State estimation for complex systems with randomly occurring nonlinearities and randomly missing measurements

This paper is concerned with the state estimation problem for the complex networked systems with randomly occurring nonlinearities and randomly missing measurements. The nonlinearities are included to describe the phenomena of nonlinear disturbances which exist in the network and may occur in a probabilistic way. Considering the fact that probabilistic data missing may occur in the process of information transmission, we introduce the randomly data missing into the sensor measurements. The aim of this paper is to design a state estimator to estimate the true states of the considered complex network through the available output measurements. By using a Lyapunov functional and some stochastic analysis techniques, sufficient criteria are obtained in the form of linear matrix inequalities under which the estimation error dynamics is globally asymptotically stable in the mean square. Furthermore, the state estimator gain is also obtained. Finally, a numerical example is employed to illustrate the effectiveness of the proposed state estimation conditions.     

Worst case control of uncertain jumping systems with multi-state and input delay information

In this paper, the problem of worst case (also called H_∞) Control for a class of uncertain systems with Markovian jump parameters and multiple delays in the state and input is investigated. The jumping parameters are modelled as a continuous-time, discrete-state Markov process and the parametric uncertainties are assumed to be real, time-varying and norm-bounded that appear in the state, input and delayed-state matrices. The time-delay factors are unknowns and time-varying with known bounds. Complete results for instantaneous and delayed state feedback control designs are developed which guarantee the weak-delay dependent stochastic stability with a prescribed H_∞-performance. The solutions are provided in terms of a finite set of coupled linear matrix inequalities (LMIs). Application of the developed theory to a typical example has been presented.     

Control of randomly varying systems with prescribed degree ofstability

The control of linear discrete-time systems with stochastic parameter matrices is discussed. Two control techniques are particularly used: infinite-horizon and finite-moving-horizon optimal regulators. It is shown that it is possible to design controllers with a guaranteed degree of exponential stochastic stability by properly modifying the performance indexes. In this way, the deterministic regulator problem with a prescribed degree of stability is extended to the case of stochastic parameter systems     

Lower and upper bounds for a capacitated plant location problem with multicommodity flow

In this paper, we introduce a capacitated plant location problem with multicommodity flow. Given a set of potential plant sites and a set of capacitated arcs linking plants, transshipment points and customers, the aim is to determine where to locate plants and how to move flows from open plants to customers through a set of transshipment points. This model extends the classical capacitated plant location problem by introducing a multicommodity flow problem in the distribution issue. The combination of the location problem and the flow distribution problem is reasonable and realistic since both of them belong to strategic planning horizons. We propose a Lagrangean-based method, including a Lagrangean relaxation, a Lagrangean heuristic and a subgradient optimization, to provide lower and upper bounds of the model. Then, we employ a Tabu search to further improve upper bounds provided by the Lagrangean procedure. The computational results demonstrate that our solution method is effective since gaps between the upper and lower bound are on average around 2%.     

Stability of solutions of dynamic systems with randomly structured aftereffect

The relation is established between the asymptotic stochastic stability of a linear functional differential equation and exponential stability of the trivial solution to this equation. The direct and inverse Lyapunov theorems on the stability of linear differential equations are proved. __________ Translated from Kibernetika i Sistemnyi Analiz, No. 2, pp. 31–38, March–April 2006.     

Stability of systems with nonlinear feedback through randomly time-varying delays

In a large class of multiloop control systems, many feedback loops are "closed" through a time-shared digital computer, using algorithms which require information from sources which are sampled at a rate which is not synchronized with the sampling of the individual "plants." This missynchronization, in conjunction with variations in the computer's task load caused by "interrupts," results in a randomly time-varying delay in the closing of the various feedback loops. Consequently, the dynamics of each controlled "plant" in such a system may be modeled by means of a stochastic delay-differential equation. This paper presents some new research results concerning the sample stability (as opposed to statistical, or ensemble stability) of nonlinear stochastic delay-differential equations.     

