Search

This paper proposes an effective control mechanism including decentralized event-triggered conditions with a coincident control signal updating strategy, which dramatically reduces massive amount of data transmission and remarkably saves network bandwidth. Meanwhile, an asymmetric Lyapunov–Krasovskii functional (LKF) with relaxed conditions is proposed to investigate the robust performance of load frequency control (LFC) in power system. The development is capable of dealing with the frequency fluctuation of power system by utilizing LKF stability theory and stochastic analysis techniques under non-ideal communication network, such as unexpected loads, network delays and random deception attacks. Furthermore, the well-designed examples are presented to assess the effectiveness of this control strategy with quantitative analyses on: (i) implementation of control designing; (ii) comparison of communication efficiency using different trigger mechanisms; and (iii) evaluation of H ∞ performance under different attack probabilities and delay upper bounds. [ABSTRACT FROM AUTHOR]

In this paper, the coordination control problem of multi-agent systems (MASs) subjected to stealthy attacks and uncertainties is considered, where the uncertainties refer to unknown external disturbances and initial states. We consider a scenario in which the sensors are maliciously attacked, rendering the traditional interval observer's bounds ineffective for estimating the system states. By solving the linear programming problem, the maximum destructive attack sequences are generated. A distributed resilient interval observer composed of a resilient framer and a control protocol is designed, in which the construction of control protocol for each agent depends on the framer information of its own and its neighbors. It is demonstrated by the cooperativity theory and the Lyapunov stability theory that the distributed resilient interval observer can not only realize interval-valued state estimation for each agent but also drive the cooperative behavior of MASs. In addition, the observer gain matrix is selected and optimized by solving a semi-definite programming problem to provide tighter bounds for each agent. Meanwhile, the bounds of stealthy attacks are calculated. Finally, through a simulation example, the superiority of the distributed resilient interval observer and the effectiveness of the resilient interval observer-based consensus control algorithms are validated. [ABSTRACT FROM AUTHOR]

This paper studies a distributed continuous-time aggregative optimization problem, which is a fundamental problem in the price-based energy management. The objective of the distributed aggregative optimization is to minimize the sum of local objective functions, which have a specific expression that relies on agents' own decisions and the aggregation of all agents' decisions. To solve the problem, a novel distributed continuous-time algorithm is proposed by combining gradient dynamics with a dynamic average consensus estimator in a two-time scale. The exponential convergence of the proposed algorithm is established under the assumption of a convex global cost function by virtue of the stability theory of singular perturbation systems. Motivated by practical applications, the implementation of the continuous-time algorithm with event-triggered communication is investigated. Simulations on the price-based energy management of distributed energy resources are given to illustrate the proposed method. [ABSTRACT FROM AUTHOR]

This paper presents a novel backstepping formation control strategy for multiple Euler–Lagrange (EL) systems. To enhance parallel communication capability, the communication channels for systems' position vectors and filters' states are independent. Subsequently, the corresponding dynamic event-triggered mechanisms are designed specifically for them to reduce the frequency of interactive communication networks, and a distributed filter is devised to eliminate the non-differentiability problem of event-triggered signals, respectively. Furthermore, we introduce a new barrier Lyapunov function (BLF) to indirectly restrict the velocity vector. The key novelty of this BLF is that the controller gain matrix caused by the designed BLF can be approximated as an identity matrix, when the distance between the velocity component and the designed boundary is substantial. To prevent the designed dynamic event-triggered mechanisms from being triggered infinitely for a period of time, Zeno behavior is excluded. By leveraging Lyapunov stability theory and Barbalat lemma, we demonstrate that all signals of the closed-loop system are bounded and the formation error asymptotically converges to the origin. Finally, simulation results are provided to demonstrate the efficacy of the proposed control schemes. [ABSTRACT FROM AUTHOR]

