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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]

The robust control problem of a class of nonlinear systems subject to external disturbances, control gain uncertainty, and nonlinear uncertainties is investigated in this paper using a nonlinearity estimator-based control approach. Different from the existing results, the crucial but highly restrictive hypothesis on the boundedness of nonlinear uncertainties is removed from this paper by means of the tools of semiglobal stabilization. By delicately constructing a specific composite Lyapunov function for the closed-loop system as well as several useful level sets, the rigorous qualitative robustness performance is presented for the closed-loop system. Finally, an example of a single-link manipulator is utilized to demonstrate the performance specification claimed by the theoretical analysis. [ABSTRACT FROM AUTHOR]

This paper investigates the existence of nonimpulsive unique solution and stochastic stability problems for the discrete-time linear rectangular descriptor Markov jump systems at two cases. For every case, the sufficient and necessary conditions, in terms of strict linear matrix inequalities, are eventually proposed to guarantee that the discrete-time linear rectangular descriptor Markov jump systems are column (row) regular, column (row) causal, stochastically stable, and have a unique solution. In addition, some assumptions are introduced to ensure that there is no impulse in the solution at the instant when the Markov process jumps. Moreover, the concrete procedures on how to apply the results obtained in this paper are presented as well. Finally, an example is provided to demonstrate the effectiveness of the results. [ABSTRACT FROM AUTHOR]

This paper introduces an explicit reference governor to supervise closed-loop linear time-delay systems. The proposed scheme enforces state and input constraints by modifying the reference of the supervised system so that the state vector always belongs to admissible sublevel sets of a suitably defined Lyapunov–Krasovskii functional. To accomplish this, this paper extends the existing definition of “dynamic safety margin” to a time-delay setting and illustrates how to employ classic Lyapunov–Krasovskii functionals even though the reference is time varying. Constraint enforcement for arbitrary reference signals and asymptotic convergence to any strictly steady-state admissible set point is rigorously proven. Experimental results are reported to demonstrate the simplicity, practicality, and robustness of the proposed method. [ABSTRACT FROM AUTHOR]

This paper proposes necessary and sufficient conditions for stability and performance analysis of 2-D mixed continuous-discrete-time systems that can be checked with convex optimization, in particular linear matrix inequalities (LMIs). Specifically, the first contribution of the paper is a condition for exponential stability based on the introduction of a complex Lyapunov function depending polynomially on a parameter and on the use of the Gram matrix method. It is shown that this condition is sufficient for any chosen degree of the complex Lyapunov function, and necessary for an a priori known degree. The second contribution is a non-Lyapunov condition for exponential stability based on eigenvalue products. This condition is necessary and sufficient, and has the advantage of requiring a significantly smaller computational burden for achieving necessity. Lastly, the third contribution is to show how upper bounds on the \cal H\infty norm of 2-D mixed continuous-discrete-time systems can be obtained through a semidefinite program based on complex Lyapunov functions. A necessary and sufficient condition is provided for establishing the tightness of the found upper bounds. [ABSTRACT FROM PUBLISHER]

Robustness as a system property describes the degree to which a system is able to function correctly in the presence of disturbances, i.e., unforeseen or erroneous inputs. In this paper, we introduce a notion of robustness termed input-output dynamical stability for cyber-physical systems (CPS) which merges existing notions of robustness for continuous systems and discrete systems. The notion captures two intuitive aims of robustness: bounded disturbances have bounded effects and the consequences of a sporadic disturbance disappear over time. We present a design methodology for robust CPS which is based on an abstraction and refinement process. We suggest several novel notions of simulation relations to ensure the soundness of the approach. In addition, we show how such simulation relations can be constructed compositionally. The different concepts and results are illustrated throughout the paper with examples. [ABSTRACT FROM AUTHOR]

This paper presents the stability and criticality analysis of integer linear programs with respect to perturbations in stochastic data given as Markov chains. These perturbations affect the initial distribution, the transition matrix, or the stationary distribution of Markov chains. Stability analysis is concerned with obtaining the set of all perturbations for which a solution remains optimal. This paper gives expressions for stability regions for perturbations in the initial distribution, the transition matrix, the stationary distribution, and the product of elements of the transition matrix and the stationary distribution. Furthermore, criticality measures that describe the sensitivity of the objective function with respect to an element of the problem data are derived. Stability regions that preserve the stochasticity of the problem data are given. Finally, stability regions for perturbations of elements of the transition matrix, given that the problem is not linear in the initial distribution or the transition matrix, are obtained using a small perturbation analysis. The results are applied to sensor placement problems and numerical examples are given. [ABSTRACT FROM PUBLISHER]

