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Monotone systems comprise an important class of dynamical systems that are of interest both for their wide applicability and because of their interesting mathematical properties. It is known that under the property of quasimonotonicity time-delayed systems become monotone, and some remarkable properties have been reported for such systems. These include, for example, the fact that for linear systems global asymptotic stability of the undelayed system implies global asymptotic stability for the delayed system under arbitrary bounded delays. Nevertheless, extensions to nonlinear systems have thus far relied primarily on the conditions of homogeneity and subhomogeneity, and it has been conjectured that these can be relaxed. Our aim in this paper is to show that this is feasible for a general class of nonlinear monotone systems by deriving convergence results in which simple properties of the undelayed system lead to delay-independent stability. In particular, one of our results shows that if the undelayed system has a convergent trajectory that is unbounded in all components as $t\rightarrow-\infty$, then the system is globally asymptotically stable for arbitrary bounded time-varying delays. This follows from a more general result derived in the paper that allows to quantify delay-independent regions of attraction, which can be used to prove global asymptotic stability for various classes of systems. These also recover various known delay-independent stability results that are discussed within the paper. [ABSTRACT FROM PUBLISHER]

This paper proposes a strategy to estimate the velocity and position of neighbor agents using distance measurements only. Since with agents executing arbitrary motions, instantaneous distance-only measurements cannot provide enough information for our objectives, we postulate that agents engage in a combination of circular motion and linear motion. The proposed estimator can be used to develop control algorithms where only distance measurements are available to each agent. As an example, we show how this estimation method can be used to control the formation shape and secure velocity consensus of the agents in a multi agent system. [ABSTRACT FROM PUBLISHER]

In this paper, we consider nonlinear stochastic systems and intersect ideas from nonlinear control theory and numerical analysis. In particular, we use the idea of relative degree. This concept guarantees smoothness properties of the output and this, in turn, allows one to establish properties that are unique to the control-theoretic perspective. The contributions of the current paper are threefold. Firstly, we define different error measures that extend the ideas of local and global approximation errors for nonlinear stochastic systems. Secondly, we demonstrate that the concept of relative degree plays a key role in obtaining higher order of accuracy for integration procedures compared to Euler-Maruyama integration. We show that a particular state-space model, named STTS model, has an improved order of accuracy when compared to an Euler-Maruyama approximation, at no significant extra computational cost. Thirdly, we show that a further approximation to the STTS model, named MSTTS model, while retaining the order of local errors, has explicit sampling zero dynamics, associated with the noise processes, that have no continuous-time counterpart. The extra zero dynamics are shown to be a function of the Euler-Frobenius polynomials. To the best of the authors' knowledge, this is the first reference to sampling zero dynamics for stochastic nonlinear systems. [ABSTRACT FROM AUTHOR]

Provides an overview of the technical articles and features presented in this issue. [ABSTRACT FROM PUBLISHER]

This paper presents an inverse problem for mean field games where we find the mean field problem statement for which the given dynamics is the solution. We use distributed traffic as an example and derive the classic Lighthill Whitham Richards (LWR) model as a solution of the non-viscous mean field game. We also derive the same model by choosing a different problem where we use travel time, which is a distributed parameter, as the cost for the optimal control. We then study the stationary versions of these two problems and provide numerical solutions for the same. [ABSTRACT FROM PUBLISHER]

In this paper, we provide a general networked controller design methodology for networked plants and apply it to solve the optimal \mathcal H2 networked control problem. Both the plant and the controller are interconnected systems, interacting over the same arbitrary directed network with noiseless and delay-free communication links. We introduce the notions of network implementability and network realizability and analyze the structure of network implementable and realizable systems. Based on the structural property of network implementable systems, under certain network-related constraints, we characterize the set of all stabilizing controllers that are implementable over the given network using the state-space version of Youla parametrization. Moreover, we provide a constructive procedure to implement the controllers as sub-systems interacting over the given network without affecting the stability of the feedback networked system. The distributed \mathcal H2 control problem is then cast as a convex optimization problem and its solution is shown to provide the optimal distributed controller over the given network in terms of its network interacting components. The results of this paper allow one to apply many classical results and approaches of multi-variable robust control theory to networked systems. [ABSTRACT FROM AUTHOR]

In this paper, a unified framework is established to investigate both the quantized and the saturated control problems for a class of sampled-data systems under noisy sampling intervals. A random variable obeying the Erlang distribution is used to describe the noisy sampling intervals. In virtue of the matrix exponential, the sampled-data control system is transformed into an equivalent discrete-time stochastic system, and the aim of this paper is to design a quantized/saturated sampled-data controller such that the resulting discrete-time stochastic system is stochastically stable when the sampling error follows the Erlang distribution. In order to deal with the case of multiple control inputs, a confluent Vandermonde matrix approach is proposed in the design process. By using the Kronecker product operation and the matrix inequality techniques, the desired quantized/saturated controller gains are designed in terms of the solution to certain matrix inequalities. Finally, a simulation example is exploited to verify the effectiveness of the proposed design approach. [ABSTRACT FROM AUTHOR]