This paper is concerned with designing two-dimensional event generators and sliding mode controllers for discrete-time two-dimensional systems described by the celebrated Roesser model with external mismatched disturbance. First of all, aimed at the characteristics of the Roesser model, the horizontal and vertical disturbance observers and sliding surface functions are established for the addressed two-dimensional systems, respectively. Then based on the disturbance estimation and rejection technique, a modified reaching law and its corresponding sliding mode controller are designed to achieve the system robustness and disturbance attenuation. To reduce the resource usage, the event-triggered strategy is further incorporated in the design of sliding mode control law. Moreover, the stability of the sliding-mode dynamics is analyzed by resorting to the Lyapunov stability theory. Finally, a simulation example is presented to verify the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

In this paper, we consider a constrained distributed optimization problem for multi-integrator agent systems with mixed neighbor interactions, where the neighbors of the agents can be classified as cooperative or noncooperative by introducing a cooperation-competition network into the modeling of the communication graph. The agent's goal is to optimize the total objective function of the cooperators. Since agents can only communicate with their neighbors, they are unable to obtain complete information about cooperators. The distributed optimization algorithm is proposed to classify cooperative subnetworks by introducing additional auxiliary variables, and the outputs of all agents exponentially converge to the optimal solution of the optimization problem under the condition of satisfying the global equality constraint of the subnetwork. The Lyapunov stability theory is used to analyze the algorithm's convergence. Simulation results show the effectiveness of the proposed algorithm in two examples of economic dispatch in smart grids and optimal area coverage in multi-sensor networks. [ABSTRACT FROM AUTHOR]

In many extremum-seeking control methods, perturbations are added to the parameter signals to estimate derivatives of the objective function (that is, the steady-state parameter-to-performance map) in order to optimize the steady-state performance of the plant using derivative-based algorithms. However, large perturbations are often undesirable or inapplicable due to practical constraints and a high cost of operation. Yet, many extremum-seeking control algorithms rely solely on perturbations to estimate all required derivatives. The corresponding derivative estimates, especially the Hessian and higher-order derivatives, may be qualitatively poor if the perturbations are small. In this work, we investigate the use of the nominal parameter signals in addition to the perturbations to improve the accuracy of the gradient estimate. In turn, a more accurate gradient estimate may result in a faster convergence and may allow for a higher tuning-gain selection. In addition, we show that, if accurate curvature information of the objective function is available via estimation or a priori knowledge, it may be used to further enhance the accuracy of the gradient estimate. [ABSTRACT FROM AUTHOR]

Reproducing kernel Hilbert spaces (RKHSs) have proved themselves to be key tools for the development of powerful machine learning algorithms, the so-called regularized kernel-based approaches.Recently, they have also inspired the design of new linear system identification techniques able to challenge classical parametric prediction error methods. These facts motivate the study of the RKHS theory within the control community. In this note, we focus on the characterization of stable RKHSs, i.e. RKHSs of functions representing stable impulse responses. Related to this, working in an abstract functional analysis framework, Carmeli et al. (2006) has provided conditions for an RKHS to be contained in the classical Lebesgue spaces ℒ p . In particular, we specialize this analysis to the discrete-time case with p = 1 . The necessary and sufficient conditions for the stability of an RKHS are worked out by a quite simple proof, more easily accessible to the control community. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

We study the existence of Hurwitz matrices in a class of Metzler sparse matrix cones, where the non-zero entries are constrained to be in a bounded set. In particular, we provide necessary and sufficient conditions for the existence of one or more Hurwitz matrices in this class of sparse matrix spaces, for scenarios with uniform and non-uniform bounds. Several examples illustrate our results. [ABSTRACT FROM AUTHOR]

This paper focuses on the reinforcement of the quantitative performance in interconnected dynamical systems. The following problem is addressed that concerns dissipativity reinforcement via interconnection: Find a class of subsystems and their interconnection rule such that the L 2 gain bound of the entire interconnected system is reduced compared with that of each individual subsystem. We assume that each subsystem has a special passivity property that is characterized by two parameters, and has a bounded L 2 gain. Then, the feedback connection and the more general interconnection of the subsystems are expressed by the transition of the two parameters inheriting the same passivity property. In addition, the L 2 gain bound of the entire interconnected system, estimated with the parameters, is strictly reduced and becomes less than that of each subsystem. Finally, special interconnection rules are considered to show that the scale-expansion of the interconnected system, i.e., increasing the number of subsystems, gradually reduces the L 2 gain bound. [ABSTRACT FROM AUTHOR]