This paper proposes a new concurrent learning-based adaptive control algorithm. The main objective behind our proposition is to relax the persistent excitation requirement for the stability guarantee, while providing the ability to identify time-varying parameters. To achieve the objective, this paper designs a directional forgetting algorithm, which is then integrated with the adaptive law. The theoretical stability analysis shows that the tracking and parameter estimation error is exponentially stable with the signal only finitely excited, not persistently excited. The analysis also shows that the proposed algorithm can guarantee the stability under time-varying parameters. Moreover, the necessary and sufficient conditions for the stability given the time-varying parameters are derived. The results of numerical simulations confirm the validity of the theoretical analysis results and demonstrate the performance of the proposed algorithm. [ABSTRACT FROM AUTHOR]

This paper is concerned with stability analysis and synthesis for discrete-time linear systems with stochastic dynamics. Equivalence is first proved for three stability notions under some key assumptions on the randomness behind the systems. In particular, we use the assumption that the stochastic process determining the system dynamics is independent and identically distributed with respect to the discrete time. Then, a Lyapunov inequality condition is derived for stability in a necessary and sufficient sense. Although our Lyapunov inequality will involve decision variables contained in the expectation operation, an idea is provided to solve it as a standard linear matrix inequality; the idea also plays an important role in state feedback synthesis based on the Lyapunov inequality. Motivating numerical examples are further discussed as an application of our approach. [ABSTRACT FROM AUTHOR]

This paper studies the problem of bearing-only formation control of multiagent systems, where the control of each agent merely relies on the relative bearings to its neighbors. Although this problem has received increasing research attention recently, it is still unsolved to a large extent due to its highly nonlinear dynamics. In particular, the existing control approaches are only able to solve the simplest scenario where the target formation is stationary and each agent is modeled as a single integrator. The main contribution of this paper is to propose new bearing-only formation control laws to 1) track moving target formations and 2) handle a variety of agent models including single-integrator, double-integrator, and unicycle models. These control laws are an important step towards the application of bearing-only formation control in practical tasks. Both numerical simulation and real experimental results are presented to verify the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

This paper studies the consensus tracking problem of uncertain Lagrangian systems. In contrast to the existing results where the command signals are sufficiently smooth, we consider a class of nonsmooth command signals generated by a switched command generator, which might be more realistic from the perspective of practical applications. The main technical innovations of this paper are threefold. First, to enable a rigorous problem formulation, some piecewise decaying function sets are defined to precisely describe the steady-state behaviors of the tracking errors. Second, to ensure the stability of the switched nonlinear closed-loop system, a system-based scaling method with the establishment of several lemmas is developed to determine the minimal dwell time of the switching signal. Third, a quantitative analysis is performed to acquire the ultimate bound for the steady-state tracking errors. The proposed control approach is evaluated by a simulation example. [ABSTRACT FROM AUTHOR]

This paper deals with the estimation of convergence rate and domain of attraction of control-Lyapunov functions in Lyapunov-based control. This pair of estimation problems has been considered only for input-affine systems with constraints on the input norm. In this paper, we propose a novel optimization framework to address the estimation of convergence rate and domain of attraction. Specifically, we formulate the estimation problems as min–max bilevel programs for the decay rate of the Lyapunov function, where the inner problem can be resolved using Karush–Kuhn–Tucker optimality conditions, and the resulting single-level programs can be transformed into and solved as mixed-integer nonlinear programs. The proposed approach is applicable to systems with input-nonaffinity or more general forms of input constraints under an input-convexity assumption. [ABSTRACT FROM AUTHOR]