This paper is concerned with the optimal distributed control (ODC) problem for linear discrete-time deterministic and stochastic systems. The objective is to design a static distributed controller with a prespecified structure that is globally optimal with respect to a quadratic cost functional. It is shown that this NP-hard problem has a quadratic formulation, which can be relaxed to a semidefinite program (SDP). If the SDP relaxation has a rank-1 solution, a globally optimal distributed controller can be recovered from this solution. By utilizing the notion of treewidth, it is proved that the nonlinearity of the ODC problem appears in such a sparse way that an SDP relaxation of this problem has a matrix solution with rank at most 3. Since the proposed SDP relaxation is computationally expensive for a large-scale system, a computationally cheap SDP relaxation is also developed with the property that its objective function indirectly penalizes the rank of the SDP solution. Various techniques are proposed to approximate a low-rank SDP solution with a rank-1 matrix, leading to near globally optimal controllers together with a bound on the optimality degree of each controller. The above results are developed for both finite-horizon and infinite-horizon ODC problems. The SDP relaxations developed in this work are exact for the design of a centralized controller, hence serving as an alternative for solving Riccati equations. The efficacy of the proposed SDP relaxations is elucidated through a case study on the distributed frequency control of power systems. [ABSTRACT FROM PUBLISHER]

In this paper, we establish results similar in nature to the invariance principle for a class of stochastic hybrid systems modeled by set-valued mappings. In particular, we characterize the set to which bounded random solutions converge in terms of a new concept called weak total recurrence. A refinement of the result under the existence of a non-increasing on average Lyapunov-like function is also established. A comparison between weak total recurrence and the frequently studied invariance concepts are presented. Finally, application of the main results to establish weak sufficient conditions for certifying stochastic stability properties like uniform global asymptotic stability in probability for compact sets and uniform global recurrence for open, bounded sets are discussed. [ABSTRACT FROM PUBLISHER]

This paper proposes an approach to control of discrete systems with incomplete information and sensing capabilities, with respect to temporal logic constraints. The approach introduces active sensing to alleviate computational effort in control design for systems interacting with uncontrollable environments under incomplete information. Particularly, it transforms a deterministic controller under complete information into a randomized, observation-based controller. Interleaving the latter with strategic queries to sensors, the temporal logic specification is proven to be satisfied almost surely. The effectiveness of the method is demonstrated with robotic motion planning examples. [ABSTRACT FROM PUBLISHER]

The author discusses about his longevity as editor-and-chief of "IEEE Transactions on Automatic Control." He notes that he lasted as editor-in-chief because the position give him opportunities to learn continually and he tried to appreciate its lighter side. He recounts the major highlights in the operation of the journal including the introduction of a web-based system for submitting and reviewing papers. He also expressed his gratitude to his colleagues including John Baillieul.

This paper addresses problems on the structural design of large-scale control systems. An efficient and unified framework is proposed to select the minimum number of manipulated/measured variables to achieve structural controllability/observability of the system, and to select the minimum number of feedback interconnections between measured and manipulated variables such that the closed-loop system has no structural fixed modes. Global solutions are computed using polynomial complexity algorithms in the number of the state variables of the system. Finally, graph-theoretic characterizations are proposed, which allow a characterization of all possible solutions. [ABSTRACT FROM PUBLISHER]

The main purpose of this correspondence is to establish that, contrary to the claims that are made in the paper by D. Y. Chao in it, the results of the paper by Park and S. A. Reveliotis concerning the liveness characterization of the S^3PGR^2 nets by means of the structural object of deadly marked siphon, are correct and complete. [ABSTRACT FROM AUTHOR]

The ability to control the behavior of intracellular networks has relevant applications, ranging from an optimized synthesis of metabolites in bacteria to the cure of human diseases. To implement a controller in vivo, one may insert synthetic biomolecules into the cell being controlled. This paper develops a formal approach, based on Supervisory Control Theory (SCT), to guide the design of synthetic genes that control the dynamics of gene regulatory networks, major players in cell dynamics, so that a set of specifications is achieved. Such a systematic procedure is important to make the control of large networks by synthetic molecules feasible. In our approach, we assume that the behavior of gene networks can be abstracted by finite state machines, where each state corresponds to a set of gene expression levels and the events are associated with the activation/repression of genes. We then extend the SCT framework to address the so-called state attraction problem, for the case where the controller is allowed to: a) enable/disable events, b) force events, and c) preempt the occurrence of some (possibly all) plant events. [ABSTRACT FROM AUTHOR]

