completely uncertain. Considering the networks with unknown or partially known nodes, we design adaptive controllers for the corresponding complex dynamical networks, respectively. Several criteria guaranteeing synchronization of such systems are established by employing the Lyapunov stability theorem. Analytical and numerical results show that the proposed controllers have high robustness against parameter variations including network topologies, coupling structures, and strength. Copyright © 2008 John Wiley & Sons, Ltd.     

A robust transportation signal control problem accounting for traffic dynamics

Transportation system analysis must rely on predictions of the future that, by their very nature, contain substantial uncertainty. Future demand, demographics, and network capacities are only a few of the parameters that must be accounted for in both the planning and every day operations of transportation networks. While many repercussions of uncertainty exist, a primary concern in traffic operations is to develop efficient traffic signal designs that satisfy certain measures of short term future system performance while accounting for the different possible realizations of traffic state. As a result,uncertainty has to be incorporated in the design of traffic signal systems. Current dynamic traffic equilibrium models accounting for signal design, however, are not suitable for quantifying network performance over the range of possible scenarios and in analyzing the robust performance of the system. The purpose of this paper is to propose a new approach—robust system optimal signal control model; a supply-side within day operational transportation model where future transportation demand is assumed to be uncertain. A robust dynamic system optimal model with an embedded cell transmission model is formulated. Numerical analysis are performed on a test network to illustrate the benefits of accounting for uncertainty and robustness.     

Uncertainty decomposition of quantum networks in SLH framework

This paper presents a systematic method to decompose uncertain linear quantum input‐output networks into uncertain and nominal subnetworks, when uncertainties are defined in SLH representation. To this aim, two decomposition theorems are stated, which show how an uncertain quantum network can be decomposed into nominal and uncertain subnetworks in cascaded connection and how uncertainties can be translated from SLH parameters into state‐space parameters. As a potential application of the proposed decomposition scheme, robust stability analysis of uncertain quantum networks is briefly introduced. The proposed uncertainty decomposition theorems take account of uncertainties in all three parameters of a quantum network and bridge the gap between SLH modeling and state‐space robust analysis theory for linear quantum networks.     

Quantitative Comparison of Bilateral Teleoperation Systems Using μ-Synthesis

This paper presents a quantitative comparison framework for bilateral teleoperation systems (BTSs) that have different dynamic characteristics and sensory configurations for a given task-dependent performance objective (TDPO). mu-synthesis is used to develop the framework since it can efficiently treat systems containing uncertainties and disturbances. The framework consists of: 1) a feasibility test and 2) a comparison methodology using prioritized TDPOs. As the formulation used is based on mu-synthesis, the system, operator, and environment models are represented in the form of linear nominal models with frequency-dependent multiplicative uncertainties. This framework is applied to a BTS including an uncertain human operator and environment in a practical case study. The validity of the proposed quantitative framework is confirmed through experiments. The proposed framework can be used as a tool to design BTSs, especially when there are constraints in designing drive mechanisms and choosing sensory configurations.     

基于学习的鲁棒自适应评判控制研究进展

在作为人工智能核心技术的机器学习领域,强化学习是一类强调机器在与环境的交互过程中进行学习的方法,其重要分支之一的自适应评判技术与动态规划及最优化设计密切相关.为了有效地求解复杂动态系统的优化控制问题,结合自适应评判,动态规划和人工神经网络产生的自适应动态规划方法已经得到广泛关注,特别在考虑不确定因素和外部扰动时的鲁棒自适应评判控制方面取得了很大进展,并被认为是构建智能学习系统和实现真正类脑智能的必要途径.本文对基于智能学习的鲁棒自适应评判控制理论与主要方法进行梳理,包括自学习鲁棒镇定,自适应轨迹跟踪,事件驱动鲁棒控制,以及自适应H_∞控制设计等,并涵盖关于自适应评判系统稳定性、收敛性、最优性以及鲁棒性的分析.同时,结合人工智能、大数据、深度学习和知识自动化等新技术,也对鲁棒自适应评判控制的发展前景进行探讨.     