In this paper, new conditions of stability and stabilization are proposed for periodic piecewise linear systems. A continuous Lyapunov function is constructed with a time-dependent homogeneous Lyapunov matrix polynomial. The exponential stability problem is studied first using square matricial representation and sum of squares form of homogeneous matrix polynomial. Constraints on the exponential order of each subsystem used in previous work are relaxed. State-feedback controllers with time-varying polynomial controller gain are designed to stabilize an unstable periodic piecewise system. The proposed stabilizing controller can be solved directly and effectively, which is applicable to more general situations than those previously covered. Numerical examples are given to illustrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

In this paper, we describe a broad class of control functions for extremum seeking problems. We show that it unifies and generalizes existing extremum seeking strategies which are based on Lie bracket approximations, and allows to design new controls with favorable properties in extremum seeking and vibrational stabilization tasks. The second result of this paper is a novel approach for studying the asymptotic behavior of extremum seeking systems. It provides a constructive procedure for defining frequencies of control functions to ensure the practical asymptotic and exponential stability. In contrast to many known results, we also prove asymptotic and exponential stability in the sense of Lyapunov for the proposed class of extremum seeking systems under appropriate assumptions on the vector fields. [ABSTRACT FROM AUTHOR]

This paper is concerned with the stability analysis for continuous-time positive singular systems with distributed delays. By introducing an auxiliary system, a necessary and sufficient positivity condition is proposed for singular systems with distributed lags. Based on this condition, we present a sufficient stability condition for positive singular systems with distributed delays and extend the result to systems with distributed delays over a bounded time-varying interval. In addition, this stability condition is also necessary when strictly positive initial conditions are available. Numerical simulations are utilized to illustrate the effectiveness of our results. [ABSTRACT FROM AUTHOR]

This paper investigates the asymptotic stability of semi-Markov switched stochastic systems. Based on the method of multiple Lyapunov functions and the structure of semi-Markov process, we provide sufficient conditions of stochastic asymptotic stability in the large for semi-Markov switched stochastic systems without the constraint of bounded transition rates. Particularly, our results generalize and improve some published results in the literature. An example and its simulation are given to illustrate the theoretical results. [ABSTRACT FROM AUTHOR]

Vehicle platooning has received considerable attention as a means to achieve more efficient transportation networks and vehicle autonomy. It is well known that certain systems experience undesired behaviours (instability and string instability) when the length of the platoon grows. In this context, we study homogeneous platoons of vehicles with linear dynamic models, having bi-directional communication and maintaining a constant (velocity independent) target inter vehicle spacing. We investigate both stability and string instability if the string length increases, where the vehicles utilise weighted information from multiple vehicles ahead and behind. We find conditions for the weighting factors and the linear systems that are necessary for stability of long platoons. We then show that by selecting a communication range that increases linearly with the platoon size, it is possible to achieve string stability in some cases. Further, we show that careful selection of the weighting factors can reduce the disturbance amplification considerably. [ABSTRACT FROM AUTHOR]

Learning from examples is one of the key problems in science and engineering. It deals with function reconstruction from a finite set of direct and noisy samples. Regularization in reproducing kernel Hilbert spaces (RKHSs) is widely used to solve this task and includes powerful estimators such as regularization networks. Recent achievements include the proof of the statistical consistency of these kernel-based approaches. Parallel to this, many different system identification techniques have been developed but the interaction with machine learning does not appear so strong yet. One reason is that the RKHSs usually employed in machine learning do not embed the information available on dynamic systems, e.g. BIBO stability. In addition, in system identification the independent data assumptions routinely adopted in machine learning are never satisfied in practice. This paper provides some new results which strengthen the connection between system identification and machine learning. Our starting point is the introduction of RKHSs of dynamic systems. They contain functionals over spaces defined by system inputs and allow to interpret system identification as learning from examples. In both linear and nonlinear settings, it is shown that this perspective permits to derive in a relatively simple way conditions on RKHS stability (i.e. the property of containing only BIBO stable systems or predictors), also facilitating the design of new kernels for system identification. Furthermore, we prove the convergence of the regularized estimator to the optimal predictor under conditions typical of dynamic systems. [ABSTRACT FROM AUTHOR]