The issue of cyber-security has become ever more prevalent in the analysis and design of networked systems. In this paper, we analyze networked control systems in the presence of denial-of-service (DoS) attacks, namely attacks that prevent transmissions over the network. We characterize frequency and duration of the DoS attacks under which input-to-state stability (ISS) of the closed-loop system can be preserved. To achieve ISS, a suitable scheduling of the transmission times is determined. It is shown that the considered framework is flexible enough so as to allow the designer to choose from several implementation options that can be used for trading-off performance versus communication resources. Examples are given to substantiate the analysis. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of determining the \cal H\infty and \cal H2 norms of 2-D mixed continuous-discrete-time systems. The first contribution is to propose a novel approach based on the use of complex Lyapunov functions with even rational parametric dependence, which searches for upper bounds on the sought norms via linear matrix inequalities (LMIs). The second contribution is to show that the upper bounds provided are nonconservative by using Lyapunov functions in the chosen class with sufficiently large degree. The third contribution is to provide conditions for establishing the tightness of the upper bounds. The fourth contribution is to show how the numerical complexity of the proposed approach can be significantly reduced by proposing a new necessary and sufficient LMI condition for establishing positive semidefiniteness of even Hermitian matrix polynomials. This result is also exploited to derive an improved necessary and sufficient LMI condition for establishing exponential stability of 2-D mixed continuous-discrete-time systems. Some numerical examples illustrate the proposed approach. It is worth remarking that nonconservative LMI methods for determining the \cal H\infty and \cal H2 norms of 2-D mixed continuous-discrete-time systems have not been proposed yet in the literature. [ABSTRACT FROM PUBLISHER]

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 energy shaping of 1-D linear boundary controlled port-Hamiltonian systems. The energy-Casimir method is first proposed to deal with power preserving systems. It is shown how to use finite dimensional dynamic boundary controllers and closed-loop structural invariants to partially shape the closed-loop energy function and how such controller finally reduces to a state feedback. When dissipative port-Hamiltonian systems are considered, the Casimir functions do not exist anymore (dissipation obstacle) and the immersion (via a dynamic controller)/reduction (through invariants) method cannot be applied. The main contribution of this paper is to show how to use the same ideas and state functions to shape the closed-loop energy function of dissipative systems through direct state feedback i.e. without relying on a dynamic controller and a reduction step. In both cases, the existence of solution and the asymptotic stability (by additional damping injection) of the closed-loop system are proven. The general theory and achievable closed-loop performances are illustrated with the help of a concluding example, the boundary stabilization of a longitudinal beam vibrations. [ABSTRACT FROM AUTHOR]

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 presents reduction theorems for stability, attractivity, and asymptotic stability of compact subsets of the state space of a hybrid dynamical system. Given two closed sets $\Gamma _1 \subset \Gamma _2 \subset \mathbb {R}^n$ , with $\Gamma _1$ compact, the theorems presented in this paper give conditions under which a qualitative property of $\Gamma _1$ that holds relative to $\Gamma _2$ (stability, attractivity, or asymptotic stability) can be guaranteed to also hold relative to the state space of the hybrid system. As a consequence of these results, sufficient conditions are presented for the stability of compact sets in cascade-connected hybrid systems. We also present a result for hybrid systems with outputs that converge to zero along solutions. If such a system enjoys a detectability property with respect to a set $\Gamma _1$ , then $\Gamma _1$ is globally attractive. The theory of this paper is used to develop a hybrid estimator for the period of oscillation of a sinusoidal signal. [ABSTRACT FROM AUTHOR]

This paper presents a systematic method to analyze the stability of systems with single delay in which the coefficient polynomials of the characteristic equation depend on the delay. Such systems often arise in, for example, life science and engineering systems. A method to analyze such systems was presented by Beretta and Kuang in a 2002 paper, but with some very restrictive assumptions. This paper extends their results to the general case with the exception of some degenerate cases. It is found that a much richer behavior is possible when the restrictive assumptions are removed. The interval of interest for the delay is partitioned into subintervals so that the magnitude condition generates a fixed number of frequencies as functions of the delay within each subinterval. The crossing conditions are expressed in a general form, and a simplified derivation for the first-order derivative criterion is obtained. Illustrative examples are also presented in this paper. [ABSTRACT FROM AUTHOR]

This paper deals with the certification problem for robust quadratic stability, robust state convergence, and robust quadratic performance of linear systems that exhibit bounded rates of variation in their parameters. We consider both continuous-time (CT) and discrete-time (DT) parameter-varying systems. In this paper, we provide a uniform method for this certification problem in both cases and we show that, contrary to what was claimed previously, the DT case requires a significantly different treatment compared to the existing CT results. In the established uniform approach, quadratic Lyapunov functions, which are affine in the parameter, are used to certify robust stability, robust convergence rates, and robust performance in terms of linear matrix inequality feasibility tests. To exemplify the procedure, we solve the certification problem for $\mathscr {L}_2$ -gain performance both in the CT and the DT cases. A numerical example is given to show that the proposed approach is less conservative than a method with slack variables. [ABSTRACT FROM AUTHOR]