An efficient framework for optimal robust stochastic system design using stochastic simulation

The knowledge about a planned system in engineering design applications is never complete. Often, a probabilistic quantification of the uncertainty arising from this missing information is warranted in order to efficiently incorporate our partial knowledge about the system and its environment into their respective models. This leads to a robust stochastic design framework where probabilistic models of excitation uncertainties and system modeling uncertainties can be introduced; the design objective is then typically related to the expected value of a system performance measure, such as reliability or expected life-cycle cost. For complex system models, this expected value can rarely be evaluated analytically and so it is often calculated using stochastic simulation techniques, which involve an estimation error and significant computational cost. An efficient framework, consisting of two stages, is presented here for the optimization in such robust stochastic design problems. The first stage implements a novel approach, called stochastic subset optimization (SSO), for iteratively identifying a subset of the original design space that has high plausibility of containing the optimal design variables. The second stage adopts some other stochastic optimization algorithm to pinpoint the optimal design variables within that subset. The focus is primarily on the theory and implementation issues for SSO but also on topics related to the combination of the two different stages for overall enhanced efficiency. An illustrative example is presented that shows the efficiency of the proposed methodology; it considers the optimization of the reliability of a base-isolated structure considering future near-fault ground motions.     

Robust scalable stabilisability conditions for large-scale heterogeneous multi-agent systems with uncertain nonlinear interactions: towards a distributed computing architecture

Large-scale dynamic systems are becoming highly pervasive in their occurrence with applications ranging from system biology, environment monitoring, sensor networks, and power systems. They are characterised by high dimensionality, complexity, and uncertainty in the node dynamic/interactions that require more and more computational demanding methods for their analysis and control design, as well as the network size and node system/interaction complexity increase. Therefore, it is a challenging problem to find scalable computational method for distributed control design of large-scale networks. In this paper, we investigate the robust distributed stabilisation problem of large-scale nonlinear multi-agent systems (briefly MASs) composed of non-identical (heterogeneous) linear dynamical systems coupled by uncertain nonlinear time-varying interconnections. By employing Lyapunov stability theory and linear matrix inequality (LMI) technique, new conditions are given for the distributed control design of large-scale MASs that can be easily solved by the toolbox of MATLAB. The stabilisability of each node dynamic is a sufficient assumption to design a global stabilising distributed control. The proposed approach improves some of the existing LMI-based results on MAS by both overcoming their computational limits and extending the applicative scenario to large-scale nonlinear heterogeneous MASs. Additionally, the proposed LMI conditions are further reduced in terms of computational requirement in the case of weakly heterogeneous MASs, which is a common scenario in real application where the network nodes and links are affected by parameter uncertainties. One of the main advantages of the proposed approach is to allow to move from a centralised towards a distributed computing architecture so that the expensive computation workload spent to solve LMIs may be shared among processors located at the networked nodes, thus increasing the scalability of the approach than the network size. Finally, a numerical example shows the applicability of the proposed method and its advantage in terms of computational complexity when compared with the existing approaches.     

不确定非线性系统的自适应反推高阶终端滑模控制

针对一类非匹配不确定非线性系统,提出一种神经网络自适应反推高阶终端滑模控制方案.反推设计的前1步利用神经网络逼近未知非线性函数,结合动态面控制设计虚拟控制律,避免传统反推设计存在的计算复杂性问题,并抑制非匹配不确定性的影响;第步结合非奇异终端滑模设计高阶滑模控制律,去除控制抖振,使系统对于匹配和非匹配不确定性均具有鲁棒性.理论分析证明了闭环系统状态半全局一致终结有界,仿真结果表明了所提出方法的有效性.     

Topology optimization of structure for dynamic properties considering hybrid uncertain parameters

In the design and manufacturing of mechanical components, the dynamic properties of continuum structure are one of the most significant performances. At the same time, the uncertainty is widespread in these dynamic problems. This paper presents a robust topology optimization methodology of structure for dynamic properties with consideration of hybrid uncertain parameters. The imprecise probability uncertainties including materials, geometry and boundary condition are treated as an interval random model, in which the probability distribution parameters of random variables are modeled as the interval variables instead of given precise values. Two dynamic properties, including dynamic-compliance and eigenvalue, are chosen as the objective function. In addition, different excitation frequency or eigenvalue is discussed. In this work, the bi-directional evolutionary structural optimization (BESO) method is adopted to find the optimal robust layout of the structure. A series of numerical examples is presented to illustrate the optimization procedure, and the effectiveness of the proposed method is demonstrated clearly.     