This paper is concerned with the solution of higher order moment stability region for Markov jump systems with respect to cases of both known and unknown transition probabilities. By exploring the cumulant generating function, the original stochastic system with Markov jumping modes is transformed to a deterministic system. Then based on the estimation of matrix eigenvalues, the explicit solution for higher order moment stability region is expressed in terms of transition probabilities, operation modes, state transition matrix and its dimension, and the moment order. Several examples are presented to illustrate the effectiveness of the proposed method and its associated algorithm. [ABSTRACT FROM AUTHOR]

Stability and power sharing properties of droop controlled inverter-based microgrid systems depend on various design factors. Little explored is the effect of component mismatches and parameters drifts on the stability, steady state behaviour and power sharing properties of these systems. In this paper, the behaviour of frequency droop controlled inverter based microgrid systems in the presence of non-identical clocks is analysed. It is shown that power sharing between converters in a microgrid can be sensitive to clock mismatches. Our proposal shows that a coordination control that uses sparse inter-node communications is useful in ensuring desired active power sharing. Conditions are derived to ensure stability in the presence of the proposed controller and simulation results are presented. [ABSTRACT FROM AUTHOR]

This paper investigates the stability and performance of the standard least mean squares (LMS)-based consensus adaptive filters under a changing network topology. We first analyze the stability for possibly unbounded, non-independent and non-stationary signals, by introducing an information condition that can be shown to be not only sufficient but also necessary for the global stability. We also demonstrate that the distributed adaptive filters can estimate a dynamic process of interest from noisy measurements by a set of sensors working in a collaborative manner, in the natural scenario where none of the sensors can fulfill the estimation task individually. Furthermore, we give an analysis of the filtering error under various assumptions without stationarity and independency constraints on the system signals, and thus do not exclude applications to stochastic systems with feedback. In contrast to the analyses of the normalized LMS-based distributed adaptive filters, we need to use stochastic averaging theorems in the stability analysis due to possible unboundedness of the system signals. [ABSTRACT FROM AUTHOR]

The paper addresses Kalman filtering over a peer-to-peer sensor network with a careful eye towards data transmission scheduling for reduced communication bandwidth and, consequently, enhanced energy efficiency and prolonged network lifetime. A novel consensus Kalman filter algorithm with event-triggered communication is developed by enforcing each node to transmit its local information to the neighbors only when this is considered as particularly significant for estimation purposes, in the sense that it notably deviates from the information that can be predicted from the last transmitted one. Further, it is proved how the filter guarantees stability (mean-square boundedness of the estimation error in each node) under network connectivity and system collective observability. Finally, numerical simulations are provided to demonstrate practical effectiveness of the distributed filter for trading off estimation performance versus transmission rate. [ABSTRACT FROM AUTHOR]

Methods for scattering-based stabilization of interconnections of nonlinear systems are developed for the case where the subsystems are non-planar conic. The notion of non-planar conicity is a generalization of the conicity notion to the case where the cone’s center is a subspace with dimension greater than one. For a feedback interconnection of non-planar conic systems, a graph separation condition for finite-gain L 2 -stability is derived in terms of relationship between the maximal singular value of the product of projection operators onto the subsystems’ central subspaces and the radii of the corresponding cones. Furthermore, a new generalized scattering transformation is developed that allows for rendering the dynamic characteristics of a non-planar conic system into an arbitrary prescribed cone with compatible dimensions. The new scattering transformation is subsequently applied to the problem of stabilization of interconnections of non-planar conic systems, with and without communication delays. Applications of the developed scattering-based stabilization methods to the problems of stable robot–environment interaction and bilateral teleoperation with multiple heterogeneous communication delays are discussed. [ABSTRACT FROM AUTHOR]

In this paper, robust adaptive control of a class of strict-feedback nonlinear systems with unknown control directions is investigated. A novel Nussbaum-type function is developed and a key theorem is drawn which involves quantifying the addition of multiple Nussbaum functions with different control directions in a single inequality. Global stability of the closed-loop system and asymptotic stabilization of system output are proved. A simulation example is given to illustrate the effectiveness of the proposed control scheme. [ABSTRACT FROM AUTHOR]

