Input-to-state stability of switched stochastic delayed systems with Lévy noise

This paper focuses on input-to-state stability of a class of switched stochastic delayed systems which are drived by Lévy noise. By multiple Lyapunov function and average dwell time approach, the sufficient conditions of the ψ^λ(t)-weighted input-to-state stability can be obtained if all the subsystems are input-to-state stable. Then utilizing comparison principle and the method of constant variation, the sufficient criteria of the e^λt-weighted input-to-state stability of the switched stochastic delayed systems containing both input-to-state stable subsystems and non-input-to-state stable subsystems can also be derived. Finally, an example is given to illustrate the effectiveness of the proposed results.     

Robust estimations of the Region of Attraction using invariant sets

The Region of Attraction of an equilibrium point is the set of initial conditions whose trajectories converge to it asymptotically. This article, building on a recent work on positively invariant sets, deals with inner estimates of the ROA of polynomial nonlinear dynamics. The problem is solved numerically by means of Sum Of Squares relaxations, which allow set containment conditions to be enforced. Numerical issues related to the ensuing optimization are discussed and strategies to tackle them are proposed. These range from the adoption of different iterative methods to the reduction of the polynomial variables involved in the optimization. The main contribution of the work is an algorithm to perform the ROA calculation for systems subject to modeling uncertainties, and its applicability is showcased with two case studies of increasing complexity. Results, for both nominal and uncertain systems, are compared with a standard algorithm from the literature based on Lyapunov function level sets. They confirm the advantages in adopting the invariant sets approach, and show that as the size of the system and the number of uncertainty increase, the proposed heuristics ameliorate the commented numerical issues.     

Rank hash similarity for fast similarity search

The paper is concerned with similarity search at large scale, which efficiently and effectively finds similar data points for a query data point. An efficient way to accelerate similarity search is to learn hash functions. The existing approaches for learning hash functions aim to obtain low values of Hamming distances for the similar pairs. However, these methods ignore the ranking order of these Hamming distances. This leads to the poor accuracy about finding similar items for a query data point. In this paper, an algorithm is proposed, referred to top k RHS (Rank Hash Similarity), in which a ranking loss function is designed for learning a hash function. The hash function is hypothesized to be made up of l binary classifiers. The issue of learning a hash function can be formulated as a task of learning l binary classifiers. The algorithm runs l rounds and learns a binary classifier at each round. Compared with the existing approaches, the proposed method has the same order of computational complexity. Nevertheless, experiment results on three text datasets show that the proposed method obtains higher accuracy than the baselines.     

Event-triggered H∞ state estimation for state-saturated complex networks subject to quantization effects and distributed delays

This paper is concerned with the event-triggered H_∞ state estimation problem for a class of discrete-time complex networks subject to state saturations, quantization effects as well as randomly occurring distributed delays. A series of Bernoulli distributed random variables is utilized to model the random occurrence of distributed delays. For the energy-saving purpose, an event-triggered mechanism is proposed to decide whether the current quantized measurement should be transmitted to the estimator or not. For the state-saturated complex networks, our aim is to design event-triggered state estimators that guarantee both the exponential mean-square stability of and the H_∞ performance constraint on the error dynamics of the state estimation. Stochastic analysis is conducted, in combination with the Lyapunov functional approach, to derive sufficient conditions for the existence of the desired estimators whose gain matrices are obtained by solving a set of matrix inequalities. An illustrative example is exploited to show the usefulness of the estimator design algorithm proposed.     

Distributed dynamic state estimation with parameter identification for large-scale systems

In this paper, we consider a distributed dynamic state estimation problem for time-varying systems. Based on the distributed maximum a posteriori (MAP) estimation algorithm proposed in our previous study, which studies the linear measurement models of each subsystem, and by weakening the constraint condition as that each time-varying subsystem is observable, this paper proves that the error covariances of state estimation and prediction obtained from the improved algorithm are respectively positive definite and have upper bounds, which verifies the feasibility of this algorithm. We also use new weighting functions and time-varying exponential smoothing method to ensure the robustness and improve the forecast accuracy of the distributed state estimation method. At last, an example is used to demonstrate the effectiveness of the proposed algorithm together with the parameter identification.     

