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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 article, we first show that the main results claimed in the paper by Bikas and Rovithakis (2021) involve some errors as the selection conditions for the design parameters are not sufficient to ensure the boundedness of all the closed-loop signals, then we provide the corresponding corrections under the same controller, so that the underlying quantized control problem can be tackled. [ABSTRACT FROM AUTHOR]

This article studies global robust output regulation of second-order nonlinear systems with input disturbances that encompass the fully-actuated Euler–Lagrange systems. We assume the availability of relative output (w.r.t. a family of reference signals) and output derivative measurements. Based on a specific separation principle and self-learning mechanism, we develop an internal model-based controller that does not require a priori knowledge of reference and disturbance signals and it only assumes that the kernels of these signals are a family of exosystems with unknown parameters (e.g., amplitudes, frequencies, or time periods). The proposed control framework has a self-learning mechanism that extricates itself from requiring absolute position measurement nor precise knowledge of the feedforward kernel signals. By requiring the high-level task/trajectory planner to use the same class of kernels in constraining the trajectories, the proposed low-level controller is able to learn the desired trajectories, to suppress the disturbance signals, and to adapt itself to the uncertain plant parameters. The framework enables a plug-and-play control mechanism in both levels of control. [ABSTRACT FROM AUTHOR]

This article aims to solve the problem of decentralized event-based finite-time control for a class of high-order interconnected nonlinear systems with an asymmetric output constraint. In order to achieve finite-time stability and reduce the update frequency of the controller, a novel controller and its event-trigger mechanism is proposed by adding a power integral technique and utilizing sign function. To fulfill the requirement of asymmetric output constraints, an asymmetric barrier Lyapunov function (BLF) is constructed, which is different from tan-type and log-type BLFs. Based on the contradictory idea and finite-time stability theory, it is proved that there is no Zeno phenomenon under this event-trigger mechanism and all state variables of the closed-loop system attenuate to the origin in the finite-time while the output signals never violate the constraint. Furthermore, the result in this article is expanded to fixed-time control. Finally, a simulation example is given to demonstrate the effectiveness of the presented strategy. [ABSTRACT FROM AUTHOR]

This article investigates the problem of how to control nonlinear systems with delays in the state by memoryless linear feedback. The notions of semiglobal asymptotic stabilization and sublevel sets are introduced in the context of time-delay systems. With the aid of Razumikhin theorem, we develop a semiglobal design method for the construction of Lyapunov functions, associated sublevel sets, and delay-free linear state feedback laws, step-by-step, achieving semiglobal asymptotic stabilization for time-delay nonlinear systems in a lower triangular form. In contrast to the global stabilization of nonlinear systems with delays in the state, which is usually achieved by dynamic state feedback (Lin and Zhang, 2020), the significance of this work is to point out that a tradeoff of the control objectives, e.g., semiglobal versus global stabilization, makes it possible to control a class of time-delay nonlinear systems by static linear feedback. Extensions to nonlinear systems with globally asymptotically locally expoentially stable (GALES)-like inverse dynamics are also included in this article. [ABSTRACT FROM AUTHOR]

For a family of genuinely nonlinear systems with delays in the input and state, global strong stabilization (GSS) in the sense of Kurzweil is shown to be possible by memoryless state and/or output feedback under two conditions: 1) The input delay is within an appropriate range although the state delays can be sufficiently large; 2) the time-delay bounding system is homogeneous of degree zero and has a lower triangular structure. The proof is based on the Lyapunov–Krasovskii functional theorem combined with the homogeneous domination philosophy. Using the emulation approach, we design memoryless homogeneous state and output feedback controllers, respectively, achieving GSS of the time-delay closed-loop systems with severe nonlinearity. Extensions to a wider class of time-delay nonlinear systems in the Hessenberg form are also given. Examples and counter-examples presented in this article illustrate not only the necessity of the homogeneous growth conditions but also the significance of the memoryless non-Lipschitz continuous feedback control strategies. [ABSTRACT FROM AUTHOR]

In this article, we aim at developing computationally tractable methods for nonlinear model/controller reduction. Recently, model reduction by generalized differential (GD) balancing has been proposed for nonlinear systems with constant input-vector fields and linear output functions. First, we study incremental properties in the GD balancing framework. Next, based on these analyses, we provide GD linear quadratic Gaussian (LQG) balancing and GD $H_\infty$ -balancing as controller reduction methods for nonlinear systems by focusing on linear feedback and observer gains. Especially for GD $H_\infty$ -balancing, we clarify when the closed-loop system consisting of the full-order system and a reduced-order controller is exponentially stable. All provided methods for controller reduction can be relaxed to linear matrix inequalities (LMIs). [ABSTRACT FROM AUTHOR]

