Search

This study is concerned with dwell time stability and stabilisation problems of switched positive linear systems (SPLSs). The dwell time refers to minimum dwell time and constant dwell time. Several stability conditions for primal and transpose SPLSs with dwell time are presented, and the relation between these conditions is illustrated. Some of these conditions are given in terms of infinite-dimensional linear programming (LP), which cannot be solved directly. Then, by utilising the piecewise linear approach, new alternative convex conditions are formulated in terms of finite-dimensional LP. Compared to the existing literature, results with lower or at least the same conservatism can be obtained under the new conditions for the same discretised order. An algorithm is given to reduce the computational cost. Meanwhile, it is proved that there exists a relation between these convex and non-convex conditions if the discretised order is sufficiently large. By utilising the transpose conditions, alternative convex conditions on stabilisation of SPLSs with dwell time are also presented. The controller gain matrices can be computed by solving a set of LP directly. Finally, the correctness and superiority of the results are verified by numerical examples.

Chlorine, UV

In this work, a data-driven modeling framework of switched dynamical systems under time-dependent switching is proposed. The learning technique utilized to model system dynamics is Extreme Learning Machine (ELM). First, a method is developed for the detection of the switching occurrence events in the training data extracted from system traces. The training data thus can be segmented by the detected switching instants. Then, ELM is used to learn the system dynamics of subsystems. The learning process includes segmented trace data merging and subsystem dynamics modeling. Due to the specific learning structure of ELM, the modeling process is formulated as an iterative Least-Squares (LS) optimization problem. Finally, the switching sequence can be reconstructed based on the switching detection and segmented trace merging results. An example of the data-driven modeling DC-DC converter is presented to show the effectiveness of the developed approach.

This paper proposes an interval observer design method to construct lower-bound and upper-bound of system state trajectories in run time. The developed interval observer consists of two auxiliary neural networks derived from the neural network in dynamical systems, and two observer gains to ensure the positivity and the convergence of the corresponding error dynamics. Particularly, if the neural network is driven by the output of the system, the developed approach contains a promising neural-network-free design feature. The developed method is validated with evaluations on an adaptive cruise control system with a neural network controller.

This letter deals with the stability analysis problem of discrete-time switched linear systems with ranged dwell time. A novel concept called $L$ -switching-cycle is proposed, which contains sequences of multiple activation cycles satisfying the prescribed ranged dwell time constraint. Based on $L$ -switching-cycle, two sufficient conditions are proposed to ensure the global uniform asymptotic stability of discrete-time switched linear systems. It is noted that two conditions are equivalent in stability analysis with the same $L$ -switching-cycle. These two sufficient conditions can be viewed as generalizations of the clock-dependent Lyapunov and multiple Lyapunov function methods, respectively. Furthermore, it has been proven that the proposed $L$ -switching-cycle can eventually achieve the nonconservativeness in stability analysis as long as a sufficiently long $L$ -switching-cycle is adopted. A numerical example is provided to illustrate our theoretical results.

Environment pollution is getting serious and various poisonous contaminants with chemical durability, biotoxicity and bioaccumulation have been widespreadly discovered in municipal wastewaters and surface water. The detection and removal of pollutants show great significance for the protection of human health and other organisms. Due to its distinctive physical and chemical properties, perylene diimide (PDI) has received widespread attention from different research fields, especially in the area of environment. In this review, a comprehensive summary of the development of PDI-based materials in fluorescence detection and advanced oxidation technology for environment was introduced. Firstly, we chiefly presented the recent progress about the synthesis of PDI and PDI-based nanomaterials. Then, their application in fluorescence detection for environment was presented and categorized, principally including the detection of heavy metal ions, harmful anions and organic contaminants in the environment. In addition, the application of PDI and PDI-based materials in different advanced oxidation technologies for environment, such as photocatalysis, photoelectrocatalysis, Fenton and Fenton-like reaction and persulfate activation, was also summarized. At last, the challenges and future prospects of PDI-based materials in environmental applications were discussed. This review focuses on presenting the practical applications of PDI and PDI-based materials as fluorescent probes or catalysts (especially photocatalysts) in the detection of hazardous substances or catalytic elimination of organic contaminants. The contents are aimed at supplying the researchers with a deeper understanding of PDI and PDI-based materials and encouraging their further development in environmental applications.

NNV (Neural Network Verification) is a framework for the verification of deep neural networks (DNNs) and learning-enabled cyber-physical systems (CPS) inspired by a collection of reachability algorithms that make use of a variety of set representations such as the star set. NNV supports exact and over-approximate reachability algorithms used to verify the safety and robustness of feed-forward neural networks (FFNNs). These two analysis schemes are also used for learning enabled CPS, i.e., closed-loop systems, and particularly in neural network control systems with linear models and FFNN controllers with piecewise-linear activation functions. Additionally, NNV supports over-approximate analysis for nonlinear plant models by combining the star set analysis used for FFNNs with the zonotope-based analysis for nonlinear plant dynamics provided by CORA. This demo paper demonstrates NNV’s capabilities by considering a case study of the verification of a learning-enabled adaptive cruise control system.