This paper studies the stability for a class of systems with time-varying delay subject to controller failure. It explores under what conditions of controller failure the system is still exponentially stable. The concept of controller failure frequency is introduced. First, the delay system with failed controller is modelled as a class of switched delay systems. Next, based on two lemmas developed in this paper and the piecewise Lyapunov functional method, sufficient conditions are provided to guarantee the exponential stability of the system when controller failure occurs, which is in terms of the solvability of a set of linear matrix inequalities (LMIs). Finally, an example of a networked control system is given to illustrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

In this paper, we consider the problem of model reduction of consensus networks. We propose a new method of model reduction based on removing edges that close cycles in the network graph. The agent dynamics of the consensus network is given by a symmetric multivariable input-state-output system. In the network, the agents exchange relative output information with their neighbors. We assume that the network graph is connected, unweighted, and undirected. The network used to approximate the original system is defined on the same number of nodes as the original graph, but its edge set is a strict subset of the original edge set. Explicit expressions and upper bounds for the approximation errors are formulated in terms of the signed path vectors of the removed edges and the eigenvalues of the Laplacian matrices of the original and reduced network graphs. [ABSTRACT FROM PUBLISHER]

Presents an editorial of the state of the IEEE Transactions on Automatic Control . [ABSTRACT FROM PUBLISHER]

This paper develops a measure-theoretic approach for generating the collective behavior of flocking of planar autonomous vehicles under all-to-all communication scheme. To obtain flocking protocol, we formulate the notion of state of styled-velocity flocking for the target state of a design problem instead of considering solution-ansatzes. This notion captures a broader class of flocking behaviors of non-parallel motions, as well as embodies the two important performances of cohesion maintenance and collision avoidance. To pose a control design problem, a measure-valued transition equation is obtained to induce an auxiliary one-body continuum-model from the exact multi-body particle-model of the collective system. The design problem is then formulated on the auxiliary continuum-model, and a systematic design procedure is presented. The state of styled-velocity flocking of the particle-model under the obtained flocking protocol is then verified with an important result on the continuous dependence on initial data of solutions of the measured-valued transition equation. Application to elliptical flocking of mobile robots is presented to illustrate the novelty of the presented theory. [ABSTRACT FROM PUBLISHER]

This paper presents a new approach to event-triggered control for nonlinear uncertain systems by using the notion of input-to-state stability (ISS) and the nonlinear small-gain theorem. The contribution of this paper is threefold. First, it is proved that infinitely fast sampling can be avoided if the system is input-to-state stabilizable with the sampling error as the external input and the corresponding ISS gain is locally Lipschitz. No assumption on the existence of known ISS-Lyapunov functions is made in the discussions. Moreover, the forward completeness problem with event-triggered control is studied systematically by using ISS small-gain arguments. Second, the proposed approach gives rise to a new self-triggered sampling strategy for a class of nonlinear systems subject to external disturbances. If an upper bound of the external disturbance is known, then the closed-loop system can be designed to be robust to the external disturbance, and moreover, the system state globally asymptotically converges to the origin if the external disturbance decays to zero. Third, a new design method is developed for event-triggered control of nonlinear uncertain systems in the strict-feedback form. It is particularly shown that the ISS gain with the sampling error as the input can be designed to satisfy the proposed condition for event-triggered control and self-triggered control. [ABSTRACT FROM PUBLISHER]

In this paper, we study fundamental properties of minimum inter-event times for several event-triggered control architectures, both in the absence and presence of external disturbances and/or measurement noise. This analysis reveals, amongst others, that for several popular event-triggering mechanisms no positive minimum inter-event time can be guaranteed in the presence of arbitrary small external disturbances or measurement noise. This clearly shows that it is essential to include the effects of external disturbances and measurement noise in the analysis of the computation/communication properties of event-triggered control systems. In fact, this paper also identifies event-triggering mechanisms that do exhibit these important event-separation properties. [ABSTRACT FROM PUBLISHER]

This work deals with the analysis and the design of minimum-time control laws for a class of nonlinear discrete-time dynamical systems characterized by \cal K-continuous transition maps and bounded control inputs. In the paper, it is shown that the reachability properties of the target set, even if not robust positively controllable in one state transition, can be exploited to assess the existence of a robust positively controllable set including the target in its interior. This result allows the formulation of a robustified minimum-time control policy, based on iterated online optimizations and guaranteeing the ultimate boundedness of the state-trajectories in the presence of bounded uncertainties, even if the target set is not robust positively controllable. [ABSTRACT FROM PUBLISHER]