In this article we study integral-input-to-state stability (iISS) of nonlinear switched systems with jumps. We demonstrate by examples that iISS is not always preserved under slow enough dwell time switching, and then we present sufficient conditions for iISS to be preserved under slow switching. These conditions involve, besides a sufficiently large dwell time, some additional properties of comparison functions characterizing iISS of the individual modes. When the sufficient conditions that guarantee iISS are only partially satisfied, we are then able to conclude weaker variants of iISS, also introduced in this work. As an illustration, we show that switched systems with bilinear zero-input-stable modes are always iISS under sufficiently large dwell time. [ABSTRACT FROM AUTHOR]

Checking uniform attractivity of a time-varying dynamic system without a strict Lyapunov function is challenging as it requires the characterization of the limiting behavior of a set of trajectories. In the context of hybrid nonlinear time-varying systems, characterizing such limiting or convergent behaviors is even harder due to the complexity stemming from both continuous-time variations as well as discrete-time jumps. In this article, an extension of the standard hybrid time domain is introduced to define limiting behaviors, using set convergence, when time approaches either positive infinity or negative infinity. In particular, it is shown how to characterize limiting behaviors under the condition that an output signal approaches zero. Such limiting behaviors and their associated limiting systems can be used to verify uniform global attractivity. Particularly, a generalization of the classic Krasovskii–LaSalle theorem is obtained for hybrid time-varying systems. Two examples are used to demonstrate the effectiveness of the results. [ABSTRACT FROM AUTHOR]

We propose a state estimation methodology using a network of distributed observers. We consider a scenario in which the local measurement at each node may not guarantee the system's observability. In contrast, the ensemble of all the measurements does ensure that the observability property holds. As a result, we design a network of observers such that the estimated state vector computed by each observer converges to the system's state vector by using the local measurement and the communicated estimates of a subset of observers in its neighborhood. The proposed estimation scheme exploits sensor redundancy to provide robustness against faults in the sensors. Under suitable conditions on the redundant sensors, we show that it is possible to mitigate the effects of a class of sensor faults on the state estimation. Simulation trials demonstrate the effectiveness of the proposed distributed estimation scheme. [ABSTRACT FROM AUTHOR]

In this article, we study positive invariance and attractivity properties for nonlinear control systems, which are monotone with respect to proper cones. Monotonicity simplifies such analysis for specific sets defined by the proper cones. Instead of Lyapunov functions, a pair of so-called paths in the state space and input space play important roles. As applications, our results are utilized for analysis of asymptotic stability and also input-to-state stability on proper cones. The results are illustrated by means of examples. [ABSTRACT FROM AUTHOR]

We consider the problem of identifying a dissipative linear model of an unknown nonlinear system that is known to be dissipative, from time-domain input–output data. We first learn an approximate linear model of the nonlinear system using standard system identification techniques and then perturb the system matrices of the linear model to enforce dissipativity, while closely approximating the dynamical behavior of the nonlinear system. Further, we provide an analytical relationship between the size of the perturbation and the radius in which the dissipativity of the linear model guarantees local dissipativity of the unknown nonlinear system. We demonstrate the application of this identification technique through two examples. [ABSTRACT FROM AUTHOR]

In this article, we present a novel data-driven model predictive control (MPC) approach to control unknown nonlinear systems using only measured input–output data with closed-loop stability guarantees. Our scheme relies on the data-driven system parameterization provided by the fundamental lemma of Willems et al. We use new input–output measurements online to update the data, exploiting local linear approximations of the underlying system. We prove that our MPC scheme, which only requires solving strictly convex quadratic programs online, ensures that the closed loop (practically) converges to the (unknown) optimal reachable equilibrium that tracks a desired output reference while satisfying polytopic input constraints. As intermediate results of independent interest, we extend the fundamental lemma to affine systems and we derive novel robustness bounds w.r.t. noisy data for the open-loop optimal control problem, which are directly transferable to other data-driven MPC schemes in the literature. The applicability of our approach is illustrated with a numerical application to a continuous stirred tank reactor. [ABSTRACT FROM AUTHOR]