A novel n-n type inorganic/organic heterojunction of flaky-like BiOCl/PDI photocatalyst was constructed by water bath heating method. Meanwhile, a simple method - secondary self-assembly was used to prepare the BiOCl/PDI with a special band structure. The photocatalytic activities were evaluated by degrading aqueous organic pollutants under visible light (λ > 420 nm). The removal rates of 5 mg L−1 phenol (non-ionic type), methyl orange (MO, anionic type), rhodamine B (RhB, cationic type) and 10 mg L−1 RhB by secondary self-assembly BiOCl/PDI (BiOCl/PDI-2) were 8.0%, 3.4%, 27.8% and 78.9% higher than self-assembly BiOCl/PDI (BiOCl/PDI-1) under visible light (λ > 420 nm). The better photocatalytic activity for BiOCl/PDI-2 was attributed to the optimization of energy-band structures, which arose from different exposed surfaces, narrower interplanar spacing and stronger visible light absorption performance. Under acidic condition, BiOCl/PDI-2 showed a good photocatalytic activity, which was not affected by neutral ionic intensity and had good recycling properties. Moreover, the photocatalytic mechanism was explored by free radical capture test and electron paramagnetic resonance (EPR), and contribution of active species was calculated. The main active species of BiOCl/PDI-2 were ·O2−, 1O2 and h+. Our work may provide a route to design efficient inorganic/organic heterojunctions for organic pollutants degradation.

Convolutional Neural Networks (CNN) have redefined state-of-the-art in many real-world applications, such as facial recognition, image classification, human pose estimation, and semantic segmentation. Despite their success, CNNs are vulnerable to adversarial attacks, where slight changes to their inputs may lead to sharp changes in their output in even well-trained networks. Set-based analysis methods can detect or prove the absence of bounded adversarial attacks, which can then be used to evaluate the effectiveness of neural network training methodology. Unfortunately, existing verification approaches have limited scalability in terms of the size of networks that can be analyzed. In this paper, we describe a set-based framework that successfully deals with real-world CNNs, such as VGG16 and VGG19, that have high accuracy on ImageNet. Our approach is based on a new set representation called the ImageStar, which enables efficient exact and over-approximative analysis of CNNs. ImageStars perform efficient set-based analysis by combining operations on concrete images with linear programming (LP). Our approach is implemented in a tool called NNV, and can verify the robustness of VGG networks with respect to a small set of input states, derived from adversarial attacks, such as the DeepFool attack. The experimental results show that our approach is less conservative and faster than existing zonotope and polytope methods.

This paper presents the Neural Network Verification (NNV) software tool, a set-based verification framework for deep neural networks (DNNs) and learning-enabled cyber-physical systems (CPS). The crux of NNV is a collection of reachability algorithms that make use of a variety of set representations, such as polyhedra, star sets, zonotopes, and abstract-domain representations. NNV supports both exact (sound and complete) and over-approximate (sound) reachability algorithms for verifying safety and robustness properties of feed-forward neural networks (FFNNs) with various activation functions. For learning-enabled CPS, such as closed-loop control systems incorporating neural networks, NNV provides exact and over-approximate reachability analysis schemes for linear plant models and FFNN controllers with piecewise-linear activation functions, such as ReLUs. For similar neural network control systems (NNCS) that instead have nonlinear plant models, NNV supports over-approximate analysis by combining the star set analysis used for FFNN controllers with zonotope-based analysis for nonlinear plant dynamics building on CORA. We evaluate NNV using two real-world case studies: the first is safety verification of ACAS Xu networks, and the second deals with the safety verification of a deep learning-based adaptive cruise control system.

In this brief, the output reachable estimation and safety verification problems for multilayer perceptron (MLP) neural networks are addressed. First, a conception called maximum sensitivity is introduced, and for a class of MLPs whose activation functions are monotonic functions, the maximum sensitivity can be computed via solving convex optimization problems. Then, using a simulation-based method, the output reachable set estimation problem for neural networks is formulated into a chain of optimization problems. Finally, an automated safety verification is developed based on the output reachable set estimation result. An application to the safety verification for a robotic arm model with two joints is presented to show the effectiveness of the proposed approaches.

In this paper, the stability analysis and H ∞ control problems for a class of continuous-time switched systems with a random switching signal are addressed. The dwell time of the switched systems is characterized with a fixed part and a random part. A new stability criterion, which is equivalent to a necessary and sufficient condition developed previously, is established first, and then it is reformulated in terms of linear matrix inequalities. Based on the stability analysis result, L 2 -gain performance analysis and H ∞ control problems are studied. Several numerical examples are given to illustrate the effectiveness of our results.