This paper presents a numerical procedure for the reachability analysis of systems with nonlinear, semi-explicit, index-1 differential-algebraic equations. The procedure computes reachable sets for uncertain initial states and inputs in an overapproximative way, i.e. it is guaranteed that all possible trajectories of the system are enclosed. Thus, the result can be used for formal verification of system properties that can be specified in the state space as unsafe or goal regions. Due to the representation of reachable sets by zonotopes and the use of highly scalable operations on them, the presented approach scales favorably with the number of state variables. This makes it possible to solve problems of industry-relevant size, as demonstrated by a transient stability analysis of the IEEE 14-bus benchmark problem for power systems. [ABSTRACT FROM AUTHOR]

In this paper a distributed algorithm for clock synchronization is proposed. This algorithm is based on an extension of the linear consensus algorithm which is able to synchronize a family of identical double integrators. Since in reality the various clocks may have different drifts, the algorithm needs to be designed in such a way that it works correctly also in case of heterogeneous double integrators. We start by reviewing an unrealistic synchronous implementation of the clock synchronization algorithm, that has been recently proposed in the context of noisy double integrators. The main contribution of this paper is to propose a realistic pseudo-synchronous implementation of this algorithm. This pseudo-synchronous algorithm is shown to be a perturbation of the synchronous one and so, through arguments related to the center manifold theorem, it is proved to be locally convergent under the assumption of absence of process noise, measurement noise and propagation delays. However, through numerical simulations, the performance of this algorithm is evaluated also in the case the communication delays are not negligible, the clock drifts are time-varying and the communication channels are unreliable. Moreover, again through numerical simulations, the strategy we propose in this paper is compared with other fully distributed strategies recently proposed in the literature. While being slightly slower to reach the asymptotic synchronization, our strategy seems to significantly outperform the other strategies in terms of robustness to process and measurement noises and time-varying clock drifts. [ABSTRACT FROM AUTHOR]

The concept of inverse feedback shapers is fully developed in this report for the case of multibody systems with strongly coupled dynamics. The presented results constitute a nontrivial extension of the previous papers by the authors on input shaping focusing on effectively decoupled controlled and flexible parts. As the main technical result, the target mode for the inverse shaper design is identified based on an input–output transformation of the multibody system into the controlled subsystem, the attached residual oscillatory dynamics, and an internal feedback loop representing the dynamical coupling. A state feedback controller, applied for the selected generalized coordinate, is considered throughout this paper. [ABSTRACT FROM AUTHOR]

The paper studies digital redesign of linear time-invariant analog controllers under intermittent sampling. The sampling pattern is only assumed to be uniformly bounded, but otherwise irregular and unknown a priori. The contribution of the paper is twofold. First, it proposes a constructive algorithm to redesign any analog stabilizing controller so that the closed-loop stability is preserved. Second, it is shown that when applied to (sub) optimal \boldsymbolH^2 and \boldsymbolH^\infty controllers, the algorithm produces (sub) optimal sampled-data solutions under any a priori unknown sampling pattern. The proposed solutions are analytic, computationally simple, implementable, and transparent. Transparency pays off in showing the optimality, under a fixed sampling density, of uniform sampling for both performance measures studied. [ABSTRACT FROM AUTHOR]

In this paper, we propose a self-triggered formulation of model predictive control for continuous-time nonlinear input-affine networked control systems. Our control method specifies not only when to execute control tasks but also provides a way to discretize the optimal control trajectory into several control samples, so that the reduction of communication load will be obtained. Stability analysis under the sample-and-hold implementation is also given, which guarantees that the state converges to a terminal region where the system can be stabilized by a local state feedback controller. Some simulation examples validate our proposed framework. [ABSTRACT FROM PUBLISHER]

Networked systems present some key new challenges in the development of fault-diagnosis architectures. This paper proposes a novel distributed networked fault detection methodology for large-scale interconnected systems. The proposed formulation incorporates a synchronization methodology with a filtering approach in order to reduce the effect of measurement noise and time delays on the fault detection performance. The proposed approach allows the monitoring of multirate systems, where asynchronous and delayed measurements are available. This is achieved through the development of a virtual sensor scheme with a model-based resynchronization algorithm and a delay compensation strategy for distributed fault-diagnostic units. The monitoring architecture exploits an adaptive approximator with learning capabilities for handling uncertainties in the interconnection dynamics. A consensus-based estimator with time-varying weights is introduced, for improving fault detectability in the case of variables shared among more than one subsystem. Furthermore, time-varying threshold functions are designed to prevent false-positive alarms. Analytical fault detectability sufficient conditions are derived, and extensive simulation results are presented to illustrate the effectiveness of the distributed fault detection technique. [ABSTRACT FROM PUBLISHER]