Optimum filtering and control of randomly sampled systems

Kalman's concept of optimum filtering is interpreted in such a way that it can be applied to both nonlinear and linear systems with Gaussian or non-Gaussian statistics. The essential idea is to synthesize a generalized Kalman filter in two stages, a) propagation and b) measurement and correction. The analysis of each stage is independent of the other, and the generalized results are quite simple. In the present paper, the application of the above result is confined to linear systems: 1) Optimum filtering and interpolation of randomly sampled signals; for the interpolation problem it is assumed that the signals are measured exactly at the sampling instant. 2) Optimum filtering of related continuous and randomly sampled signals. 3) Optimum control of randomly sampled linear systems with quadratic cost criterion.     

Maximum achievable precision of linear systems with discrete controllers

Consideration was given to the problem of maximum achievable precision of linear systems with discrete state and output controllers. The external perturbations affecting the system are the bounded step-type and harmonic (of unknown frequency) vector functions of time which the control theory regards as standard. The condition for asymptotic stability of the closed-loop system is the only requirement on the controllers aside from their physical realizability. Therefore, the conclusions of the present paper apply to the entire set of the discrete stabilizing controllers, no matter what method was used to design them.     

The consensus of multi-agent systems with uncertainties and randomly occurring nonlinearities via impulsive control

In many real-world multi-agent systems, the intrinsic dynamics of the agents are usually dynamic rather than static as the environmental uncertainty and the additive exogenous disturbance input. This paper aims at investigating the consensus problem of multi-agent systems with uncertainties and randomly occurring nonlinearities (RONs). Consider the robust and lost-cost, an effective impulsive control protocol is designed. Based on the Lyapunov stability theory and hybrid control theory, sufficient conditions are obtained to ensure consensus of multi-agent systems. Furthermore, both mathematical investigations and numerical simulations are presented to demonstrate the effectiveness of the proposed approaches.     

Optimal and suboptimal smoothing algorithms for identification of time-varying systems with randomly drifting parameters

Noncausal estimation algorithms, which involve smoothing, can be used for off-line identification of nonstationary systems. Since smoothing is based on both past and future data, it offers increased accuracy compared to causal (tracking) estimation schemes, incorporating past data only. It is shown that efficient smoothing variants of the popular exponentially weighted least squares and Kalman filter-based parameter trackers can be obtained by means of backward-time filtering of the estimates yielded by both algorithms. When system parameters drift according to the random walk model and the adaptation gain is sufficiently small, the properly tuned two-stage Kalman filtering/smoothing algorithm, derived in the paper, achieves the Cramér-Rao type lower smoothing bound, i.e. it is the optimal noncausal estimation scheme. Under the same circumstances performance of the modified exponentially weighted least-squares algorithm is often only slightly inferior to that of the Kalman filter-based smoother.     

Robust stabilisation of 2D state-delayed stochastic systems with randomly occurring uncertainties and nonlinearities

This paper is concerned with the state feedback control problem for a class of two-dimensional (2D) discrete-time stochastic systems with time-delays, randomly occurring uncertainties and nonlinearities. Both the sector-like nonlinearities and the norm-bounded uncertainties enter into the system in random ways, and such randomly occurring uncertainties and nonlinearities obey certain mutually uncorrelated Bernoulli random binary distribution laws. Sufficient computationally tractable linear matrix inequality–based conditions are established for the 2D nonlinear stochastic time-delay systems to be asymptotically stable in the mean-square sense, and then the explicit expression of the desired controller gains is derived. An illustrative example is provided to show the usefulness and effectiveness of the proposed method.     

Decision making procedure of demand satisfaction and production policy for capacitated production systems

This paper develops a reliability-based decision making procedure for production systems to (i) evaluate the system reliability and (ii) determine the reliable production policy. The production system is represented as a capacitated production network (CPN) for system reliability evaluation, in which the system reliability is defined as the probability of demand satisfaction. The decision making to determine a reliable production policy is based on the derived system reliability. Two layouts are considered in this paper: the first layout is for the CPN with parallel lines; while the second layout is for the CPN with joint lines. Transformation and decomposition techniques are proposed to generate all minimal capacity vectors that workstations should provide to satisfy demand. In terms of the minimal capacity vectors, the system reliability is derived by applying the recursive sum of disjoint products (RSDP) algorithm. A case study in the context of footwear production system is utilized to demonstrate the decision making procedure.     