In this note, the global exponential stability of discrete-time switched systems under arbitrary switching is investigated. First, for discrete-time switched nonlinear systems, the global exponential stability is found to be equivalent to the existence of an $M$ -step sequence with sufficient length and a family of Lyapunov functions, and then a stability criterion is proposed for the nominal linear case in the framework of quadratic Lyapunov function. In order to extend the stability criterion to handle uncertainties, an equivalent condition which has a promising feature that is convex in system matrices is derived, leading to a robust stability criterion for uncertain discrete-time switched linear systems. Moreover, also taking the advantage of the convex feature, the disturbance attenuation performance in the sense of $\ell _2$ -gain is studied. Several numerical examples are provided to illustrate our approach.

In this paper, a novel parameter-memorized Lyapunov function is proposed for stability analysis of discrete-time linear systems with time-varying parametric uncertainties. The parameter-memorized Lyapunov function depends on the uncertain parameters with a memory of a certain interval. It is shown that the previous parameter-dependent Lyapunov function is a special memoryless case of the parameter-memorized Lyapunov function, and as a result, the parameter-memorized Lyapunov function approach leads to less conservative results. Furthermore, if the length of the interval for parameter memory is sufficiently long, a nonconservative stability analysis result can be achieved. Numerical examples are provided to evaluate the obtained theoretical results.

This paper deals with the problems of stability analysis and L 1 -gain characterization for continuous-time switched systems consisting of positive subsystems. With the aid of a discretized copositive Lyapunov function, a sufficient condition ensuring the asymptotic stability of continuous-time switched positive systems under dwell-time constraint is obtained, which can be checked via linear programming. Furthermore, the conservatism of the proposed approach is studied and the result with least conservatism in the framework of discretized copositive Lyapunov function is obtained. The result is then extended to L 1 -gain characterization for switched positive systems. With a prescribed dwell time, an unweighted L 1 -gain can be computed via solving a linear programming problem. A numerical example and a practical traffic example are given to illustrate our results.

This paper addresses the output reachable set estimation problem for continuous-time switched linear systems consisting of Hurwtiz stable subsystems. Based on a common Lyapunov function approach, the output reachable set is estimated by a union of bounding ellipsoids. Then, multiple Lyapunov functions with time-scheduled structure are employed to estimate the output reachable set for switched systems under dwell-time constraint. Furthermore, the safety verification problem of uncertain switched systems is investigated based on the result of output reachable set estimation. First, a sufficient condition ensuring the existence of an approximate bisimulation relation between two switched linear systems with a prescribed precision is proposed. Then, the safety verification for an uncertain switched system can be performed through an alternative safety verification for a switched system with exact parameters. Numerical examples are provided to illustrate our results.

The event-triggered control problem for switched linear system is addressed in this study. The periodical sampling scheme and event-triggering condition are incorporated in the closed-loop. The feedback control updates its value only at sampling instants as long as event-triggering condition is satisfied as well. In addition, the switchings are only allowed to occur at sampling instants and meanwhile the switching condition is satisfied. Three equivalent sufficient conditions are proposed to ensure the asymptotic stability of switched systems. In particular, one condition has a promising feature of affineness in system matrices, and as a consequence, it is extended to robust sampling case and ℒ 2 -gain analysis. Several examples are provided to illustrate the authors' results.

Rail Guided Vehicle (RGV) is used in the field of automated logistics system and automated warehouse. It has the characteristics of high speed, high reliability and low cost. The combination of RGV and Computer Number Controller (CNC) can greatly improve production efficiency. This paper designs an optimal dynamic scheduling strategy and a shortest walking path of RGV for an intelligent machining system composed of one RGV and eight CNC. Firstly, based on the shortest path algorithm and the principle of "nearest priority", this paper designs three optimal RGV dynamic scheduling models to adapt the three different cases. In these models, the optimization objective is the total number of clinkers produced by eight CNC, the decision variable is the number of clinkers produced by each CNC, and the constraints are determined by the time when each CNC issues instructions. Secondly, according to the different properties of the three models, the corresponding solutions have been given. Meanwhile, in order to describe the RGV scheduling strategy and the operational efficiency of the system, this paper uses the cost-time and average time spent for generating a clinker to measure the operational efficiency of the system. If their ratio were closer to 1, the work efficiency is higher. If the ratio were closer to 0, the work efficiency is lower. Finally, in order to test the practicability and validity about the three models, we import the known data into the three models to find how to manage the CNC and when to carry out the downloading and uploading operations by MATLAB simulation. The practicability of the optimized dynamic scheduling model and the corresponding calculation are verified.