In the recent paper by Hamadeh et al. (2012) an elegant analytic criterion for incremental output feedback passivity (iOFP) of cyclic feedback systems (CFS) has been reported, assuming that the constituent subsystems are incrementally output strictly passive (iOSP). This criterion was used to prove that a network of identical CFS can be synchronized under sufficiently strong linear diffusive coupling. A very important class of CFS consists of biological oscillators, named after Brian Goodwin and describing self-regulated chains of enzymatic reactions, where the product of each reaction catalyzes the next reaction, while the last product inhibits the first reaction in the chain. Goodwin's oscillators are used, in particular, to model the dynamics of genetic circadian pacemakers, hormonal cycles and some metabolic pathways. In this technical note we point out that for Goodwin's oscillators, where the individual reactions have nonlinear (e.g., Mikhaelis-Menten) kinetics, the synchronization criterion, obtained by Hamadeh et al., cannot be directly applied. This criterion relies on the implicit assumption of the solution boundedness, dictated also by the chemical feasibility (the state variables stand for the concentrations of chemicals). Furthermore, to test the synchronization condition one needs to know an explicit bound for a solution, which generally cannot be guaranteed under linear coupling. At the same time, we show that these restrictions can be avoided for a nonlinear synchronization protocol, where the control inputs are “saturated” by a special nonlinear function (belonging to a wide class), which guarantees nonnegativity of the solutions and allows to get explicit ultimate bounds for them. We prove that oscillators synchronize under such a protocol, provided that the couplings are sufficiently strong. [ABSTRACT FROM AUTHOR]

A geometric homogeneity is introduced for evolution equations in a Banach space. Scalability property of solutions of homogeneous evolution equations is proven. Some qualitative characteristics of stability of trivial solution are also provided. In particular, finite-time stability of homogeneous evolution equations is studied. Theoretical results are illustrated on important classes of partial differential equations. [ABSTRACT FROM PUBLISHER]

An introduction is presented in which the editor discusses various reports within the issue on topics including system identification and adaptive control of automatic control system, the computational aspects of control system design, and nuclear norm relaxation of rank minimization problems.

In this paper, tools to study forward invariance properties with robustness to disturbances, referred to as robust forward invariance, are proposed for hybrid dynamical systems modeled as hybrid inclusions. Hybrid inclusions are given in terms of differential and difference inclusions with state and disturbance constraints, for whose definition only four objects are required. The proposed robust forward invariance notions allow for the diverse type of solutions to such systems (with and without disturbances), including solutions that have persistent flows and jumps, that are Zeno, and that stop to exist after finite amount of (hybrid) time. Sufficient conditions for sets to enjoy such properties are presented. These conditions are given in terms of the objects defining the hybrid inclusions and the set to be rendered robust forward invariant. In addition, as special cases, these conditions are exploited to state results on nominal forward invariance for hybrid systems without disturbances. Furthermore, results that provide conditions to render the sublevel sets of Lyapunov-like functions forward invariant are established. Analysis of a controlled inverter system is presented as an application of our results. Academic examples are given throughout this paper to illustrate the main ideas. [ABSTRACT FROM AUTHOR]

The cooperative output regulation (COR) problem of heterogeneous linear multi-agent networks [multi-agent systems (MASs)] is studied in the paper. Agents are allowed to be inherently heterogeneous linear time-invariant systems and the communication graph is not restricted to be acyclic. Both state- and output-feedback control protocols that make use of neighbors’ output information are considered. In light of robust control theory and robust output regulation theory, small-gain solvability conditions with closed-loop pole specifications are first derived. Then, an ${H_{\infty }}$ performance allocation approach is proposed for protocol design, where algorithms for optimizing graph weights and designing protocol gains are constructed, respectively. Both continuous-time (CT) and discrete-time MASs are investigated in a unified framework. In addition, solvability of the COR problem is further discussed from the graph, agent, and exosystem aspects, respectively. It is proved that the proposed approach pre-explicitly ensures the solvability of the COR problem for either of the three cases: the graph is acyclic; for CT MASs, agents are minimum-phase and right-invertible; and for CT MASs, the poles of the exosystem have zero real part and agents are right-invertible. [ABSTRACT FROM AUTHOR]

This paper considers the problem of asynchronous $\mathcal H_{\infty }$ control for two-dimensional (2-D) Markov jump systems. The underlying system is described based upon the Roesser model. Especially, the hidden Markov model is employed when dealing with the asynchronization between a controlled system and a controller, and the relation between them is constructed through a conditional probability matrix. Based on the Lyapunov function technique, the asymptotic mean square stability and $\mathcal H_{\infty }$ noise attenuation performance are investigated for the closed-loop 2-D system. Moreover, the controller gain can be obtained by solving a convex optimization problem. An example is presented to show the effectiveness and potential of the proposed new design technique. [ABSTRACT FROM AUTHOR]