In this article, we propose a new approach to design globally convergent reduced-order observers for nonlinear control systems via contraction analysis and convex optimization. Despite the fact that contraction is a concept naturally suitable for state estimation, the existing solutions are either local or relatively conservative when applying to physical systems. To address this, we show that this problem can be translated into an offline search for a coordinate transformation after which the dynamics is (transversely) contracting. The obtained sufficient condition consists of some easily verifiable differential inequalities, which, on one hand, identify a very general class of “detectable” nonlinear systems, and on the other hand, can be expressed as computationally efficient convex optimization, making the design procedure more systematic. Connections with some well-established approaches and concepts are also clarified in this article. Finally, we illustrate the proposed method with several numerical and physical examples, including polynomial, mechanical, electromechanical, and biochemical systems. [ABSTRACT FROM AUTHOR]

This article develops data-driven methods to identify eigenfunctions of the Koopman operator associated with a dynamical system and subspaces that are invariant under the operator. We build on Extended Dynamic Mode Decomposition (EDMD), a data-driven method that finds a finite-dimensional approximation of the Koopman operator on the span of a predefined dictionary of functions. We propose a necessary and sufficient condition to identify Koopman eigenfunctions based on the application of EDMD forward and backward in time. Moreover, we propose the Symmetric Subspace Decomposition (SSD) algorithm, an iterative method that provably identifies the maximal Koopman-invariant subspace and the Koopman eigenfunctions in the span of the dictionary. We also introduce the Streaming SSD algorithm, an online extension of SSD that only requires a small fixed memory and incorporates new data as is received. Finally, we propose an extension of SSD that approximates Koopman eigenfunctions and invariant subspaces when the dictionary does not contain sufficient informative eigenfunctions. [ABSTRACT FROM AUTHOR]

In this article, we investigate the distributed state estimation problem for a nonlinear dynamical system. Relying upon the assumption of the existence of a block-triangular “uniform observability” canonical form, local high-gain observers are used to stabilize the estimation error for the observable portion of the state, and exchange of information between neighbors is used to achieve consensus in the estimation of the state of the unobservable part. This article addresses, first, the case of an autonomous system and, then, the case of a controlled dynamical system under the assumption that the exogenous input is accessible by each node in the network. Based on the designed state estimator, each distributed sensor node can achieve asymptotic estimation of the full state, with an arbitrarily fixed decay rate of the observation error. [ABSTRACT FROM AUTHOR]

In this article, we provide several characterizations of integral input-to-state stability (iISS) of time-delay systems. These characterizations differ in the way the considered Lyapunov–Krasovskii functionals (LKFs) dissipate along the solutions of the system. This dissipation can involve the LKF itself, as in existing iISS characterizations, but can alternatively involve the instantaneous value of the solution’s norm (pointwise dissipation), the supremum norm of the state history (historywise dissipation), or a mix of the two (${\mathcal K}{\mathcal L}$ dissipation). We show that all of them guarantee iISS. By relying on a recent converse result by Y. Lin and Y. Wang, we show that most of them are also necessary for iISS. These relaxed dissipation rates simplify the iISS analysis of time-delay systems and contribute to uniforming iISS theory with that of input-free systems. Proofs rely on several results for time-delay systems that may be of interest on their own, including a novel characterization of global asymptotic stability and the fact that iISS is equivalent to global asymptotic stability of the input-free system plus a uniform bounded energy-bounded state property. [ABSTRACT FROM AUTHOR]

Quasilinear control (QLC) theory provides a set of methods intended for the analysis and design of stochastic feedback systems with static nonlinearities. QLC leverages the method of stochastic linearization (SL), which linearizes the nonlinear functions by utilizing the statistical properties of the inputs to the nonlinearities. In the traditional QLC literature, SL has been thoroughly applied to systems having nonlinearities with only a single input. This article investigates the case of SL applied to feedback systems with nonlinear functions of multiple inputs. More specifically, the formulas for the SL gains and bias are derived for multivariate functions and then employed to explore SL of a trivariate saturation nonlinearity and study the SL of control systems with feedback loops. The developed theory is then applied to the analysis and optimal controller design of stochastic systems having randomly varying parameters or state-multiplicative noise. Finally, a recipe for investigating the robustness of SL is provided. [ABSTRACT FROM AUTHOR]