Artificial neural networks (ANN) have displayed considerable utility in a wide range of applications such as image processing, character and pattern recognition, self-driving cars, evolutionary robotics, and non-linear system identification and control. While ANNs are able to carry out complicated tasks efficiently, they are susceptible to unpredictable and errant behavior due to irregularities that emanate from their complex non-linear structure. As a result, there have been reservations about incorporating them into safety-critical systems. In this paper, we present a reachability analysis method for feed-forward neural networks (FNN) that employ rectified linear units (ReLUs) as activation functions. The crux of our approach relies on three reachable-set computation algorithms, namely exact schemes, lazy-approximate schemes, and mixing schemes. The exact scheme computes an exact reachable set for FNN, while the lazy-approximate and mixing schemes generate an over-approximation of the exact reachable set. All schemes are designed efficiently to run on parallel platforms to reduce the computation time and enhance the scalability. Our methods are implemented in a MATLAB® toolbox called, NNV, and is evaluated using a set of benchmarks that consist of realistic neural networks with sizes that range from tens to a thousand neurons. Notably, NNV successfully computes and visualizes the exact reachable sets of the real world ACAS Xu deep neural networks (DNNs), which are a variant of a family of novel airborne collision detection systems known as the ACAS System X, using a representation of tens to hundreds of polyhedra.

This paper proposes novel reachability algorithms for both exact (sound and complete) and over-approximation (sound) analysis of deep neural networks (DNNs). The approach uses star sets as a symbolic representation of sets of states, which are known in short as stars and provide an effective representation of high-dimensional polytopes. Our star-based reachability algorithms can be applied to several problems in analyzing the robustness of machine learning methods, such as safety and robustness verification of DNNs. The star-based reachability algorithms are implemented in a software prototype called the neural network verification (NNV) tool that is publicly available for evaluation and comparison. Our experiments show that when verifying ACAS Xu neural networks on a multi-core platform, our exact reachability algorithm is on average about 19 times faster than Reluplex, a satisfiability modulo theory (SMT)-based approach. Furthermore, our approach can visualize the precise behavior of DNNs because the reachable states are computed in the method. Notably, in the case that a DNN violates a safety property, the exact reachability algorithm can construct a complete set of counterexamples. Our star-based over-approximate reachability algorithm is on average 118 times faster than Reluplex on the verification of properties for ACAS Xu networks, even without exploiting the parallelism that comes naturally in our method. Additionally, our over-approximate reachability is much less conservative than DeepZ and DeepPoly, recent approaches utilizing zonotopes and other abstract domains that fail to verify many properties of ACAS Xu networks due to their conservativeness. Moreover, our star-based over-approximate reachability algorithm obtains better robustness bounds in comparison with DeepZ and DeepPoly when verifying the robustness of image classification DNNs.

Safety-critical distributed cyber-physical systems (CPSs) have been found in a wide range of applications. Notably, they have displayed a great deal of utility in intelligent transportation, where autonomous vehicles communicate and cooperate with each other via a high-speed communication network. Such systems require an ability to identify maneuvers in real-time that cause dangerous circumstances and ensure the implementation always meets safety-critical requirements. In this paper, we propose a real-time decentralized safety verification approach for a distributed multi-agent CPS with the underlying assumption that all agents are time-synchronized with a low degree of error. In the proposed approach, each agent periodically computes its local reachable set and exchanges this reachable set with the other agents with the goal of verifying the system safety. Our method, implemented in Java, takes advantages of the timing information and the reachable set information that are available in the exchanged messages to reason about the safety of the whole system in a decentralized manner. Any particular agent can also perform local safety verification tasks based on their local clocks by analyzing the messages it receives. We applied the proposed method to verify, in real-time, the safety properties of a group of quadcopters performing a distributed search mission.

Reachability analysis is a fundamental problem for safety verification and falsification of Cyber-Physical Systems (CPS) whose dynamics follow physical laws usually represented as differential equations. In the last two decades, numerous reachability analysis methods and tools have been proposed for a common class of dynamics in CPS known as ordinary differential equations (ODE). However, there is lack of methods dealing with differential algebraic equations (DAE), which is a more general class of dynamics that is widely used to describe a variety of problems from engineering and science, such as multibody mechanics, electrical circuit design, incompressible fluids, molecular dynamics, and chemical process control. Reachability analysis for DAE systems is more complex than ODE systems, especially for high-index DAEs because they contain both a differential part (i.e., ODE) and algebraic constraints (AC). In this paper, we propose a scalable reachability analysis for a class of high-index large linear DAEs. In our approach, a high-index linear DAE is first decoupled into one ODE and one or several AC subsystems based on the well-known Marz decoupling method utilizing admissible projectors. Then, the discrete reachable set of the DAE, represented as a list of star-sets, is computed using simulation. Unlike ODE reachability analysis where the initial condition is freely defined by a user, in DAE cases, the consistency of the initial condition is an essential requirement to guarantee a feasible solution. Therefore, a thorough check for the consistency is invoked before computing the discrete reachable set. Our approach successfully verifies (or falsifies) a wide range of practical, high-index linear DAE systems in which the number of state variables varies from several to thousands.