Information value functions based on the Kullback–Leibler (KL) divergence have been shown the most effective for planning sensor measurements by means of greedy strategies. The problem of optimizing information value over a finite time horizon to date has been considered computationally intractable and, as proven here, is $\text{NP}$ -hard. This paper presents new information value functions that are additive and can be optimized efficiently over time by deriving a lower bound of the KL divergence. Combined with a convex approximation of the sensor field of view, these information value functions can be used to obtain real-time sensor control by a lexicographic approach, and to derive performance guarantees. Numerical and experimental results on pedestrian data show that the lexicographic control system significantly improves target modeling and prediction performance when compared to existing algorithms. [ABSTRACT FROM AUTHOR]

This paper aims to solve the finite-time stabilization problem for stochastic high-order nonlinear systems with stochastic inverse dynamics. By characterizing unmeasured stochastic inverse dynamics with finite-time stochastic input-to-state stability (FT-SISS), borrowing from some ideas of the Lyapunov function, sign function, backstepping and FT-SISS methods, and using stochastic finite-time stability theory, a new design and analysis method is given to guarantee global finite-time stability in probability of the closed-loop stochastic systems. [ABSTRACT FROM AUTHOR]

This paper studies performance preserving event design in nonlinear event-based control systems based on a local $\mathcal{L}_2$ -type performance criterion. Considering a finite gain local $\mathcal{L}_2$ -stable disturbance driven continuous-time system, we propose a triggering mechanism so that the resulting sampled-data system preserves similar disturbance attenuation local $\mathcal{L}_2$ -gain property. The results are applicable to nonlinear systems with exogenous disturbances bounded by some Lipschitz-continuous function of state. It is shown that an exponentially decaying function of time, combined with the proposed triggering condition, extends the interevent periods. Compared to the existing works, this paper analytically estimates the increase in intersampling periods at least for an arbitrary period of time. We also propose a so-called discrete triggering condition to quantitatively find the improvement in interevent times at least for an arbitrary number of triggering iterations. Illustrative examples support the analytically derived results. [ABSTRACT FROM AUTHOR]

Sliding mode control (SMC), which is known to present strong robustness against various disturbances, has been extensively employed on underactuated systems, whose control problem has been a research focus in recent years. However, though received great attention, the study on SMC for underactuated systems still remains quite open since it is very challenging to construct a proper manifold which can simultaneously stabilize both actuated and unactuated system states. Motivated to promote the corresponding research, we propose an improved second-order SMC (IS-SMC) method for a class of nonlinear underactuated systems in this paper, which guarantees that the closed-loop system's equilibrium point is asymptotically stable even in the presence of unknown nondiminishing disturbances. Different from traditional SMC methods presenting with chattering problem, the control inputs of the proposed method are essentially continuous, which brings much convenience for practical applications. Moreover, for the disturbances which are second-order differentiable, an enhanced IS-SMC (EIS-SMC) method is derived to guarantee the smoothness for both the control inputs and their derivatives. Finally, the proposed approach is applied to a practical underactuated system: The overhead crane system, with sufficient simulation results provided to validate the efficiency of the proposed method. [ABSTRACT FROM AUTHOR]

By using a delay line as a signal generator, we design a simple robust controller for the approximate regulation (i.e., approximate asymptotic tracking and rejection) of almost periodic signals for linear systems. As opposed to the related existing results, our controller design does not require online parameter tuning. Besides the usual assumptions about stabilizability, detectability, and nonexistence of transmission zeros for the plant, the controller design algorithm of this paper only requires knowledge of the desired tracking accuracy ϵ > 0. Based on this information alone, we can only design a robust controller achieving, in the presence of unknown trigonometric polynomial disturbances and additive perturbations to the plant and the controller, lim supt→ ∞ ∥ y(t) - yref(t) ∥ < ϵ ∥ yref ∥. Here, y is the output of the plant and yref is an arbitrary almost periodic reference signal taken from an infinite-dimensional generalized Sobolev space of almost periodic functions. In this paper, we also study robust output regulation in the limiting case where ϵ → 0. It turns out that, due to the general loss of exponential closed loop stability, asymptotic tracking/rejection can also be lost as ϵ → 0, unless the exogenous signals are smooth enough. This last result extends some recent theorems on (nonrobust) open loop output regulation for infinite-dimensional exosystems. The results of this paper are new and potentially useful for finite-dimensional plants, but the main results are also true for infinite-dimensional systems with bounded control and observation operators. [ABSTRACT FROM AUTHOR]