We establish a new condition for global consensus of continuous-time multiagent systems with undirected switching interaction graphs. The condition is strictly weaker than the persistency of excitation, one recently shown in , to be necessary and sufficient for global exponential consensus. The price paid for the relaxation of the excitation requirement is twofold; on one hand, we establish only global asymptotic consensus without the “exponential” qualifier. On the other hand, we prove that our condition is not necessary. We also prove in this paper that an additional assumption is needed in to extend the consensus result to the case of negatively weighted edges. [ABSTRACT FROM AUTHOR]

This paper studies the quantized feedback stabilization problem for nonlinear systems with external disturbance. A dynamic quantizer with a quantization parameter is implemented in this paper. To extract more information, the quantization parameter is updated according to an updating protocol at the discrete-time instants. Three quantization cases are studied in this paper, i.e., state quantization case, input quantization case, and output quantization case. Based on the updating protocol and Lyapunov approach, sufficient conditions are developed for quantized feedback stabilization of the closed-loop system. [ABSTRACT FROM AUTHOR]

Lyapunov's second theorem is an essential tool for stability analysis of differential equations. The paper provides an analog theorem for incremental stability analysis by lifting the Lyapunov function to the tangent bundle. The Lyapunov function endows the state-space with a Finsler structure. Incremental stability is inferred from infinitesimal contraction of the Finsler metrics through integration along solutions curves. [ABSTRACT FROM AUTHOR]

In this article, we develop a tracking model predictive control (MPC) scheme for nonlinear systems using the linearized dynamics at the current state as a prediction model. Under reasonable assumptions on the linearized dynamics, we prove that the proposed MPC scheme exponentially stabilizes the optimal reachable equilibrium w.r.t. a desired target setpoint. Our theoretical results rely on the fact that, close to the steady-state manifold, the prediction error of the linearization is small, and hence, we can slide along the steady-state manifold toward the optimal reachable equilibrium. The closed-loop stability properties mainly depend on a cost matrix, which allows us to trade off performance, robustness, and the size of the region of attraction. In an application to a nonlinear continuous stirred tank reactor, we show that the scheme, which only requires solving a convex quadratic program online, has comparable performance to a nonlinear MPC scheme while being computationally significantly more efficient. Furthermore, our results provide the basis for controlling nonlinear systems based on data-dependent linear prediction models, which we explore in our companion paper. [ABSTRACT FROM AUTHOR]

In this paper, we consider the l\infty gain characterizations of linear switched systems (LSS) and present various relevant results on their exact computation and optimization. Depending on the role of the switching sequence, we study two broad cases: first, when the switching sequence attempts to maximize, and second, when it attempts to minimize the l\infty gain. The first, named as worst-case throughout the paper, can be related to robustness of the system to uncontrolled switching; the second relates to situations when the switching can be part to the overall decision making. Although, in general, the exact computation of l\infty gains is difficult, we provide specific classes, the input-output switching systems, for which it is shown that linear programming can be used to obtain the worst-case l\infty gain. This is a sufficiently rich class of systems as any stable LSS can be approximated by one. Certain applications to robust control design are provided where we show that a switched compensation independently of the plant has no advantage over a linear time invariant (LTI) compensation, and further, if the plant is strictly causal, even a switched compensation which has a matched switching with the plant does not provide a better performance over an LTI compensation. Also, we present a new necessary and sufficient condition to check the stability of LSS in form of a model matching problem. On the other hand, if one is interested in minimizing the l\infty gain over the switching sequences, we show that, for finite impulse response (FIR) switching systems the minimizing switching sequence can be chosen to be periodic. For input-only or output-only switching an exact, readily computable, characterization of the minimal l\infty gain is provided, and it is shown that the minimizing switching sequence is constant, which, as also shown, is not true for input-output switching. [ABSTRACT FROM AUTHOR]