A novel Co3O4/g-C3N4/Bi2O2CO3 (BCCN) photocatalyst with p-n/n-n heterojunction was synthesized through a solvent-thermal method. The degradation efficiency of 20 mg/L iohexol reached 94 % in 60 min (kapp =0.0417 min−1) in BCCN/light/PS system, which was 2.8 and 6.5 times higher than systems of BCCN/light (kapp =0.0150 min−1) and BCCN/PS (kapp =0.0064 min−1). The g-C3N4 addition lowered conduction band of the prepared material to produce superoxide radicals, activate persulfate and further prevent the recombination of photoelectrons and holes. Superoxide radicals and singlet oxygens were dominant radicals for iohexol degradation. Besides, persulfate could act as electron acceptor to enhance efficiency of electron transfer. The interaction between sulfate, superoxide and hydroxyl radicals improved singlet oxygens production. Furthermore, theoretical calculation and liquid chromatography mass spectrometry were performed to analyze degradation pathway of iohexol in the system. Ultimately, the BCCN/light/PS system can provide a new method to degrade organic pollutants in aquatic environments.

A novel PDI/PS/Vis system was constructed and the photocatalytic activity of PDI with various degrees of self-assembly was explored. Perylene diimide (PDI) as photocatalysts possesses excellent charge separation efficiency and the electron injection from the PDI to persulfate (PS) can produce active species more efficiently. With the PDI/PS/Vis system, 5 mg/L bisphenol A (BPA, 50 mL) could be completely removed in 15 min with 0.5 g/L photocatalyst and 1.5 mM PS under visible light (λ>420 nm). Nearly 71.1 % of BPA was mineralized after 1 h degradation. Radical quenching tests and electron paramagnetic resonance (EPR) spectra revealed that h+, ·O2−, ·OH and SO4·- all contributed to organics elimination with radical process. Based on the results of theoretical calculations and toxicity assessment, BPA will eventually be converted into non-toxic ring-opening products. Therefore, the highly efficient PDI/PS/Vis system has great potential for application in water environment remediation.

In this technical note, a necessary and sufficient stability criterion for switched linear systems under dwell-time constraint is proposed by employing a class of time-scheduled homogeneous polynomial Lyapunov functions with a sufficiently large degree. The key feature of this nonconservative condition lies in its convexity in the system matrices, which explicitly facilitates its further extension to uncertain systems. Then, in order to obtain numerically testable condition, a family of LMI conditions are presented with the aid of the idea of dividing the dwell-time interval into a finite number of segments. It is proved that the non-conservativeness can be maintained with a sufficiently large interval dividing parameter. In the end, the result is straightforwardly extended to the uncertain case in virtue of the convexity in the system matrices. Numerical examples are presented to illustrate our findings.

In this technical note, the stability and failure tolerant control are investigated for linear time-invariant (LTI) control systems with occasional controller failures. At first, a collection of non-convex sufficient conditions ensuring the closed loop to be globally asymptotically stable is presented, which are simple to use but difficult to consider for control purpose. To overcome this, a time-scheduled Lyapunov function approach is considered and alternative convex conditions are obtained. Based on this result, a time-dependent failure-tolerant controller is designed. The approach is finally illustrated on a networked control system.

In this paper, an elementary time unit (ETU) method is proposed to study the problem of estimating the admissible delay in the identification of the active mode in the analysis and design of switched systems. The activation interval of a subsystem is considered to consist of a finite-time number of segments called ETUs, by which a novel class of time-scheduled Lyapunov function is used to estimate the admissible delay in mode identification for switched systems. Further, the ETU method is applied for switching-delay tolerant control problem, and a class of time-scheduled state feedback controllers are designed to achieve the exponentially stability. Several numerical examples are presented to validate the theoretic findings.

Iohexol (IOH), as a typical iodinated X-ray contrast media (ICMs) with potential threat to human health, is difficult to be removed with the conventional wastewater treatment methods. In this work, new boron nitride coupled Bi2MoO6 layered microspheres (BN/Bi2MoO6) composites were applied to remove IOH from water via photocatalytic degradation. The degradation constant kapp of IOH over 3.5 wt% BN/Bi2MoO6 was 0.016 min−1, which was 3.2 times that of Bi2MoO6 (0.005 min−1). The degradation rate of IOH on 3.5 wt% BN/Bi2MoO6 reached 92% in 150 min. The enhanced photocatalytic activity of BN/Bi2MoO6 can be attributed to the heterojunction between BN and Bi2MoO6. The matched type-I band alignment heterojunction of two semiconductors prominently improved the charge separation. Based on the trapping experiments, holes and superoxide radicals were proved to be the main active species for photocatalytic IOH degradation. Besides, the degradation products of IOH were analyzed by LC–HRMS and the possible degradation mechanism of IOH was also proposed in this work.