This paper investigates the problem of robust H∞ estimation for uncertain systems subject to limited communication capacity. The parameter uncertainty belongs to a given convex polytope and the communication limitations include measurement quantization, signal transmission delay, and data packet dropout, which appear typically in a network environment. The problem of H∞ filter design is first solved for a nominal system subject to the aforementioned information limitations, which is then extended to the uncertain case based on the notion of quadratic stability. To further reduce the overdesign in the quadratic framework, this paper also proposes a parameter-dependent filter design procedure, which is much less conservative than the quadratic approach. The quadratic and parameter-dependent approaches provide alternatives for designing robust H∞ filters with different degrees of conservativeness and computational complexity. Two examples, including a mass-spring system, are utilized to illustrate the design procedures proposed in this paper. [ABSTRACT FROM AUTHOR]

This paper investigates the stabilizability of uncertain linear time-invariant (LTI) systems via structurally constrained controllers. First, an LTI uncertain system is considered whose state-space matrices depend polynomially on the uncertainty vector, defined over some region. It is shown that if the system is stabilizable by a structurally constrained controller in one point belonging to the region, then it is stabilizable by a controller with the same structure in all points belonging to the region, except for those located on an algebraic variety. Thus, if a system is stabilizable via a constrained controller at the nominal point, then it is almost always stabilizable at any operating point around the nominal model. It is also shown how this algebraic variety (or the dominant subvariety of it) can be computed efficiently. The results obtained in this paper encompass a broad range of the existing results in the literature on robust stability of the LTI systems, in addition to new ones. [ABSTRACT FROM AUTHOR]

This paper presents new results that allow one to compute the set of states that can be robustly steered in a finite number of steps, via state feedback control, to a given target set. The assumptions that are made in this paper are that the system is discrete-time, nonlinear and time-invariant and subject to mixed constraints on the state and input. A persistent disturbance, dependent on the current state and input, acts on the system. Existing results are not able to address state- and input-dependent disturbances and the results in this paper are, therefore, a generalization of previously published results. One of the key aims of this paper is to present results such that one can perform the relevant set computations using polyhedral algebra and computational geometry software, provided the system is piecewise affine and the constraints are polygonal. Existing methods are only applicable to piecewise affine systems that either have no control inputs or no disturbances, whereas the results in this paper remove this limitation. Some simple examples are also given that show that, even if all the relevant sets are convex and the system is linear, convexity of the set of controllable states cannot be guaranteed. [ABSTRACT FROM AUTHOR]

In this paper, the application of the dynamic programming approach to constrained stochastic control problems with expected value constraints is demonstrated. Specifically, two such problems are analyzed using this approach. The problems analyzed are the problem of minimizing a discounted cost infinite horizon expectation objective subject to an identically structured constraint, and the problem of minimizing a discounted cost infinite horizon minimax objective subject to a discounted expectation constraint. Using the dynamic programming approach, optimality equations, which are the chief contribution of this paper, are obtained for these problems. In particular, the dynamic programming operators for problems with expectation constraints differ significantly from those of standard dynamic programming and problems with worst-case constraints. For the discounted cost infinite horizon cases, existence and uniqueness of solutions to the dynamic programming equations are explicitly shown by using the Banach fixed point theorem to show that the corresponding dynamic programming operators are contractions. The theory developed is illustrated by numerically solving the constrained stochastic control dynamic programming equations derived for simple example problems. The example problems are based on a two-state Markov model that represents an error prone system that is to be maintained. [ABSTRACT FROM AUTHOR]

The root locus is an important tool for analyzing the stability and time constants of linear finite-dimensional systems as a parameter, often the gain, is varied. However, many systems are modelled by partial differential equations or delay equations. These systems evolve on an infinite-dimensional space and their transfer functions are not rational. In this paper a rigorous definition of the root locus for infinite-dimensional systems is given and it is shown that the root locus is well-defined for a large class of infinite-dimensional systems. As for finite-dimensional systems, any limit point of a branch of the root locus is a zero. However, the asymptotic behavior can be quite different from that for finite-dimensional systems. This point is illustrated with a number of examples. It is shown that the familiar pole-zero interlacing property for collocated systems with a Hermitian state matrix extends to infinite-dimensional systems with self-adjoint generator. This interlacing property is also shown to hold for collocated systems with a skew-adjoint generator. [ABSTRACT FROM AUTHOR]

This paper formulates and studies the concept of quasi-Disturbance-to-Error Stability (qDES) which characterizes robustness of a nonlinear observer to an output measurement disturbance. In essence, an observer is qDES if its error dynamics are input-to-state stable (ISS) with respect to the disturbance as long as the plant's input and state remain bounded. We develop Lyapunov-based sufficient conditions for checking the qDES property for both full-order and reduced-order observers. We use these conditions to show that several well-known observer designs yield qDES observers, while some others do not. Our results also enable the design of novel qDES observers, as we demonstrate with examples. When combined with a state feedback law robust to state estimation errors in the ISS sense, a qDES observer can be used to achieve output feedback control design with robustness to measurement disturbances. As an application of this idea, we treat a problem of stabilization by quantized output feedback. [ABSTRACT FROM AUTHOR]