We propose a framework for designing observers for noisy nonlinear systems with global convergence properties and performing robustness and noise sensitivity. This framework comes out from the combination of a state norm estimator with a chain of filters, adaptively tuned by the state norm estimator. The state estimate is sequentially processed through the chain of filters. Each filter contributes to improving, by a certain amount, the estimation error performances of the previous filter in terms of noise sensitivity, and this amount is quantitatively evaluated using a comparison criterion, which considers the ratio of the asymptotic error norm bounds of two consecutive filters in the chain. A recursive algorithm is given for implementing the chain of filters and guaranteeing a sequential error performance optimization process. Simulations show the effectiveness of these chains of filters. [ABSTRACT FROM AUTHOR]

Complex networked systems can be modeled and represented as graphs, with nodes representing the agents and the links describing the dynamic coupling between them. The fundamental objective of network identification for dynamic systems is to identify causal influence pathways. However, dynamically related data streams that originate from different sources are prone to corruption caused by asynchronous time-stamps, packet drops, and noise. In this article, we show that identifying causal structure using corrupt measurements results in the inference of spurious links. A necessary and sufficient condition that delineates the effects of corruption on a set of nodes is obtained. Our theory applies to nonlinear systems, and systems with feedback loops. Our results are obtained by the analysis of conditional directed information (DI) in dynamic Bayesian networks. We provide consistency results for the conditional DI estimator that we use by showing almost-sure convergence. [ABSTRACT FROM AUTHOR]

This article is devoted to the adaptive asymptotic tracking for a class of uncertain nonlinear systems. The presence of unknown time-varying parameters and uncertain disturbances makes the systems in question essentially different from those in the related works. By skillfully combining adaptive technique and command filter-based backstepping, a novel command filter adaptive tracking controller is successfully designed to achieve asymptotic tracking. The typical feature of the proposed controller lies in the introduction of a smooth function with positive integrable time-varying function, which makes the controller powerful enough to compensate the unknown time-varying parameters and uncertain disturbances. Remarkably, a novel Lyapunov function by incorporating the lower bounds of control gains is used to prove the stability of the closed-loop system. Compared with some existing command filter-based backstepping, the conditions on the virtual control coefficients and disturbances are relaxed. Finally, the effectiveness of the proposed method is shown by a simulation example. [ABSTRACT FROM AUTHOR]

In this article, we propose a dual set membership filter for nonlinear dynamic systems with additive unknown but bounded noises, and it has three distinct advantages. First, the nonlinear system is translated into the linear system by leveraging a semi-infinite programming, rather than linearizing the nonlinear function. The semi-infinite programming is to find an ellipsoid bounding the nonlinear transformation of an ellipsoid, which aims to compute a tight ellipsoid to cover the state. Second, the duality result of the semi-infinite programming is derived by rigorous analysis; then, a first-order Frank–Wolfe method is developed to efficiently solve it with a lower computation complexity. Third, the proposed filter enjoys stability for some special nonlinear dynamic systems and succeeds the advantages of the classic linear set membership filter. Finally, two illustrative examples in the simulations reveal the effectiveness of the dual set membership filter. [ABSTRACT FROM AUTHOR]

Originating in the artificial intelligence literature, optimistic planning (OP) is an algorithm that generates near-optimal control inputs for generic nonlinear discrete-time systems whose input set is finite. This technique is, therefore, relevant for the near-optimal control of nonlinear switched systems for which the switching signal is the control, and no continuous input is present. However, OP exhibits several limitations, which prevent its desired application in a standard control engineering context, as it requires, for instance, that the stage cost takes values in $[0, 1]$ , an unnatural prerequisite, and that the cost function is discounted. In this article, we modify OP to overcome these limitations, and we call the new algorithm ${\rm OP}_{\text{min}}$. We then analyze ${\rm OP}_{\text{min}}$ under general stabilizability and detectability assumptions on the system and the stage cost. New near-optimality and performance guarantees for ${\rm OP}_{\text{min}}$ are derived, which have major advantages compared to those originally given for OP. We also prove that a system whose inputs are generated by ${\rm OP}_{\text{min}}$ in a receding-horizon fashion exhibits stability properties. As a result, ${\rm OP}_{\text{min}}$ provides a new tool for the near-optimal, stable control of nonlinear switched discrete-time systems for generic cost functions. [ABSTRACT FROM AUTHOR]