In this paper, a novel framework to address the problem of parametric estimation for continuous-time linear time-invariant dynamic systems is dealt with. The proposed methodology entails the design of suitable kernels of non-anticipative linear integral operators thus obtaining estimators showing, in the ideal case, “non-asymptotic” (i.e., “finite-time”) convergence. The analysis of the properties of the kernels guaranteeing such a convergence behaviour is addressed and a novel class of admissible kernel functions is introduced. The operators induced by the proposed kernels admit implementable (i.e., finite-dimensional and internally stable) state-space realizations. Extensive numerical results are reported to show the effectiveness of the proposed methodology. Comparisons with some existing continuous-time estimators are addressed as well and insights on the possible bias affecting the estimates are provided. [ABSTRACT FROM PUBLISHER]

Pre-orders and equivalence relations between processes, like simulation and bisimulation, have played a central role in the minimization and abstraction based verification and analysis of discrete-state systems for modal and temporal properties. In this paper, we investigate the pre-orders and equivalence relations on hybrid systems which preserve stability. We first show that stability with respect to reference trajectories is not preserved by either the traditional notion of bisimulation or the more recently proposed stronger notions with additional continuity constraints. We introduce the concept of uniformly continuous simulation and bisimulation—namely, simulation and bisimulation with some additional uniform continuity conditions on the relation—that can be used to reason about stability of trajectories. Finally, we show that uniformly continuous simulations and bisimulations are widely prevalent, by recasting many classical results on proving stability of dynamical and hybrid systems as establishing the existence of a simple, obviously stable system that (bi)-simulates the given system through uniformly continuous (bi)-simulations. We also discuss briefly a new abstraction method for stability analysis which is based on the foundations developed in the paper. [ABSTRACT FROM PUBLISHER]

In this paper, we study the chain stability of vehicles under bilateral control (BCM), and prove that vehicles under bilateral control are chain stable, i.e., all input perturbations to the chain decay exponentially (with the length of the chain). Chain stability analysis tells us how vehicles under bilateral control will act in traffic when mixed with cars driven by human drivers. It shows that self-driving cars using bilateral control can reduce traffic flow instabilities in mixed traffic. Indeed, chains of BCM vehicles become perturbation-consuming dampers when inserted in traffic, since they split chains of human-driven vehicles and prevent perturbations from being transmitted from one chain of car-following cars to the next. Thus, today's traffic can be improved greatly by the insertion of BCM vehicles. The simulation results validate the theoretical analysis. [ABSTRACT FROM AUTHOR]

In this paper, we study mixed traffic flow in which some cars are under car-following control and others are under bilateral control. We also provide the necessary (modular string) stability condition for this type of mixed traffic, which can be viewed as an extension of the condition for pure car-following control-based traffic. This necessary stability condition provides some indication of how the introduction of self-driving cars (under bilateral control) will affect today's traffic. [ABSTRACT FROM AUTHOR]

This paper addresses the event-triggered dynamic output feedback control for switched linear systems with frequent asynchronism. Different from existing work, which limits at most once switching during an interevent interval, we adopt the average dwell time approach without limiting the minimum dwell time of each subsystem, and thus frequent switching is allowed to happen in an interevent interval. Since the difficulty in acquiring the full information of system states, the dynamic output feedback controller is taken into account to stabilize the switched system. By employing a controller-mode-dependent Lyapunov functional, stability criterion is proposed for the resulting closed-loop system, based on which the dynamic output feedback controller together with the mode-dependent event-triggered mechanism is codesigned. Besides, the existence of the lower bound on interevent intervals is attentively discussed, which gets rid of the Zeno behavior. Finally, the effectiveness of the proposed method is illustrated by numerical simulations. [ABSTRACT FROM AUTHOR]

In this paper, two control schemes producing a continuous control signal are presented for a perturbed triple integrator: The continuous twisting algorithm (3-CTA) and the output feedback continuous twisting algorithm (3-OFCTA). The first one is a state feedback controller that ensures global finite-time stability of the origin, despite of Lipschitz, nonvanishing, and matched disturbances. It provides steady-state precision of fourth order of the output w.r.t. sampling step. The second one is an output feedback controller, which uses a third-order robust and exact differentiator as an observer. By requiring only information of the measurable output, the 3-OFCTA preserves all features of robustness, convergence, and precision of the state feedback 3-CTA. Moreover, it is proven that a separation principle applies, so that the gains of the controller and of the observer can be selected independently to assure stability. [ABSTRACT FROM AUTHOR]