This paper studies the real-time implementation of distributed controllers on networked cyber-physical systems. We build on the strengths of event- and self-triggered control to synthesize a unified approach, termed team-triggered, where agents make promises to one another about their future states and are responsible for warning each other if they later decide to break them. The information provided by these promises allows individual agents to autonomously schedule information requests in the future and sets the basis for maintaining desired levels of performance at lower implementation cost. We establish provably correct guarantees for the distributed strategies that result from the proposed approach and examine their robustness against delays, packet drops, and communication noise. The results are illustrated in simulations of a multi-agent formation control problem. [ABSTRACT FROM AUTHOR]

A Petri net (PN) is said to be live if it is possible to fire any transition, although not immediately, from every reachable marking. A liveness enforcing supervisory policy (LESP) determines which controllable transition is to be prevented from firing at a marking, to ensure the supervised Petri net (PN) is live. In this paper, we restrict our attention to a class of general Petri nets (PN) structures, where the existence of an LESP for an instance initialized at a marking, implies the existence of an LESP when the same instance is initialized with a termwise-larger initial marking. We show that the minimally restrictive LESP for an instance N from this class is characterized by a collection of boolean formulae {\{\Theta_{t_{c}}(N)\}}_{t_{c}\in T_{c}}, where T_{c} $ is the set of controllable transitions in the PN. The literals in \Theta_{t_{c}} (N) are true if and only if the token-load of specific places meet a threshold. Consequently, appropriately placed threshold-sensors, which detect if the token-load of a place is greater than or equal to a predetermined threshold, provide sufficient information to implement the minimally restrictive LESP. The paper concludes with some directions for future research. [ABSTRACT FROM AUTHOR]

In this paper, we introduce an event-based boundary control for a $2\times 2$ coupled linear hyperbolic system. We use a well-established backstepping controller which stabilizes the system along with a dynamic triggering condition which determines when the controller must be updated. The main contributions rely on the definition of an event-based controller under which global exponential stability of the system is achieved and, furthermore, the existence of a minimal dwell-time between two triggering times is guaranteed. The well-posedness of the system under the event-based controller is stated. A simulation example is presented to illustrate the results. [ABSTRACT FROM AUTHOR]

In this paper, we develop a compositional approach to abstraction and safety synthesis for a general class of discrete-time nonlinear systems. Our approach makes it possible to define a symbolic abstraction by composing a set of symbolic subsystems that are overlapping in the sense that they can share some common state variables. We develop compositional safety synthesis techniques using such overlapping symbolic subsystems. Comparisons, in terms of conservativeness and of computational complexity, between abstractions and controllers obtained from different system decompositions are provided. Numerical experiments show that the proposed approach for symbolic control synthesis enables a significant complexity reduction with respect to the centralized approach, while reducing the conservatism with respect to compositional approaches using nonoverlapping subsystems. [ABSTRACT FROM AUTHOR]

In this paper, we consider a class of infinite horizon forward and backward stochastic difference equations (FBSDEs) that are fully coupled. The adapted solution is given by establishing an explicit relation between the forward and backward components in terms of a generalized algebraic Riccati equation. The equivalence between the exponential stabilizability of the stochastic control system and the infinite horizon FBSDEs is derived. As an application, the FBSDEs are used to characterize the maximum principle of the infinite horizon stochastic optimal control problem. [ABSTRACT FROM PUBLISHER]

This paper is concerned with the ultimate boundedness control problem for a class of networked nonlinear systems subject to the try-once-discard (TOD) protocol scheduling and uniform quantization effects. To prevent the transmission data from collisions, the communication between sensor nodes and the controller is implemented via a constrained communication channel, where only one sensor node is permitted to transmit data at each time instant. The TOD protocol is utilized to regulate the signal transmission over the communication network under which the scheduling behavior is described by a special switching function. On the other hand, the uniform quantization effects of the network are characterized by a round function (i.e., the nearest integer function). The purpose of the addressed problem is to design an observer-based controller for the networked nonlinear systems such that, in the presence of TOD protocol and uniform quantization effects, the closed-loop system is ultimately bounded and the controlled output is locally minimized. Sufficient conditions are established to guarantee the ultimate boundedness of the dynamics of the closed-loop system in mean square by applying the stochastic analysis approach. Furthermore, the desired controller gains are derived by solving a convex optimization problem. Finally, a numerical example is given to illustrate the effectiveness of the proposed controller design scheme. [ABSTRACT FROM PUBLISHER]