For a practical system with switching actions, it is necessary to restrict the switching frequency under the limit of its physical constraints, avoiding potential damage to the equipment. In this paper, a mixed switching scheme with both state-dependent and time-dependent functions is designed to reduce the switching frequency. First, a constant dwell-time constraint is considered and a switching logic called dwell-time min-switching rule is designed to ensure the asymptotic stability of switched system. Particularly, our result is found to be able to cover some previous results for min-switching strategy. Subsequently, a switching function with ranged dwell time scheme which means the dwell time belongs to a range other than a fixed value is taken into account. Furthermore, L 2 stabilization is studied, and the feedback controller design is incorporated into the framework of dwell-time min-switching logic. Finally, several numerical examples are presented to illustrate our results.

Neural networks have been widely used to solve complex real-world problems. Due to the complex, nonlinear, non-convex nature of neural networks, formal safety and robustness guarantees for the behaviors of neural network systems are crucial for their applications in safety-critical systems. In this paper, the reachable set estimation and safety verification problems for Nonlinear Autoregressive-Moving Average (NARMA) models in the forms of neural networks are addressed. The neural networks involved in the model are a class of feed-forward neural networks called Multi-Layer Perceptrons (MLPs). By partitioning the input set of an MLP into a finite number of cells, a layer-by-layer computation algorithm is developed for reachable set estimation of each individual cell. The union of estimated reachable sets of all cells forms an over-approximation of the reachable set of the MLP. Furthermore, an iterative reachable set estimation algorithm based on reachable set estimation for MLPs is developed for NARMA models. The safety verification can be performed by checking the existence of non-empty intersections between unsafe regions and the estimated reachable set. Several numerical examples are provided to illustrate the approach.

In photovoltaic system, the maximum power point tracking technology (MPPT)makes the input voltage and current of the pre-stage DC-DC converter in a two-stage grid connected inverter variable because of external factors such as light and temperature. In order to improve the stability of pre-stage boost converter under variable input, a switching liner parameter varying (LPV)model of boost converter is established. Based on the established model, a stable switching signal of boost converter is derived from Lyapunov stability criterion of nonlinear stability analysis. Then a new control strategy of boost converter is designed by the switching signal. Based on the bifurcation theory, the stability of the control model is analyzed. The results show that the control strategy can make the boost converter output the voltage with less ripple, and the analysis of a series of bifurcation diagrams shows that the boost converter will not be unstable under the control strategy. Finally, the theoretical results are verified by simulation.

In this work, the reachable set estimation and safety verification problems for a class of piecewise linear systems equipped with neural network controllers are addressed. The neural network is considered to consist of Rectified Linear Unit (ReLU) activation functions. A layer-by-layer approach is developed for the output reachable set computation of ReLU neural networks. The computation is formulated in the form of a set of manipulations for a union of polytopes. Based on the output reachable set for neural network controllers, the output reachable set for a piecewise linear feedback control system can be estimated iteratively for a given finite-time interval. With the estimated output reachable set, the safety verification for piecewise linear systems with neural network controllers can be performed by checking the existence of intersections of unsafe regions and output reach set. A numerical example is presented to illustrate the effectiveness of our approach., 6 pages, 2 figures, ACC 2018

This benchmark suite consists of a number of examples of autonomous multi-agent systems where the agent number ranges from two to ten. The benchmarks are derived from the field of position-based formation control in autonomous robotics and vehicles. Their models are given as network of hybrid automata in the SpaceEx XML model format and can be transformed to other verification tools model formats using HyST, a model trans- formation tool. Safety of a small benchmark with two agents is analyzed using SpaceEx.

In this work we address the problem of (outer) estimation of reachable sets in switched linear systems subject to dwell-time switching. After giving some conditions that exploit the well-known properties of exponential decrease/bounded increase of the Lyapunov function (i.e. exponential decrease in between switching times and bounded increase at switching times), we overcome the need for such properties. This is done by introducing a new notion of τ-reachable set, i.e. the set that can be reached by the trajectories defined at time τ after the switch. Such extended notion of reachable set can be used to parametrize the estimate of the reachable set as a function of the distance in time from the switch. Two approaches are provided to implement such parametrization: the first approach exploits the evolution of the system in between switches via the matrix exponential of the state subsystem matrix; the second approach exploits a time-scheduled Lyapunov function. A numerical example is provided to show the effectiveness of the proposed methods and computational cost is addressed.