This paper considers the problem of designing adaptive feedforward control (AFC) systems for uncertain single-input single-output linear systems perturbed by multisinusoidal disturbances of known frequencies. The proposed approach removes the longstanding assumption that either the sign of the real part or the imaginary part of the transfer function of a stable plant at the frequency of excitation is known for AFC to be applicable, which is referred to in this paper as a strictly positive real (SPR)-like condition. Notable features of the solution are that persistence of excitation is not required, and stability analysis tools based on averaging are avoided; hence, the requirement of an exponentially stable equilibrium for the closed-loop system is circumvented. [ABSTRACT FROM AUTHOR]

In this paper, we propose a state-dependent switching controller for multiple-input multiple-output (MIMO) bilinear systems with constant delays in both the state and the input. The control input is assumed to be restricted to take only a finite number of values. The stability analysis of the closed loop is based on a Lyapunov–Krasovskii functional, and the design is reduced to solve a system of linear matrix inequalities. The controller can be designed by considering (state) delay-dependent or delay-independent conditions. [ABSTRACT FROM AUTHOR]

In this paper, we design a novel observer for a class of semilinear heat one dimmensional (1-D) equations under the delayed and sampled point measurements. The main novelty is that the delay is arbitrary. To handle any arbitrary delay, the observer is constituted of a chain of subobservers. Each subobserver handles a fraction of the considered delay. The resulting estimation error system is shown to be exponentially stable under a sufficient number of subobservers is used. The stability analysis is based on a specific Lyapunov–Krasovskii functional and the stability conditions are expressed in terms of linear matrix inequalities (LMIs). [ABSTRACT FROM AUTHOR]

This paper addresses the problem of local stabilization of nonlinear polynomial control systems subject to time-varying input delay and polytopic parameter uncertainty. A linear matrix inequality approach based on the Lyapunov–Krasovskii theory is proposed for designing a nonlinear polynomial state feedback controller ensuring the robust local uniform asymptotic stability of the system origin along with an estimate of its region of attraction. Two convex optimization procedures are presented to compute a stabilizing controller ensuring either a maximized set of admissible initial states for given upper bounds on the delay and its variation rate or a maximized lower bound on the maximum admissible input delay considering a given set of admissible initial states. Numerical examples demonstrate the potentials of the proposed stabilization approach. [ABSTRACT FROM AUTHOR]

In this paper, we present a method to robustify asymptotically stable nonlinear systems by adding an integral action that rejects unknown additive disturbances. The proposed approach uses a port-Hamiltonian (pH) representation of the open-loop dynamics, which, relying on the asymptotic stability property, is guaranteed to exist. The integral action controller preserves the pH structure, and, by adding a suitable cross term between the plant and the controller states to the closed-loop energy function, it avoids the unnatural coordinate transformation used in the past. The controller is shown to be robust against some common types of modeling uncertainty, including unknown friction dynamics in mechanical systems. [ABSTRACT FROM AUTHOR]

This paper considers the consensus problem of linear multiagent systems with distributed infinite transmission delays. A novel low gain controller is proposed and it is shown that the proposed controller can solve the consensus problem if the open loop agent dynamics have no exponentially unstable eigenvalues and the communication topology is fixed and contains a spanning tree. One of the distinctive advantages of the proposed controller is that it does not require the knowledge of transmission delays. Our proofs are established based on a stability result on infinite delays, which can be seen as an extension of the commonly used frequency domain method. Our results include those results on distributed bounded delays and constant delays as their special cases. Simulation examples are provided to illustrate the effectiveness of the proposed controller. [ABSTRACT FROM AUTHOR]

Reinforcement learning (RL) is a powerful tool to perform data-driven optimal control without relying on a model of the system. However, RL struggles to provide hard guarantees on the behavior of the resulting control scheme. In contrast, nonlinear model predictive control (NMPC) and economic NMPC (ENMPC) are standard tools for the closed-loop optimal control of complex systems with constraints and limitations, and benefit from a rich theory to assess their closed-loop behavior. Unfortunately, the performance of (E)NMPC hinges on the quality of the model underlying the control scheme. In this paper, we show that an (E)NMPC scheme can be tuned to deliver the optimal policy of the real system even when using a wrong model. This result also holds for real systems having stochastic dynamics. This entails that ENMPC can be used as a new type of function approximator within RL. Furthermore, we investigate our results in the context of ENMPC and formally connect them to the concept of dissipativity, which is central for the ENMPC stability. Finally, we detail how these results can be used to deploy classic RL tools for tuning (E)NMPC schemes. We apply these tools on both, a classical linear MPC setting and a standard nonlinear example, from the ENMPC literature. [ABSTRACT FROM AUTHOR]