This article considers the design and analysis of a distributed sensor fault accommodation scheme for a class of nonlinear systems, modeled as interconnected subsystems. Each subsystem is subject to possible local sensor faults or may be impacted by a sensor fault in a neighboring subsystem due to the exchange of information between neighboring controllers. The proposed adaptive approximation-based distributed fault accommodation scheme is triggered in the event that a sensor fault is detected. The stability of the closed-loop system in the presence of sensor faults is rigorously analyzed both for the period prior to the detection of the fault, as well as after the detection of the fault when the fault accommodation scheme is activated. The effectiveness of the proposed scheme is illustrated by a simulation example. [ABSTRACT FROM AUTHOR]

We address the problem of synthesizing provably correct controllers for linear systems with reach-avoid specifications. Discrete abstraction-based controller synthesis techniques have been developed for linear and nonlinear systems with various types of specifications. However, these methods typically suffer from the state space explosion problem. Our solution decomposes the overall synthesis problem into two smaller, and more tractable problems: one synthesis problem for an open-loop controller, which can produce a reference trajectory, and a second for synthesizing a tracking controller, which can enforce the other trajectories to follow the reference trajectory. As a key building-block result, we show that, once a tracking controller is fixed, the reachable states from an initial neighborhood, subject to any disturbance, can be overapproximated by a sequence of ellipsoids, with shapes that are independent of the open-loop controller. Hence, the open-loop controller can be synthesized independently to meet the reach-avoid specification for an initial neighborhood. Moreover, we are able to reduce the problem of synthesizing open-loop controllers to satisfiability problems over quantifier-free linear real arithmetic. The number of linear constraints in the satisfiability problem is linear to the number of hyperplanes as the surfaces of the polytopic obstacles and goal sets. The overall synthesis algorithm, computes a tracking controller, and then iteratively covers the entire initial set to find open-loop controllers for initial neighborhoods. The algorithm is sound and, for a class of robust systems, is also complete. We implement this synthesis algorithm in a tool RealSyn ver 2.0 and use it on several benchmarks with up to 20 dimensions. Experiment results are very promising: RealSyn ver 2.0 can find controllers for most of the benchmarks in seconds. [ABSTRACT FROM AUTHOR]

We present a predictive feedback control method for a class of quasilinear hyperbolic systems with one boundary control input. Assuming exact model knowledge, convergence to the origin or tracking at the uncontrolled boundary is achieved in finite time. A robustness certificate is provided, showing that at least under more restrictive assumptions on the system coefficients, the control method has inherent robustness properties with respect to small errors in the model, measurements, and control input. Rigorous, although conservative conditions on the time derivative of the initial condition and on the design parameter controlling the convergence speed are given to ensure global existence of the solution for initial conditions with arbitrary infinity-norm. [ABSTRACT FROM AUTHOR]

This article is concerned with robust stability analysis of feedback interconnections of nonlinear systems using integral quadratic constraints (IQCs). Its main purpose involves reconciling hard (a.k.a. unconditional) IQC and soft (a.k.a. conditional) IQC-based analysis. In particular, it is shown that the hard IQC stability result can be recovered from the soft IQC theory. The hard IQC approach is closely related to the dissipativity theory, whereas the soft IQC approach makes use of homotopies that are continuous in the gap distance measure. [ABSTRACT FROM AUTHOR]

This article investigates input-to-state stability (ISS) of nonlinear systems via event-triggered impulsive control method. A novel impulsive event-triggered mechanism (IETM) which can exclude the Zeno behavior for nonlinear impulsive systems is designed. Some sufficient conditions which establish the relationship between impulse strength and IETM for ISS property are proposed. It is shown that under the designed IETM, a flexible impulsive control strategy can be provided. Since impulses only occur when the event which is related to the states of the system is triggered, the burden of the transmission of information can be reduced dramatically. Examples are presented to show the effectiveness of our proposed results. [ABSTRACT FROM AUTHOR]

We solve the prescribed-time mean-square stabilization and inverse optimality control problems for stochastic strict-feedback nonlinear systems by developing a new nonscaling backstepping design scheme. A key novel design ingredient is that the time-varying function is not used to scale the coordinate transformations and is only suitably introduced into the virtual controllers. The advantage of this approach is that a simpler controller results and the control effort is reduced. By using this method, we design a new controller to guarantee that the equilibrium at the origin of the closed-loop system is prescribed-time mean-square stable. Then, we redesign the controller and solve the prescribed-time inverse optimal mean-square stabilization problem, with an infinite gain margin. Specifically, the designed controller is not only optimal with respect to a meaningful cost functional but also globally stabilizes the closed-loop system in the prescribed-time. Finally, two simulation examples are given to illustrate the stochastic nonlinear prescribed-time control design. [ABSTRACT FROM AUTHOR]