H∞ control of periodic piecewise polynomial time-varying systems with polynomial Lyapunov function

In this paper, the H_∞ control problem of periodic piecewise systems with polynomial time-varying subsystems is addressed. Based on a periodic Lyapunov function with a continuous time-dependent Lyapunov matrix polynomial, the H_∞ performance is studied. The result can be easily reduced to the conditions for periodic piecewise systems with constant subsystems or linear time-varying systems based on a common Lyapunov function or a linear time-varying Lyapunov matrix. Moreover, an H_∞ controller with time-varying polynomial controller gain is proposed as well, which could be directly solved with the linear matrix inequalities. A numerical example is presented to demonstrate the effectiveness of the proposed method.     

Prescribed-time stabilization for high-order nonlinear systems with a pre-specified asymmetric output constraint

This article considers the problem of prescribed-time stabilization for a class of uncertain high-order nonlinear systems (i.e., systems in the $p$-normal form) with a pre-specified asymmetric output constraint. A core ingredient, tangent-type barrier function, is proposed first by skillfully excavating and assimilating the inherent properties of system nonlinearities. Based on the barrier function, as well as a serial of nested signum functions, the celebrated technique of adding a power integrator is renovated finely to establish a new design approach by which a continuous state feedback prescribed-time stabilizer, along with a tangent-type asymmetric barrier Lyapunov function, can be constructed in a systematic fashion, thereby guaranteeing the performance of prescribed-time state convergence and ensuring the fulfillment of pre-specified output constraints surely. Benefiting from the composite characteristics of the presented tangent-type barrier Lyapunov function and the signum functions, the proposed approach further offers a unified nature in design enabling us to organize a prescribed-time stabilizer that is simultaneously valid and executable for the system undergone or free from output constraints, without the need of changing the controller structure. The effectiveness and superiority of the developed approach are illustrated by a numerical example.     

Robust H∞ filtering for switched stochastic systems under asynchronous switching

This paper investigates the problem of robust H_∞ filtering for switched stochastic systems under asynchronous switching. The so-called asynchronous switching means that the switching between the filters and system modes is asynchronous. The aim is to design a filter ensuring robust exponential mean square stability and a prescribed H_∞ performance level for the filtering error systems. Based on the average dwell time approach and piecewise Lyapunov functional technique, sufficient conditions for the existence of the robust H_∞ filter are derived, and the proposed filter can be obtained by solving a set of LMIs(linear matrix inequalities). Finally, a numerical example is given to show the effectiveness of the proposed approach.     

Quality versus efficiency in document scoring with learning-to-rank models

Learning-to-Rank (LtR) techniques leverage machine learning algorithms and large amounts of training data to induce high-quality ranking functions. Given a set of documents and a user query, these functions are able to precisely predict a score for each of the documents, in turn exploited to effectively rank them. Although the scoring efficiency of LtR models is critical in several applications – e.g., it directly impacts on response time and throughput of Web query processing – it has received relatively little attention so far.The goal of this work is to experimentally investigate the scoring efficiency of LtR models along with their ranking quality. Specifically, we show that machine-learned ranking models exhibit a quality versus efficiency trade-off. For example, each family of LtR algorithms has tuning parameters that can influence both effectiveness and efficiency, where higher ranking quality is generally obtained with more complex and expensive models. Moreover, LtR algorithms that learn complex models, such as those based on forests of regression trees, are generally more expensive and more effective than other algorithms that induce simpler models like linear combination of features.We extensively analyze the quality versus efficiency trade-off of a wide spectrum of state-of-the-art LtR, and we propose a sound methodology to devise the most effective ranker given a time budget. To guarantee reproducibility, we used publicly available datasets and we contribute an open source C++ framework providing optimized, multi-threaded implementations of the most effective tree-based learners: Gradient Boosted Regression Trees (GBRT), Lambda-Mart (λ-MART), and the first public-domain implementation of Oblivious Lambda-Mart (Ω_λ-MART), an algorithm that induces forests of oblivious regression trees.We investigate how the different training parameters impact on the quality versus efficiency trade-off, and provide a thorough comparison of several algorithms in the quality-cost space. The experiments conducted show that there is not an overall best algorithm, but the optimal choice depends on the time budget.     