In this paper, the dissipativity and dwell time specifications of switched discrete-time system are investigated. In general case, the dissipativity and the desirable induced Lyapunov stability of switched systems can be established by imposing non-increasing condition on multiple storage functions at switching instants. Then, a novel dwell-time dependent storage function (DTDSF) is introduced to characterize non-increasing condition in linear case, and a corresponding LMI-based sufficient condition is proposed for the dissipativity. Since the derived conditions are all convex in system matrices, it is very convenient to be applied into controller design. As applications, the H ∞ and robust passive control problem are considered. Particularly, a solution is proposed for the open problem on the computation of ? 2 -induced gains versus dwell time, which is covered by the control problems in this paper. Based on the DTDSF approach, the control synthesis procedures including both controller and switching law design are unified into a one-step method which explicitly facilitates the control synthesis process. Finally, several numerical examples are provided to illustrate our theoretic findings.

In this paper, the traffic-responsive signalization problem for an oversaturated intersection is addressed. A static state feedback control strategy is presented to relieve the waiting vehicles in lanes. By modeling the intersection as a discrete-time switched system and with the aid of quadratic Lyapunov function method, the green time of each phase in signalization is determined by a set of linear state feedback controllers, and moreover, in order to avoid the risk of overflow of waiting vehicles which could lead to the traffic congestion, the boundary of waiting queue length is estimated and further minimized by the state feedback control. Then, linear matrix inequality (LMI) technique is employed to numerically tackle the design problem through solving a set of LMI optimization problems. Furthermore, the design results are extended to the case with unknown disturbance, and H ∞ controller is designed to achieve the disturbance attenuation performance. In the end, a simulation study in comparison with traditional Webster method is presented to illustrate the effectiveness of state feedback control in relieving the oversaturated situation for an intersection.

In this note, a study on the equivalence of two stability criteria for continuous-time switched linear systems with dwell time constraint is presented. It is demonstrated that, for any dwell time satisfying the conditions in stability criterion proposed in Geromel and Colaneri (2006), the conditions in stability criterion of Allerhand and Shaked (2011) also hold as long as the number of decision variables and related LMIs is sufficiently large, which implies the two stability criteria are intrinsically equivalent. The equivalence is obtained by showing that two criteria can be derived from each other with a sufficiently large number of decision variables and LMIs. A numerical example is proposed to illustrate the theoretical results, and an extension to uncertain case is briefly presented.

This paper addresses the problem of reachable set estimation for discrete-time switched systems under arbitrary switching. By introducing a novel conception called M-step sequence which is capable of characterizing all possible subsystem activation orders during M discrete-time steps, a Lyapunov function based approach is proposed to derive a set of bounding ellipsoids to estimate the reachable set. The proposed approach can cover the previous switched Lyapunov function approach and yields less conservativeness. Moreover, it can be shown that the M-step sequence method can also reduce the conservativeness in stability analysis for discrete-time switched systems under arbitrary switching in contrast to switched Lyapunov function method. Several numerical examples are provided to illustrate our approach.

In this paper, the stability and failure tolerant control are investigated for discrete-time time-invariant linear systems with occasional controller failure due to physical or purposeful reason. By introducing the conceptions of minimal controller reliable time and maximal controller failure time, a novel time-varying piecewise quadratic Lyapunov function (TPQLF) approach is proposed to analyse the stability property of closed-loop system in presence of controller failure. The presented TPQLF method combines both merits of previous Lyapunov function based results such as common Lyapunov function and piecewise Lyapunov function approaches. Furthermore, based on TPQLF, the feasible region described by pairs of minimal controller reliable time and maximal controller failure time can be easily computed by an iterative algorithm. Then, on the basis of the analysis results, time-varying state feedback gains are formulated to construct failure tolerant controller. It is demonstrated that the time-varying struct...

In this technical note, the l 2 gain analysis and asynchronous H ∞ control problems for switched discrete-time linear systems are addressed. Under the dwell time constraint, the computation of l 2 gains versus dwell time is viewed as an open problem. By introducing a novel dwell time dependent Lyapunov function, an LMI-based sufficient condition is proposed to solve the l 2 gain analysis problem. Since the derived conditions are all convex in system matrices, it is convenient to be applied into H ∞ controller design. Thus, in the presence of asynchronous switching, an H ∞ controller is presented to ensure the closed-loop system with a desired non-weighted H ∞ performance. The proposed approach can also easily characterize the relationship between H ∞ performance, dwell time and asynchronous time. Finally, several academic examples are provided to illustrate our results.

In this paper, a new type of switched parallel distributed compensation (PDC) controller is presented, in which a novel switching scheme, namely, membership function ranking (MFR) scheme is proposed. The MFR scheme can be viewed as an improvement and extension of previous results named largest membership function (LMF) scheme concerned with piece-wise quadratic Lyapunov function (PQLF) approach, since it provides a denser subdivision of normalized membership function space and therefore essentially yields less conservative results. Moreover, it shows that MFR scheme covers LMF scheme as a particular case. Based on MFR scheme, a family of ℋ ∞ controllers and a switching scheme is designed to ensure the closed-loop system asymptotically stable and has a required ℋ ∞ performance. A design example is presented to illustrate the advantages of MFR scheme.