A new technique is proposed to construct observers and to achieve output feedback stabilization of a class of continuous-time switched linear systems with a time-varying delay in the output. The delay is a piecewise continuous bounded function of time and no constraint is imposed on the delay derivative. For stability analysis, an extension of a recent trajectory based approach is used; this is fundamentally different from classical Lyapunov function based methods. A stability condition is given in terms of the upper bound on the time-varying delay to ensure global uniform exponential stability of the switched feedback system. The main result applies in cases where some of the subsystems of the switched system are not stabilizable and not detectable. [ABSTRACT FROM AUTHOR]

Recently, some novel inequalities have been proposed such as the auxiliary function-based integral inequality and the Bessel–Legendre inequality which can be obtained from the former by choosing Legendre polynomials as auxiliary functions. These inequalities have been successfully applied to systems with constant delays but there have been some difficulties in application to systems with time-varying delays since the resulting bounds contain the reciprocal convexity which may not be tractable as it is. This paper proposes an equivalent form of the Bessel–Legendre inequality, which has the advantage of being easily applied to systems with time-varying delays without the reciprocal convexity. [ABSTRACT FROM AUTHOR]

Stochastic calculus indicates that allowing a Lyapunov candidate function to be non-differentiable at the origin helps its expected value to decrease. To utilize this observation, this paper investigates stability of stochastic systems, supposing that the origin of the state space is an equilibrium before influenced by Gaussian white noises. For identifying such stability properties, notions of instantaneous points and almost sure equilibria, which are mutually exclusive, are introduced. This paper clarifies the relationship between the stability properties, and develops their Lyapunov-type characterizations without differentiability at the origin. Discussions are given in relation to the notion of noise-to-state stability, and this paper proposes a method to address both transient and global-in-time properties simultaneously with a single positive definite function even when stochastic noises prevent the origin from being an equilibrium. [ABSTRACT FROM AUTHOR]

To understand the sophisticated control mechanisms of the human’s endocrine system is a challenging task that is a crucial step towards precise medical treatment of many dysfunctions and diseases. Although mathematical models describing the endocrine system as a whole are still elusive, recently some substantial progress has been made in analyzing theoretically its subsystems (or axes ) that regulate the production of specific hormones. Secretion of many vital hormones, responsible for growth, reproduction and metabolism, is orchestrated by feedback mechanisms that are similar in structure to the model of simple genetic oscillators, proposed first by B.C. Goodwin. Unlike the celebrated Goodwin’s model, the endocrine regulation mechanisms are in fact known to have non-cyclic structures and involve multiple feedbacks; a Goodwin-type model thus represents only a part of such a complicated mechanism. In this paper, we examine a non-cyclic feedback system of hormonal regulation, obtained from the classical Goodwin’s oscillator by introducing an additional negative feedback. We establish global properties of this model and show, in particular, that the local instability of its unique equilibrium implies that almost all system’s solutions oscillate; furthermore, under additional restrictions these solutions converge to periodic or homoclinic orbits. [ABSTRACT FROM AUTHOR]

Motivated by the seminal work of Dupire (2009) on functional Itô formulas, this work investigates asymptotic properties of systems represented by stochastic functional differential equations (SFDEs). Stability of general delay-dependent SFDEs is investigated using degenerate Lyapunov functionals, which are only positive semi-definite rather than positive definite as used in the classical work. This paper first establishes boundedness and regularity of SFDEs by using degenerate Lyapunov functionals. Then moment and almost sure exponential stabilities are obtained based on degenerate Lyapunov functionals and the semi-martingale convergence theorem. As an application of the stability criteria, consentability of stochastic multi-agent systems with nonlinear dynamics is studied. [ABSTRACT FROM AUTHOR]