For a multiple-input–multiple-output (MIMO) nonlinear feedback system, the robustness against uncertain time-variation (slow or infrequently large) in the feedback loop is investigated in an input–output framework. A couple of sufficient conditions in terms of bounds on average rates of time-variation for the system to be stable are derived. The conditions provide a useful tool for designing adaptive controllers for systems against uncertain large time-variation. [ABSTRACT FROM AUTHOR]

Given a plant whose trajectories of interest remain in a known compact set and an associated observer, we propose a general framework to modify this observer so that its state remains in a given convex set for all times, without altering the observer guaranteed performances in terms of convergence and robustness to external disturbances. The methodology can be applied to any time-varying continuous-time, discrete-time, and hybrid system/observer, for which a quadratic Lyapunov function is used for the analysis. The proposed approach is relevant, for instance, to remove the peaking phenomenon, to attenuate the effect of impulsive outliers in the measurement, to avoid aberrant estimates during transients, or to guarantee a given range for variables in embedded systems. [ABSTRACT FROM AUTHOR]

This article studies the event-triggered control problem of general nonlinear systems with time delay. A novel event-triggering scheme is presented with two tunable design parameters, based on a Lyapunov functional result for the input-to-state stability of time-delay systems. The proposed event-triggered control algorithm guarantees the resulting closed-loop systems to be globally asymptotically stable, uniformly bounded, and/or globally attractive for different choices of these parameters. Sufficient conditions on the parameters are derived to exclude Zeno behavior. Two illustrative examples are studied to demonstrate our theoretical results. [ABSTRACT FROM AUTHOR]

Principles of feedback control have been shown to naturally arise in biological systems and have been applied with success to build synthetic circuits. Here, we present an implementation of a proportional–integral–derivative (PID) controller as a chemical reaction network with mass-action kinetics. This makes the controller synthesizable in vitro using DNA strand displacement technology, owing to its demonstrated capability of realizing arbitrary reaction-network designs as interacting DNA molecules. Previous related work has studied biological PID architectures using linearizations of nonlinear dynamics arising in both the controller components and in the plant. In this article, we present a proof of correctness of our nonlinear design in closed loop using arguments from singular perturbation theory. As an application to show the effectiveness of our controller, we provide numerical simulations on a genetic model to perform PID feedback control of protein expression. [ABSTRACT FROM AUTHOR]

This article studies the distributed optimal output agreement problem for multiagent systems described by uncertain nonlinear models. By using the partial information of an objective function, the design aims to steer the outputs of the agents to an agreement on the optimal solution to the objective function. To solve this problem, this article introduces distributed coordinators to calculate the desired outputs, and designs reference-tracking controllers for the agents to follow the desired outputs. To deal with the nonlinear uncertain dynamics, the closed-loop multiagent system is considered as a dynamical network, and Sontag's input-to-state stability is employed to characterize the interconnections. It is shown that output agreement in multiagent nonlinear systems is achievable by means of distributed optimal controllers via a small-gain approach. The proposed design features a three-layer architecture, and the reference-tracking controllers can be implemented as successive nonlinear proportional-integral loops. A numerical example is employed to show the effectiveness of the design. [ABSTRACT FROM AUTHOR]

We study the convergence properties of social Hegselmann–Krause (HK) dynamics, a variant of the HK model of opinion dynamics where a physical connectivity graph that accounts for the extrinsic factors that could prevent interaction between certain pairs of agents is incorporated. As opposed to the original HK dynamics (which terminates in finite time), we show that for any underlying connected and incomplete graph, under a certain mild assumption, the expected termination time of social HK dynamics is infinity. We then investigate the rate of convergence to the steady state, and provide bounds on the maximum $\epsilon$ -convergence time in terms of the properties of the physical connectivity graph. We extend this discussion and observe that for almost all $n$ , there exists an $n$ -vertex physical connectivity graph on which social HK dynamics may not even $\epsilon$ -converge to the steady state within a bounded time frame. We then provide nearly tight necessary and sufficient conditions for arbitrarily slow merging (a phenomenon that is essential for arbitrarily slow $\epsilon$ -convergence to the steady state). Using the necessary conditions, we show that complete $r$ -partite graphs have bounded $\epsilon$ -convergence times. [ABSTRACT FROM AUTHOR]