Characterization of chaotic multiscale features on the time series of melt index in industrial propylene polymerization system

The chaos characteristics of melt index have been first explored, and the Hilbert–Huang transform method and time delay embedding method are applied to multiscale dynamic analysis on the time series of the melt index (MI) in the propylene polymerization industry. The research results show that the embedding delay is 2, the embedding dimension is 5, the correlation dimension D₂ is 1.57, and the maximum Lyapunov exponent is 0.143 for the melt index series, which provide clear evidence of chaotic multiscale features in the propylene polymerization process. Three intrinsic mode functions (IMFs) are decomposed from the melt index time series; the presence of non-integer fractal correlation dimension and positive finite maximum Lyapunov exponent are found in some IMF components. The PP melt index series are divided into two chaotic signals, a determined signal and a random signal respectively, and its complexity is therefore reduced. Furthermore, the coupling of subscale structures of the propylene polymerization is explored with the dimension of interaction dynamics and a robust algorithm for detecting interdependence. It is found that IMF(2) is the main driver in the coupling system of IMF(1)and IMF(2). All these provide a guideline for studying propylene polymerization process with chaotic multiscale theory and may offer more candidate tools to model and control propylene polymerization system in the future.     

Distributed consensus-based multi-agent convex optimization via gradient tracking technique

This paper considers solving a class of optimization problems over a network of agents, in which the cost function is expressed as the sum of individual objectives of the agents. The underlying communication graph is assumed to be undirected and connected. A distributed algorithm in which agents employ time-varying and heterogeneous step-sizes is proposed by combining consensus of multi-agent systems with gradient tracking technique. The algorithm not only drives the agents’ iterates to a global and consensual minimizer but also finds the optimal value of the cost function. When the individual objectives are convex and smooth, we prove that the algorithm converges at a rate of $O(1/\sqrt{t})$ if the homogeneous step-size does not exceed some upper bound, and it accelerates to O(1/t) if the homogeneous step-size is sufficiently small. When at least one of the individual objectives is strongly convex and all are smooth, we prove that the algorithm converges at a linear rate of O(λ^t) with 0?<?λ?<?1 even though the step-sizes are time-varying and heterogeneous. Two numerical examples are provided to demonstrate the efficiency of the proposed algorithm and to validate the theoretical findings.     

Stability analysis of linear continuous-time delay-difference systems with multiple time-delays

This paper is concerned with the stability analysis of linear continuous-time delay-difference systems with multiple delays. Firstly, a new method for testing the L₂-exponential stability of the considered system is proposed, which is easier to use than the one in the existing literature. In view of the conservatism and the complexity of the obtained stability conditions in the existing literature, a complete Lyapunov–Krasovskii functional (LKF) is constructed by analyzing the relationship among the multiple delays. Sufficient conditions for both L₂-exponential stability and exponential stability are then derived based on the constructed LKFs, which are delay-independent. Exponential convergence rate for the considered system is also investigated by a new method, which is shown to be equivalent to the existing approach by using weighted LKFs. Robust stability under parameter uncertainties is also investigated. Numerical examples are provided to demonstrate the effectiveness and less conservativeness of the proposed method.     