Probabilistic Robust Linear Parameter-varying Control of a Small Helicopter Using Iterative Scenario Approach

In this paper, we present an iterative scenario approach (ISA) to design robust controllers for complex linear parameter-varying (LPV) systems with uncertainties. The robust controller synthesis problem is transformed to a scenario design problem, with the scenarios generated by identically extracting random samples on both uncertainty parameters and scheduling parameters. An iterative scheme based on the maximum volume ellipsoid cutting-plane method is used to solve the problem. Heuristic logic based on relevance ratio ranking is used to prune the redundant constraints, and thus, to improve the numerical stability of the algorithm. And further, a batching technique is presented to remarkably enhance the computational efficiency. The proposed method is applied to design an output-feedback controller for a small helicopter. Multiple uncertain physical parameters are considered, and simulation studies show that the closed-loop performance is quite good in both aspects of model tracking and dynamic decoupling. For robust LPV control problems, the proposed method is more computationally efficient than the popular stochastic ellipsoid methods.      

Robust near-optimal output feedback control of non-linear systems

This work proposes a robust near-optimal non-linear output feedback controller design for a broad class of non-linear systems with time-varying bounded uncertain variables. Both vanishing and non-vanishing uncertainties are considered. Under the assumptions of input-to-state stable (ISS) inverse dynamics and vanishing uncertainty, a robust dynamic output feedback controller is constructed through combination of a high-gain observer with a robust optimal state feedback controller synthesized via Lyapunov's direct method and the inverse optimal approach. The controller enforces exponential stability and robust asymptotic output tracking with arbitrary degree of attenuation of the effect of the uncertain variables on the output of the closed-loop system, for initial conditions and uncertainty in arbitrarily large compact sets, provided that the observer gain is sufficiently large. Utilizing the inverse optimal control approach and singular perturbation techniques, the controller is shown to be near-optimal in the sense that its performance can be made arbitrarily close to the optimal performance of the robust optimal state feedback controller on the infinite time-interval by selecting the observer gain to be sufficiently large. For systems with non-vanishing uncertainties, the same controller is shown to ensure boundedness of the states, uncertainty attenuation and near-optimality on a finite time-interval. The developed controller is successfully applied to a chemical reactor example.     

Robust energy cost optimization of water distribution system with uncertain demand

A new methodology for the optimizing daily operations of pumping stations is proposed, which takes into account the fact that a water distribution system in reality is unavoidably affected by uncertainties. For operation control, the main source of uncertainty is the uncertainty in the demand. Traditional methods for optimizing dynamical systems under uncertainty (Multistage Stochastic Programming) results in computationally intractable models already for small water distribution networks. The most popular optimization method for these problems is Dynamic Programming; however, in practice applications of this approach are restricted to networks with 1–2 pumping stations and/or 1–2 storages, because of severe computational difficulties arising in when state dimension of the controlled dynamical system exceeds 1–2. The new approach presented in this paper provides a computationally tractable alternative to the outlined traditional methods in the cases when the problem under consideration, in the absence of uncertainty, can be formulated as a Linear Programming problem.     

Robust observer design for uncertain one‐sided Lipschitz systems with disturbances

In this paper, we study the robust observer design problem for a class of uncertain one‐sided Lipschitz systems with disturbances. Not only the system matrices but also the nonlinear functions are assumed to be uncertain. The nominal models of nonlinearities are assumed to satisfy both the one‐sided Lipschitz condition and the quadratically inner‐bounded condition. By utilizing a novel approach, our observer designs are robust against unknown nonlinear uncertainties and system and measurement noises. The new approach also relaxes some conservativeness in related existing results, ie, less conservative observer design conditions are obtained. Furthermore, the problem of designing reduced‐order observers is considered in case the output measurement is not subject to uncertainty and disturbance. Two examples are provided to show the efficiency and advantages of our results over existing works.