Dissipative control for state-saturated discrete time-varying systems with randomly occurring nonlinearities and missing measurements

In this paper, the dissipative control problem is investigated for a class of discrete time-varying systems with simultaneous presence of state saturations, randomly occurring nonlinearities as well as multiple missing measurements. In order to render more practical significance of the system model, some Bernoulli distributed white sequences with known conditional probabilities are adopted to describe the phenomena of the randomly occurring nonlinearities and the multiple missing measurements. The purpose of the addressed problem is to design a time-varying output-feedback controller such that the dissipativity performance index is guaranteed over a given finite-horizon. By introducing a free matrix with its infinity norm less than or equal to 1, the system state is bounded by a convex hull so that some sufficient conditions can be obtained in the form of recursive nonlinear matrix inequalities. A novel controller design algorithm is then developed to deal with the recursive nonlinear matrix inequalities. Furthermore, the obtained results are extended to the case when the state saturation is partial. Two numerical simulation examples are provided to demonstrate the effectiveness and applicability of the proposed controller design approach.     

Adaptive efficient global optimization of systems with independent components

We present a novel approach for efficient optimization of systems consisting of expensive to simulate components and relatively inexpensive system-level simulations. We consider the types of problem in which the components of the system problem are independent in the sense that they do not exchange coupling variables, however, design variables can be shared across components. Component metamodels are constructed using Kriging. The metamodels are adaptively sampled based on a system level infill sampling criterion using Efficient Global Optimization. The effectiveness of the technique is demonstrated by applying it on numerical examples and an engineering case study. Results show steady and fast converge to the global deterministic optimum of the problems.     

Leader-following consensus of nonlinear multi-agent systems with randomly occurring uncertainties and stochastic disturbances under impulsive control input

This paper focuses on the leader-following consensus problem of nonlinear multi-agent systems with randomly occurring uncertainties and stochastic disturbances under impulsive control input. Based on the average impulsive interval, a unified consensus criterion is derived for multi-agent systems. On the other hand, our consensus criterion is applicable to impulsive control sequences in which the lower bound of impulsive interval is allowed to be arbitrarily small and the upper bound of impulsive interval is allowed to be big enough. The proposed consensus criterion is theoretically and numerically proved to be less conservative than existing results. Two numerical simulations illustrate the effectiveness of theoretical results.     

Reliability analysis for k-out-of-n systems with shared load and dependent components

Many structural systems require a minimal number of components to be operational, and predicting the reliability of such systems is a challenge because surviving components share the original system workload with higher component loads after the failure of some components. The states of all the components are also dependent. Such dependence, however, is generally neglected in many existing methods. In this study, we develop a new reliability method for systems with dependent components that share the system load equally before and after other components have failed. The components are also subjected to other loads, such as a preload. The new method is based on limit-state functions that predict the states of components, and the First Order Reliability Method is used. The advantage of the proposed method is that it can directly link the system reliability with design variables and random parameters because of the use of a physics-based approach. High accuracy is maintained with the consideration of dependent component states. Two examples are used to demonstrate the good accuracy and efficiency of the proposed method.     

Early verification and validation of mission critical systems

Complex software and systems are pervasive in today’s world. In a growing number of fields they come to play a critical role. In order to provide a high assurance level, verification and validation (V&V) should be considered early in the development process. This paper shows how this can be achieved based on a goal-oriented requirements engineering framework which combines complementary semi-formal and formal notations. This allows the analyst to formalize only when and where needed and also preserves optimal communication with stakeholders and developers. For the industrial application of the methodology, a supporting toolbox was developed. It consist of a number of tightly integrated tools for performing V&V tasks at requirements level. This is achieved through the use of (1) a roundtrip mapping between the requirements language and the specific formal languages used in the underlying formal tools (such as SAT or constraint solvers) and (2) graphical views using domain-based representations. This paper will focus on two major and representative tools: the Refinement Checker (about verification) and the Animator (about validation).