Optimal design of probabilistically robust PIλDμ controller to improve small signal stability of PV integrated power system

With the rapidly increasing penetration level of power generated by large scale photovoltaic (PV) units into the power systems, the effect of the variable output power of the PV unit on the stability of the system cannot be ignored. This paper presents a mathematical approach to study the effect of high infiltration of PV power plant on the small signal stability of a power network and design of optimal fractional order PID (PI^λD^μ) controller for improving the probabilistic small signal stability of the power systems, taking into consideration the uncertainty of system operating conditions. Due to the probabilistic characteristics of large scale PV power generation, deterministic analysis approaches are not able to fully reveal the impact of high-level PV penetration. At first, this work introduces the main module and mathematical modeling of the large scale PV generation jointly with the single-machine infinite-bus power system. In the following, the paper proposes an efficient method that tunes power system stabilizer (PSS) to have the robustness for damping electro-mechanical oscillations in power systems with incorporated random PV power. For this reason, a robust PSS based on hybridization of PI^λD^μ controller and Non-dominated Sorting Genetic Algorithm (NSGAII) is designed. This paper targets at finding the optimal gain scheduling of the PI^λD^μ through the use of the advanced heuristic optimization technique with two objective functions in PV-grid connected systems. The performance of the proposed NSGAII-based PI^λD^μ controller (NSGAII- PI^λD^μ) under different solar irradiation, temperature conditions and disturbances is tested. Simulation results illustrate that the model presented can be used in designing of essential controllers for large scale PV power plant.     

Stability, L1-gain analysis and asynchronous L1-gain control of uncertain discrete-time switched positive linear systems with dwell time

In this paper, the stability, L₁-gain analysis and asynchronous L₁-gain control problems of uncertain discrete-time switched positive linear systems (DSPLSs) with dwell time are investigated. First, several convex and non-convex conditions on dwell time stability of DSPLSs with interval and polytopic uncertainties are presented, and the relation between these conditions is revealed. Then, via a switched dwell-time-dependent co-positive Lyapunov functions (SDTLFs) approach, convex sufficient conditions on L₁-gain analysis and asynchronous L₁-gain control of DSPLSs with interval uncertainties are derived. Meanwhile, via the switched parameter-dwell-time-dependent co-positive Lyapunov functions (SPDTLFs) approach, the L₁-gain analysis and asynchronous L₁-gain controller design problems of DSPLSs with polytopic uncertainties are also solved. The stability and L₁-gain analysis results are given in terms of linear programming (LP). The controller design results are presented in terms of bilinear programming (BP), which can be solved with the help of iterative algorithm. At last, both numerical and practical examples are provided to show the effectiveness of the results.     

Stability analysis for a class of switched systems with state constraints via time-varying Lyapunov functions

This article investigates the stability analysis for a class of continuous-time switched systems with state constraints under pre-specified dwell time switchings. The state variables of the studied system are constrained to a unit closed hypercube. Firstly, based on the definition of set coverage, the system state under saturation is confined to a convex polyhedron and the saturation problem is converted into convex hull. Then, sufficient conditions are derived by introducing a class of multiple time-varying Lyapunov functions in the framework of pre-specified dwell time switchings. Such a dwell time is an arbitrary pre-specified constant which is independent of any other parameters. In addition, the proposed Lyapunov functions can efficiently eliminate the “jump” phenomena of adjacent Lyapunov functions at switching instants. The feature of this paper is that the definition of set coverage is utilized to replace the restriction on the row diagonally dominant matrices with negative diagonal elements to analyze stability. The other feature of the constructed time-varying Lyapunov functions is that there are two time-varying functions. One of the two time-varying functions contains the jump rate, which will present a certain degree of freedom in designing the dwell time switching signal. An iterative linear matrix inequality (LMI) algorithm is presented to verify the sufficient conditions. Finally, two examples are presented to show the validity of the method.     