This paper addresses the stability issue of delayed switched nonlinear systems whose subsystem is of the form x ̇ ( t ) = A ( t , x ( t ) , x t − d ( t ) ) x ( t ) + B ( t , x ( t ) , x t − d ( t ) ) x t − d ( t ) , that is, the system matrices depend on time and the present and past states. By means of a trajectory-based comparison approach, stability of original switched nonlinear system is transformed into that of a switched positive linear system called a comparison system. The involved delays are piecewise continuous and may be unbounded. The comparison switched system may consist of unstable subsystems. It is shown that if the comparison system is asymptotically or exponentially stable, then the original system is asymptotically or exponentially stable, globally or locally, depending on the domain chosen to form the comparison system. [ABSTRACT FROM AUTHOR]

This paper is concerned with stability analysis of stochastic neutral-type time-delay systems with two different delays in both the state variables and the retarded derivatives of state variables. Sufficient conditions in terms of linear matrix inequalities (LMIs) are obtained by applying the Lyapunov–Krasovskii functional (LKF) based approach. A novel spectral radius based condition is imposed to guarantee the stability of the associated difference operator and a novel method is also proposed to analyze the stability of the overall system. Moreover, by carefully analyzing the relationship between these two different delays, a method is provided to construct all possible yet the minimal number of simple quadratic integral functions in the LKF, which helps to reduce both the conservatism and complexity of the resulting stability conditions. The effectiveness of the proposed approaches is illustrated by two numerical examples. [ABSTRACT FROM AUTHOR]

This paper is concerned with strong delay-independent stability of linear time-invariant (LTI) systems with a single time-delay. Stability analysis of linear delay-systems is complicated by the need to locate the roots of a transcendental characteristic equation. In this paper we propose a convex necessary and sufficient condition for strong delay-independent stability. This result mainly follows from the Kronecker sum properties and the Kalman–Yakubovich–Popov lemma, which allows us to present the main result in terms of a single linear matrix inequality (LMI) feasibility test. The result is illustrated by simple numerical examples. [ABSTRACT FROM AUTHOR]

While various control techniques have been developed for optical manipulation, the Brownian movement of microscopic objects in the medium is usually ignored for simplicity of analyzing the control systems. Nevertheless, due to the universality of the Brownian movement and its effect on optical manipulation of cells or micro-objects, it is required for the Brownian effect to be properly taken into consideration so as to ensure the stability and performance of the control systems. In this paper, we derive a stochastic control technique to achieve a theoretical framework for optical manipulation of multiple microscopic objects in the presence of the Brownian perturbations. In the proposed control methodology, a region control technique and a dynamic interaction approach are developed for collision-free manipulation of the target micro-objects with random perturbations. All the target micro-objects are trapped and manipulated simultaneously while being kept inside the desired dynamic region, and at the same time, preserving a minimum distance with each other to avoid collisions. While a bounded tracking or region error exists in current control techniques for optical manipulation due to the effect of the Brownian perturbations, this paper provides a new approach which guarantees that all the target micro-objects are kept inside the desired region during the course of manipulation. Rigorous mathematical formulation has been developed for automated manipulation of multiple microscopic objects in the presence of the Brownian perturbations, and experimental results are presented to demonstrate the feasibility and effectiveness of the proposed control technique. [ABSTRACT FROM AUTHOR]

The problem of p th moment stability for time-varying stochastic time-delay systems with Markovian switching is investigated in this paper. Some novel stability criteria are obtained by applying the generalized Razumikhin and Krasovskii stability approaches. Both p th moment asymptotic stability and (integral) input-to-state stability are considered based on the notion and properties of uniformly stable functions and the improved comparison lemmas. The established results show that time-derivatives of the constructed Razumikhin functions and Krasovskii functionals are allowed to be indefinite, which improve the existing results on this topic. By applying the obtained results for stochastic systems, we also analyze briefly the stability of time-varying deterministic time-delay systems. Finally, examples are provided to illustrate the effectiveness of the proposed results. [ABSTRACT FROM AUTHOR]

In this note, the stability of an uncertain system with actuator saturation using super-twisting controller (STC) is analysed. First, a new proof of STC ensuring finite-time stability of the system is proposed using geometric method which gives a new gain conditions. Then, using the proposed proof the domain of attraction (DOA) is explicitly calculated for the system with bounded control. [ABSTRACT FROM AUTHOR]