This paper is concerned with the robust event-triggered model predictive control (MPC) of discrete-time constrained linear systems subject to bounded additive disturbances. We make use of the interpolation technique to construct a feedback policy and tighten the original system constraint accordingly to fulfill robust constraint satisfaction. A dynamic event trigger that allows the controller to solve the optimization problem only at triggering time instants is developed, where the triggering threshold is related to the interpolating coefficient of the feedback policy and determined via optimization. We show that the proposed algorithm is recursively feasible and the closed-loop system is input-to-state stable in the attraction region. Finally, a numerical example is provided to verify the theoretical results. [ABSTRACT FROM AUTHOR]

This paper develops a new partial-state feedback model reference adaptive control (MRAC) scheme, which has full capability to deal with plant uncertainties for output tracking and desired flexibility to combine the advantages of full-state feedback MRAC and output feedback MRAC. For partial-state feedback MRAC, plant-model matching is achievable as with full-state feedback control, while the controller structure enjoys less complexity as compared with an output feedback MRAC design. Adaptive partial-state feedback control designs are developed for relative-degree-one plants and for general plants. Both adaptive control designs ensure closed-loop system stability and asymptotic output tracking. New results are presented for plant-model matching, error model, adaptive law, and stability analysis. New features of partial-state feedback MRAC are addressed, including its design flexibility. Simulation studies are conducted whose results verify the effectiveness of partial-state feedback MRAC. [ABSTRACT FROM AUTHOR]

This paper studies a distributed continuous-time bi-virus model in which two competing viruses spread over a network consisting of multiple groups of individuals. Limiting behaviors of the network are characterized by analyzing the equilibria of the system and their stability. Specifically, when the two viruses spread over possibly different directed infection graphs, the system may have the following: first, a unique equilibrium, the healthy state, which is globally stable, implying that both viruses will eventually be eradicated, second, two equilibria including the healthy state and a dominant virus state, which is almost globally stable, implying that one virus will pervade the entire network causing a single-virus epidemic while the other virus will be eradicated, or third, at least three equilibria including the healthy state and two dominant virus states, depending on certain conditions on the healing and infection rates. When the two viruses spread over the same directed infection graph, the system may have zero or infinitely many coexisting epidemic equilibria, which represents the pervasion of the two viruses. Sensitivity properties of some nontrivial equilibria are investigated in the context of a decentralized control technique, and an impossibility result is given for a certain type of distributed feedback controller. [ABSTRACT FROM AUTHOR]

This paper investigates the stabilization problem for uncertain nonlinear systems with quantized states. All states in the system are quantized by a static bounded quantizer, including uniform quantizer, hysteresis-uniform quantizer, and logarithmic-uniform quantizer as examples. An adaptive backstepping-based control algorithm, which can handle discontinuity, resulted from the state quantization and a new approach to stability analysis are developed by constructing a new compensation scheme for the effects of the state quantization. Besides showing the global ultimate boundedness of the system, the stabilization error performance is also established and can be improved by appropriately adjusting design parameters. Simulation results illustrate the effectiveness of our proposed scheme. [ABSTRACT FROM AUTHOR]

The aim of this paper is to study the second-order practical consensus of homogeneous sampled-data multiagent systems (MASs). To do this, a new nonlinear emulation strategy based on homogeneity is developed. It is then applied to MASs under synchronously variable sampling. Finally, a comparison with the classical linear strategy is provided in the case of MASs under synchronously periodic sampling. [ABSTRACT FROM AUTHOR]