In this article, we study the problem of model reduction by moment matching for stochastic systems. We characterize the mathematical object that generalizes the notion of moment to stochastic differential equations, and find a class of models that achieve moment matching. However, differently from the deterministic case, these reduced-order models cannot be considered “simpler” because of the high computational cost paid to determine the moment. To overcome this difficulty, we relax the moment matching problem in two different ways and present two classes of reduced-order models that approximately matching the stochastic moment, are computationally tractable. [ABSTRACT FROM AUTHOR]

This article aims at presenting novel square-root unscented Kalman filters (UKFs) for treating various continuous-discrete nonlinear stochastic systems, including target tracking scenarios. These new methods are grounded in the commonly used singular value decomposition (SVD), that is, they propagate not the covariance matrix itself but its SVD factors instead. The SVD based on orthogonal transforms is applicable to any UKF with only nonnegative weights, whereas the remaining ones, which can enjoy negative weights as well, are treated by means of the hyperbolic SVD based on $J$ -orthogonal transforms. The filters constructed are presented in a concise algorithmic form, which is convenient for practical utilization. Their two particular versions grounded in the classical and cubature UKF parameterizations and derived with use of the It $\hat{\rm o}$ -Taylor discretization are examined in severe conditions of tackling a seven-dimensional radar tracking problem, where an aircraft executes a coordinated turn, in the presence of ill-conditioned measurements. [ABSTRACT FROM AUTHOR]

This article studies the problem of when a globally asymptotically stabilizable nonlinear system by smooth feedback is tolerable with respect to input delay. We illustrate, by means of theoretic and practical examples, some fundamental limitations including: 1) A globally exponentially stabilizable (GES) nonlinear system may not guarantee global asymptotic stabilizability (GAS) of the nonlinear system even with an arbitrarily small input delay; 2) GAS cannot even ensure semiglobal asymptotic stabilizability of the nonlinear system with a small input delay. To overcome these obstacles, we introduce the notion of semiglobal input delay tolerance (SGIDT) and present a semiglobal control framework for the asymptotic analysis/synthesis of input delay tolerance of multi-input–multi-output (MIMO) nonlinear systems under smooth feedback. With the aid of Razumikhin theorem and the converse Lyapunov theorem on global asymptotic local exponential stability (GALES), it is proved that in the case of state feedback, GALES does ensure the SGIDT of a MIMO nonlinear system. In the case of output feedback, it is further proved that GALES and uniform observability imply the SGIDT of the nonlinear system. [ABSTRACT FROM AUTHOR]

We introduce a novel method of model reduction for nonlinear systems by extending the Loewner framework developed for linear time-invariant systems. This objective is achieved by defining Loewner functions obtained by utilizing a state-space interpretation of the Loewner matrices. A Loewner equivalent model using these functions is derived. This allows constructing reduced order models achieving interpolation in the Loewner sense. [ABSTRACT FROM AUTHOR]

In this article, we propose an observer for a class of Lipschitz nonlinear systems affected by time-varying and known measurement delays, which is an improvement of the one presented by Cacace et al., 2014. Under the assumption that the delay function is piecewise continuous and differentiable, we prove that exponential convergence to zero of the observation error can be achieved with any desired decay rate, by suitably tuning a gain vector. The delay bound achieved with the observer proposed here is less conservative than the one obtained by Cacace et al., 2014, as confirmed by numerical tests. For the sake of brevity, in this article, only one-step observers are considered. However, a cascade observer can be arranged to cope with arbitrarily long delays. [ABSTRACT FROM AUTHOR]

This article presents a small-gain theorem for networks composed of a countably infinite number of finite-dimensional subsystems. Assuming that each subsystem is exponentially input-to-state stable, we show that if the gain operator, collecting all the information about the internal Lyapunov gains, has a spectral radius less than one, the overall infinite network is exponentially input-to-state stable. The effectiveness of our result is illustrated through several examples including nonlinear spatially invariant systems with sector nonlinearities and a road traffic network. [ABSTRACT FROM AUTHOR]