In this paper, we analyze ℓ 2 -stability of infinite dimensional discrete autonomous systems given in a state space form with state transition matrix being a Laurent polynomial matrix A ( σ , σ − 1 ) in the shift operator σ . We give sufficient conditions and necessary conditions for ℓ 2 -stability of such systems. We then use the theory of ℓ 2 -stability, thus developed, to analyze ℓ 2 -stability of discrete 2-D autonomous systems. We achieve this by showing how a discrete 2-D autonomous system can be converted to an equivalent infinite dimensional state space discrete autonomous system, where the state transition matrix turns out to be a Laurent polynomial matrix in the shift operator. Finally, we provide some easy-to-check numerical tests for ℓ 2 -stability of the above-mentioned type of systems. [ABSTRACT FROM AUTHOR]

Recent MEA (More Electric Aircraft) concepts require new approaches to design and management of the electric system onboard. Bidirectional Buck-Boost Converter Units (BBCU’s) used like bridges between power buses with different voltage require intelligent supervisory control for autonomous selection of operating modes. In this paper at low-level, sliding manifold-based strategies are employed to track desired current references, or to recover from overload within a prescribed time. At a higher level, three working modes are defined, (Buck-, Boost- and Intermediate-Mode), and scheduled by a high-level supervisory strategy. Stability proofs of the overall strategy require estimates of the Region of Attraction (ROA) for each controller, that are discussed in the paper. A typical aeronautic scenario is presented, with standard operating conditions followed by two types of overloads (the second more severe than the first) and finally a return to standard condition. Detailed numerical simulations show the effectiveness of the proposed novel control strategy in terms of stability and performance of the smart converter. [ABSTRACT FROM AUTHOR]

We consider multi-input single-output (MISO) fractional systems of commensurate fractional orders with different input or output delays. We derive explicit expressions of left and right coprime factorizations over H ∞ and of the associated Bézout factors of the transfer matrix of the systems. These factors allow the construction of the Youla–Kučera parametrization of the set of stabilizing controllers which guarantee the internal stability of the closed-loop systems. [ABSTRACT FROM AUTHOR]

A reverse-transfer method is proposed to study the stabilization problem of k -valued logical control networks (LCNs). Main results consist of two parts. (1) Two necessary and sufficient stabilization conditions are derived for k -valued LCNs. The stabilization results are much superior to the existing relevant results in the literature. (2) Based on the above conditions, some algorithms for solving the open-loop stabilization problem of k -valued LCNs are developed. These algorithms cut useless control paths off as many as possible, which, compared with existing results, reduce the related computational cost markedly. [ABSTRACT FROM AUTHOR]

Backstepping is one of the most popular nonlinear controller and differentiable control Lyapunov function (CLF) design techniques. However, for asymptotic stabilization of systems defined on noncontractible manifolds, there exists no differentiable CLF; the semiconcave CLF design problem based on the backstepping has not been discussed. In this paper, we propose a backstepping based controller design method for asymptotic stabilization of systems defined on noncontractible manifolds. In the method, we design a controller and a CLF on an étale space. Then, we obtain a semiconcave CLF on the original space by the minimum projection method. The effectiveness of the proposed method is confirmed by computer simulation. [ABSTRACT FROM AUTHOR]

This paper deals with the stabilization in the sample-and-hold sense of nonlinear, control affine, retarded systems, affected by actuation disturbances and observation errors. Input-to-state stability redesign methods are used in order to design a new sampled-data controller. It is shown that stabilization in the sample-and-hold sense can be preserved by means of this new controller, regardless of the above disturbances and errors. It is assumed that both actuator disturbance and observation error are bounded, and the (arbitrary) bounds are known a-priori . It is moreover assumed that the observation errors do not affect or affect marginally the new control term obtained by input-to-state stability redesign. Simulations on a continuous stirred tank reactor with recycle validate the theoretical results. [ABSTRACT FROM AUTHOR]

This paper is concerned with the development of novel stability criteria for time-varying delayed systems. To this end, a new function which consisted of two quadratic functions with a special structural matrix is established to be a Lyapunov functional candidate. The proposed Lyapunov functional plays key role to decrease the conservatism of derived conditions which is verified by three numerical examples. [ABSTRACT FROM AUTHOR]