Finite-time positiveness and distributed control of Lipschitz nonlinear multi-agent systems

The finite-time positiveness and distributed control problem is studied for a class of Lipschitz nonlinear multi-agent systems. The objective is to design a suitable distributed controller which makes the closed-loop multi-agent systems be positive and finite-time stabilizable and satisfy the given H_∞ performance index. Sufficient conditions are initially established on the existence of the finite-time distributed controller by using proper multiple Lyapunov functions and the design criteria are presented in the form of linear matrix inequalities. Finally, an example of multi-agent systems with six agents is presented to illustrate the feasibility and validity of the proposed methods.     

A new optimized fuzzy FOPI-FOPD controller for automatic generation control of electric power systems

In the rapidly expanding size and complexity of the electricity network, automatic generation control (AGC) is contemplated to be the most remarkable option for offering good quality electric power supply to the end users. An AGC system entails highly vigorous, competent and intelligent control technique to deliver a healthy power under stochastic nature of consumers’ power demand. Hence, in this paper, a hybrid fuzzy fractional order proportional integral-fractional order proportional derivative (FFOPI-FOPD) controller is proposed as a new expert control technique to tackle AGC profitably in isolated and interconnected multi-area power systems. A recently developed imperialist competitive algorithm (ICA) is utilized for the optimization of the output gains (K_P/K_P1/K_I/K_D) and other parameters such as order of integrator (λ) and differentiator (μ) of FFOPI-FOPD controller exercising integral of squared error criterion. The proposed technique is firstly implemented on 1-area thermal system, then to express its potential and extensibility, the work is extended to 2-area hydro-thermal and 3-area thermal power systems widespread in the literature. The eminence of the method is betokened by comparing the results with the various newly published control methodologies and FPI/FFOPI controller designed in the study via ICA in terms of minimum values of various error criteria and undershoots/overshoots/settling times of frequency and tie-line power deviations following a sudden load demand in an area. The sensitivity analysis substantiates that the suggested controller is robust and performs staunchly under the wide variations in the system parameters, random load pattern and in the company of physical constraints to produce more clean electricity.     

The pth moment boundedness of stochastic functional differential equations with Markovian switching

This paper gives some Razumikhin-type theorems on pth moment boundedness of stochastic functional differential equations with Markovian switching (SFDEwMS) by using Razumikhin technique and comparison principle. Some improved conditions on pth moment stability are also proposed. The main results of this paper allow the estimated upper bound of the diffusion operator associated with the underlying SFDEwMS of the Lyapunov function to have time-varying coefficients (the coefficients may even be sign-changing functions). Examples are provided to illustrate the effectiveness of the proposed results.     

Event-triggered control for active vehicle suspension systems with network-induced delays

This paper presents a novel event-triggered H_∞ static output-feedback control for active vehicle suspension systems with network-induced delays. The proposed control schema introduces an event-triggering mechanism in the suspension system such that the communication resources can be significantly saved. By applying some improved slack inequalities and an augmented Lyapunov–Krasovskii functional (LKF), a new design condition expressed in the form of linear matrix inequalities (LMIs) is developed to derive the desired event-triggered controller. The obtained algorithm is then employed to solve the static output-feedback control gain. Compared with the traditional sampled-data H_∞ control scheme, the proposed controller is able to provide an enhanced disturbance attenuation level while saving the control cost. Finally, comparative simulation results are provided to show the performance of the proposed event-triggered controller.     

Finite-time asynchronous filtering for switched linear systems with an event-triggered mechanism

This paper investigates the event-triggered finite-time H_∞ filtering for a class of continuous-time switched linear systems. Considering that the system may switch within an inter-event interval, the asynchronous problem is taken into account for the system and filter modes. By adopting the average dwell time (ADT) technique and multiple Lyapunov functions, new conditions are obtained to guarantee that the filtering error system is finite-time bounded with a prescribed disturbance attenuation performance. Further, the finite-time H_∞ filter together with event-triggered mechanism is co-designed for the switched linear systems. Finally, a numerical example is provided to demonstrate the effectiveness of the method proposed in this paper.