This paper considers a class of reinforcement-based learning (namely, perturbed learning automata) and provides a stochastic-stability analysis in repeatedly played, positive-utility, finite strategic-form games. Prior work in this class of learning dynamics primarily analyzes asymptotic convergence through stochastic approximations, where convergence can be associated with the limit points of an ordinary-differential equation (ODE). However, analyzing global convergence through an ODE-approximation requires the existence of a Lyapunov or a potential function, which naturally restricts the analysis to a fine class of games. To overcome these limitations, this paper introduces an alternative framework for analyzing asymptotic convergence that is based upon an explicit characterization of the invariant probability measure of the induced Markov chain. We further provide a methodology for computing the invariant probability measure in positive-utility games, together with an illustration in the context of coordination games. [ABSTRACT FROM AUTHOR]

In this paper, the main issues of model-based control methods are first reviewed, followed by the motivations and the state of the art of the model-free adaptive control (MFAC). MFAC is a novel data-driven control method for a class of unknown nonaffine nonlinear discrete-time systems since neither explicit physical model nor Lyapunov stability theory or key technical lemma is used in the controller design and theoretical analysis except only for the input/output (I/O) measurement data. The basis of MFAC is the dynamic linearization data modeling method at each operating point of the closed-loop system. The established dynamic linearization data model is a virtual equivalent data relationship in the I/O sense to the original nonlinear plant by means of a novel concept called pseudo-partial derivative (PPD) or pseudo-gradient (PG) vector. Based on this virtual equivalent dynamic linearization data model and the time-varying PPD or PG estimation algorithm designed merely using the I/O measurements of a controlled plant, the MFAC system is constructed. The main contribution of this paper is that the theoretical analysis of the bounded-input bounded-output stability, the monotonic convergence of the tracking error dynamics, and the internal stability of the full form dynamic linearization based MFAC scheme are rigorously presented by the contraction mapping principle; the well known PID control and the traditional adaptive control for linear time-invariant systems are explicitly shown as the special cases of this MFAC. The simulation results verify the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

Bilateral control can suppress traffic flow instabilities. The simplest form of bilateral control uses information about the relative positions and relative velocities of leading and trailing vehicles. In this paper, we provide a multinode version of bilateral control, in which information about the state of more than just the immediately leading and trailing cars is used. In this mode of control, the question arises: “How much weight should information about vehicles at different positions be given?” Two different methods—a Taylor series approach and a least-squares approach—are explored. We show that the least-squares approach generates sets of coefficients that can damp out low-frequency components of perturbations faster. This means that traffic under multinode bilateral control will approach an equilibrium state more rapidly than under the traditional version of bilateral control. Simulation results confirm our analysis. [ABSTRACT FROM AUTHOR]

This paper is concerned with the problem of discrete-time two-dimensional (2-D) sliding mode control (SMC) for Fornasini–Marchesini (FM) systems subject to exogenous nonlinear disturbances. With the introduction of the time instant and global state in the 2-D case, the discrete-time sliding surface function for 2-D systems is constructed. Then, based on the corresponding sliding mode dynamics, the solvability condition for the desired sliding surface function is derived. Subsequently, a sliding mode controller is designed to guarantee that the state trajectories can enter into a neighborhood of the specified sliding surface. Meanwhile, the stability of the 2-D sliding mode dynamics is also ensured. Finally, a simulation example is provided to illustrate the feasibility and the effectiveness of the presented new 2-D SMC design method. Different from existing results, the proposal focuses on the features of multi-dimension and the dynamics of 2-D systems, which is expected to develop a completely different SMC design approach for discrete-time 2-D systems. [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 address the design and analysis of multi-variable extremum seeking for static maps subject to arbitrarily long time delays. Both Gradient and Newton-based methods are considered. Multi-input systems with different time delays in each individual input channel as well as output delays are dealt with. The phase compensation of the dither signals and the inclusion of predictor feedback with a perturbation-based (averaging-based) estimate of the Hessian allow to obtain local exponential convergence results to a small neighborhood of the optimal point, even in the presence of delays. The stability analysis is carried out using backstepping transformation and averaging in infinite dimensions, capturing the infinite-dimensional state due the time delay. In particular, a new backstepping-like transformation is introduced to design the predictor for the Gradient-based extremum seeking scheme with multiple and distinct input delays. The proposed Newton-based extremum seeking approach removes the dependence of the convergence rate on the unknown Hessian of the nonlinear map to be optimized, being user-assignable as in the literature free of delays. A source seeking example illustrates the performance of the proposed delay-compensated extremum seeking schemes. [ABSTRACT FROM PUBLISHER]

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]