We present mean-nonovershooting tracking control designs for stochastic strict-feedback nonlinear systems. Compared with the existing stochastic nonlinear tracking designs, the advantage of our design is that arbitrary reference trajectories can be tracked “from below.” We first consider a special class of stochastic nonlinear systems where the diffusion terms satisfy the linear growth condition and the drift terms are in special triangular forms. A new controller is designed to guarantee that the mean of the system output can asymptotically track a given trajectory without overshooting while keeping all of the states mean-square bounded. In this case, an appealing feature in our design is that strict mean-nonovershooting tracking is achieved while the existing results on nonlinear systems with deterministic disturbance can only achieve practical nonovershooting tracking. Then, we design a new controller for general stochastic strict-feedback nonlinear systems to ensure that the mean of overshoot can be tuned to be arbitrarily small while all the states of the closed-loop system remain bounded in probability. In this case, the new design ingredient is that our control gains are independent of the initial conditions of system states, and the initial conditions of derivatives of the reference trajectory. This is in contrast with the existing results on corresponding deterministic systems whose control gains heavily rely on these initial conditions. Finally, two simulation examples are given to illustrate the stochastic nonlinear nonovershooting tracking designs. [ABSTRACT FROM AUTHOR]

In this article, we consider the joint problems of state estimation and model identification for a class of continuous-time nonlinear systems in the output-feedback canonical form. An adaptive observer is proposed that combines an extended high-gain observer and a discrete-time identifier. The extended observer provides the identifier with a dataset permitting the identification of the system model and the identifier adapts the extended observer according to the new estimated model. The design of the identifier is approached as a system identification problem and sufficient conditions are presented that, if satisfied, allow different identification algorithms to be used for the adaptation phase. The cases of recursive least-squares and multiresolution black-box identification via wavelet-based identifiers are specifically addressed. Stability results are provided relating the asymptotic estimation error to the prediction capabilities of the identifier. Robustness with respect to additive disturbances affecting the system equations and measurements is also established in terms of an input-to-state stability property relative to the noiseless estimates. [ABSTRACT FROM AUTHOR]

In this article, we address a problem of output regulation for a broad class of invertible multi-input–multi-output (MIMO) nonlinear systems. The system that we consider is assumed to possess a globally defined normal form, in which appropriate invertibility conditions are fulfilled, and to be strongly minimum phase. Asymptotic output regulation is achieved by means of a controller consisting of a preprocessing internal model and of a robust stabilizer. For the design of the latter, a recently developed method is proposed, consisting of interlaced design of dynamic extensions and extended observers that provides a robust version of standard stabilization methods based on feedback-linearization. The method does not presume the knowledge of an accurate model of the plant and only needs access to the regulated variables. [ABSTRACT FROM AUTHOR]

An output robust adaptive control is designed for a class of Lipschitz nonlinear systems under assumption that the measurements are available with a constant bias and the state equations linearly parameterized by unknown parameters and external disturbances. A dynamic state reconstruction (synthesis of an observer) is avoided by using delayed values of the output in the feedback and adaptation laws. The analysis of robust stability for the resulted time-delay system is performed by using the Lyapunov–Krasovskii approach. The control and adaptation gains can be selected as a solution of the proposed linear matrix inequalities. This research is motivated by a nonlinear pendulum control problem, and the efficacy of the developed control is demonstrated on this application through experiments. [ABSTRACT FROM AUTHOR]

This article considers the small-time local controllability (STLC) of switched nonlinear systems (SNSs). First, the original SNS is associated with a nilpotent Lie algebra, on which the solutions of the SNS are approximated by the hybrid Lie power series. Second, the concepts of high-order control variations and bad Lie brackets are defined for SNSs from a geometrical point of view. This helps to establish a new high-order sufficient STLC condition that is closely related to “neutralized” bad Lie brackets. Finally, it is shown that the obtained general condition is compatible with the existing controllability conditions of switched linear systems and nonswitched linear and nonlinear systems. [ABSTRACT FROM AUTHOR]

In this article two limitations in current distributed model based approaches for anomaly detection in large-scale uncertain nonlinear systems are addressed. The first limitation regards the high conservativeness of deterministic detection thresholds, against which a novel family of set-based thresholds is proposed. Such set-based thresholds are defined in a way to guarantee robustness in a user-defined probabilistic sense, rather than a deterministic sense. They are obtained by solving a chance-constrained optimization problem, thanks to a randomization technique based on the Scenario Approach. The second limitation regards the requirement, in distributed anomaly detection architectures, for different parties to regularly communicate local measurements. In settings where these parties want to preserve their privacy, communication may be undesirable. In order to preserve privacy and still allow for distributed detection to be implemented, a novel privacy-preserving mechanism is proposed and a so-called privatized communication protocol is introduced. Theoretical guarantees on the achievable level of privacy, along with a characterization of the robustness properties of the proposed distributed threshold set design, taking into account the privatized communication scheme, are provided. Finally, simulation studies are included to illustrate our theoretical developments. [ABSTRACT FROM AUTHOR]