In this paper, the fault detection problem for a class of state-dependent switched nonlinear systems with linear switching surface is addressed. The investigation of fault detection problem includes two parts: design sub-filters for each subsystem, and determine a proper update of estimated state. A fault detection filter is proposed incorporating the update of estimated state at switching instants and the multiple Lyapunov function approach is employed in the design process to reduce the conservativeness. It should be pointed out that the state update relation is derived based upon multiple Lyapunov functions and also on the information of switching surface. In the end, a special case in which the state space is divided into several polyhedral cells is discussed. A numerical example is given to illustrate the effectiveness of proposed results.

Stabilization of switched systems composed fully of unstable subsystems is one of the most challenging problems in the field of switched systems. In this brief paper, a sufficient condition ensuring the asymptotic stability of switched continuous-time systems with all modes unstable is proposed. The main idea is to exploit the stabilization property of switching behaviors to compensate the state divergence made by unstable modes. Then, by using a discretized Lyapunov function approach, a computable sufficient condition for switched linear systems is proposed in the framework of dwell time; it is shown that the time intervals between two successive switching instants are required to be confined by a pair of upper and lower bounds to guarantee the asymptotic stability. Based on derived results, an algorithm is proposed to compute the stability region of admissible dwell time. A numerical example is proposed to illustrate our approach.

Mathematical models are an approximate of physical systems and design procedures are only complete when modeling errors have been quantified. Uncertainties are incorporated in design procedure to compensate such discrepancies and to add robustness. This paper investigates the design problem of parameter-dependent switched observers for polytopic uncertain switched systems. State-space model is considered subject to time-varying uncertainties, and designated observer gains ensuring stability of overall system are also parameter-dependent. Synthesis procedure is demonstrated by employing ℋ ∞ performance criteria which has become a standard for robust system design against external disturbances. This investigation is carried out in the framework of finite-time stability (FTS) and finite-time boundedness (FTB) which is the focus of researchers recently because of its apparent practical significance, especially after the emergent utilization of linear matrix inequalities.

In this brief article, the stability and disturbance attenuation property in the sense of l2 gain for switched linear discrete-time systems are investigated. The computation of l2 gains against dwell time has been viewed as an open problem so far. A novel dwell-time dependent Lyapunov function (DTDLF) is introduced to study the stability and l2 gain analysis problems. The main advantage of DTDLF approach is that the derived conditions are all convex in system matrices, thus it is capable to be generalised to switched systems with uncertainties. Then, as an application, the ℋ∞ control problem is considered. Based on the DTDLF approach, the control synthesis procedures including state-feedback controllers and switching law design are unified into one-step method that explicitly facilitates the control synthesis process. Finally, numerical examples are provided to illustrate the proposed results.

The state estimation problem for a class of switched linear systems which only switches in some short interval is addressed. Besides the asymptotic stability of error dynamics, the boundness of error state is a significant issue for short-time switched systems. By introducing the concept of finite-time stability, the state estimation procedure is formulated to determine appropriate observer gains ensuring the error dynamics is finite-time stable in the short-time switching intervals of interest. Optimal finite-time observers are designed through iterative algorithms to minimize the bound of error state, in the cases with and without disturbances. Particularly, when the total activation time is known, a less conservative result can be derived and an optimization problem can be solved with the help of the genetic algorithm. A numerical example is provided to illustrate the theoretical findings in this paper.

The Luenberger observer technique has long been used for reliable state estimation of feedback control systems. In this paper it is employed for asynchronously switched control systems. The theory of finite-time stability (FTS) and finite-time boundedness (FTB) is incorporated, which is a relatively new concept offering open and challenging problems, especially in the field of robust state estimation for switched control systems. Many real-world systems are supposed to run for a fixed interval of time and hence the design of finite-time state observers has more significance from the point of view of many engineering applications. This investigation considers asynchronous switching between observer and physical systems, which accounts for inherent delays in practical applications caused by measurement and sensing mechanisms, and crafts a more practical and accurate design method. Furthermore, H∞ performance index which is a vital technique for robust system design against external disturbances is integrated in the design procedure.

SUMMARY In this paper, the control synthesis problem for a class of large-scale systems with multi-modes that are called large-scale switched systems is addressed. By introducing the concept of decentralized switching signal and the relevant decentralized average dwell time, the asymptotic stability and weighted l2 gain performance are investigated. It should be noted that the decentralized switching covers general switching cases for large-scale switched systems, namely, it admits both time-dependent switching signal and arbitrary switching signal blended in the decentralized switching. Then, on the basis of the analysis results, the decentralized weighted control scheme including state feedback controller gains and switching signals is studied. Several design algorithms are proposed to meet different controller design problems. Finally, numerical examples are provided to illustrate theoretical findings within this paper. Copyright © 2013 John Wiley & Sons, Ltd.