A continuous output feedback control scheme rendering the closed-loop double integrator system globally stable in finite-time is presented. In particular, the convergence time is independent of initial conditions. The bi-limit homogeneous technique is used for controller and observer designs with fixed-time convergence. Then, a continuous output feedback control law is proposed for nominal double-integrator system and its perturbed version. The homogeneity and Lyapunov techniques are used to ensure the fixed-time stability of the closed-loop system under output feedback control framework. Finally, the efficiency of the proposed algorithms is illustrated by numerical simulations. [ABSTRACT FROM AUTHOR]

A stability criterion for the exponential stability of systems with multiple pointwise and distributed delays is presented. Conditions in terms of the delay Lyapunov matrix are obtained by evaluating a Lyapunov–Krasovskii functional with prescribed derivative at a pertinent initial function that depends on the system fundamental matrix. The proof relies on properties connecting the delay Lyapunov matrix and the fundamental matrix, which are proven to be valid for both stable and unstable systems. The conditions are applied to the determination of the exact stability region for some examples. [ABSTRACT FROM AUTHOR]

We present the first sufficient conditions that guarantee stability of two-timescale stochastic approximation schemes. Our analysis is based on the ordinary differential equation (ODE) method and is an extension of the results in Borkar and Meyn (2000) for single-timescale schemes. As an application of our result, we show the stability of iterates in a two-timescale stochastic approximation scheme arising in reinforcement learning. [ABSTRACT FROM AUTHOR]

In this brief paper, using results from the theory of averaging of bilinear systems, we provide a graph theoretic characterization for the existence of periodic control inputs that stabilize a sparse matrix system to the origin. In particular, we introduce a class of extensions to the directed graph corresponding to a given sparse matrix system, which when contains a stable sparse matrix system implies that the original system is stabilizable using periodic inputs. When this condition holds, we provide a systematic procedure for designing such controllers. Our technical approach combines ideas from the theory of bilinear control systems and averaging theory with graph theoretic results. [ABSTRACT FROM AUTHOR]

This paper shows that the modified gradient control law proposed in Tian and Wang (2013) does not globally stabilize rigid formation shapes. Also, further analysis on the control law and a numerical example showing that the control law cannot drive the agents out from a stable incorrect equilibrium of the corresponding gradient control system are provided. [ABSTRACT FROM AUTHOR]

This communique proposes a novel second-order sliding mode (SOSM) control method to handle sliding mode dynamics with mismatched term, so as to reduce the terms in the control channel. Meanwhile, it is shown that the proposed control approach can be used to design SOSM controllers under disturbances bounded by positive functions rather than conventional constant upper bounds. The finite-time stability of the sliding variables has been shown by using finite-time Lyapunov theory. The validity of the proposed approach is verified by controlling a Buck converter. [ABSTRACT FROM AUTHOR]

The paper deals with sampled-data stabilization of continuous-time dynamics in strict-feedback form via Immersion and Invariance. Starting from the characterization of the sampled-data target dynamics and its invariant manifold, a multi-rate control law is designed to achieve attractiveness and invariance of such a manifold. Simulations on an academic example and a practical case illustrate the performances. [ABSTRACT FROM AUTHOR]

This paper is concerned with the delay-dependent stability of systems with time-varying delays. The novelty relies on the use of the second-order Bessel–Legendre integral inequality which is less conservative than the Jensen and Wirtinger-based inequalities. Unlike similar contributions, the features of this inequality are fully integrated into the construction of augmented Lyapunov–Krasovskii functionals leading to novel stability criteria expressed in terms of linear matrix inequalities. The stability condition is tested on some classical numerical examples illustrating the efficiency of the proposed method. [ABSTRACT FROM AUTHOR]

We solve a disturbance rejection problem for a general class of heterodirectional 1-D linear hyperbolic partial differential equations (PDEs). The disturbance enters at one boundary, while sensing and actuation is limited to the opposite boundary. We do this by combining a separately designed controller and observer into an output feedback controller, and proving stability of the overall closed loop system and exponential regulation of the control objective to zero. The theory is demonstrated in a simulation. [ABSTRACT FROM AUTHOR]