Search

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]

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]

Ensuring safety is crucial for the successful deployment of autonomous systems, such as self-driving vehicles, unmanned aerial vehicles, and robots acting close to humans. While there exist many controllers that optimize certain criteria, such as energy consumption, comfort, or low wear, they are usually not able to guarantee safety at all times for constrained nonlinear systems affected by disturbances. Many controllers providing safety guarantees, however, have no optimal performance. The idea of this article is, therefore, to synthesize a formally correct controller that serves as a safety net for an unverified, optimal controller. This way, most of the time, the optimal controller is in charge and leads to a desired, optimal control performance. The safety controller constantly monitors the actions of the optimal controller and takes over if the system would become unsafe. The safety controller utilizes a novel concept of backward reachable set computation, where we avoid the need of computing underapproximations of reachable sets. We have further developed a new approach that analytically describes reachable sets, making it possible to efficiently maximize the size of the backward reachable set. We demonstrate our approach by a numerical example from autonomous driving. [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]

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]

This article provides an extension of the observability rank condition to time-varying nonlinear systems. Previous conditions to check the state observability only hold for nonlinear systems that do not explicitly depend on time, or, for time-varying systems, they only account for the linear case. In this article, a general analytic condition is provided. The new condition reduces to the well-known observability rank condition in the two simpler cases of time-varying linear systems and time-invariant nonlinear systems. The proposed condition is applied to aerospace robotics to study the observability of a lunar-module-type system equipped with monocular vision and inertial sensors. [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]

This article investigates the transformation of Hamiltonian structures under sampling. It is shown that the exact sampled equivalent model associated to a given port-Hamiltonian continuous-time dynamics exhibits a discrete-time representation in terms of the discrete gradient, with the same energy function but modified damping and interconnection matrices. By construction, the proposed sampled-data dynamics guarantees exact matching of both the state evolutions and the energy-balance at all sampling instants. Its generalization to port-controlled Hamiltonian dynamics leads to characterize a new power conjugate output so recovering the concept of average passivation. On these bases, energy-management control strategies can be proposed. An energetic interpretation of the approach is confirmed by its formulation in the Dirac formalism. Two classical examples are worked out to validate the proposed sampled-data modeling in a comparative way with the literature. [ABSTRACT FROM AUTHOR]

Dissipativity properties have proven to be very valuable for systems analysis and controller design. With the rising amount of available data, there has, therefore, been an increasing interest in determining dissipativity properties from (measured) trajectories directly, while an explicit model of the system remains undisclosed. Most existing approaches for data-driven dissipativity, however, guarantee the dissipativity condition only over a finite-time horizon and provide weak or no guarantees on robustness in the presence of noise. In this article, we present a framework for verifying dissipativity properties from measured data with desirable guarantees. We first consider the case of input-state measurements, where we provide computationally attractive conditions in the presence of process noise. We extend this approach to input–output data, where similar results hold in the noise-free case, and finally provide results for the case of noisy input–output trajectories. [ABSTRACT FROM AUTHOR]

In a recent article, we have shown how to learn controllers for unknown linear systems using finite-length noisy data by solving linear matrix inequalities. In this article, we extend this approach to deal with unknown nonlinear polynomial systems by formulating stability certificates in the form of data-dependent sum of squares programs, whose solution directly provides a stabilizing controller and a Lyapunov function. We then derive variations of this result that lead to more advantageous controller designs. The results also reveal connections to the problem of designing a controller starting from a least-square estimate of the polynomial system. [ABSTRACT FROM AUTHOR]

A linear dynamical system is called $k$ -positive if its dynamics maps the set of vectors with up to $k-1$ sign variations to itself. For $k=1$ , this reduces to the important class of positive linear systems. Since stable positive linear time-invariant systems always admit a diagonal quadratic Lyapunov function, i.e., they are diagonally stable, we may expect that this holds also for stable $k$ -positive systems. We show that, in general, this is not the case both in the continuous-time and discrete-time (DT) case. We then focus on DT $k$ -positive linear systems and introduce the new notion of the DT $k$ -diagonal stability. It is shown that this is a necessary condition for the standard DT diagonal stability. We demonstrate an application of this new notion to the analysis of a class of DT nonlinear systems. [ABSTRACT FROM AUTHOR]

We consider optimal control problems for continuous-time systems with time-dependent dynamics, in which the time-dependence arises from the presence of a known exogenous signal. The problem has been elegantly solved in the case of linear input-affine systems, for which it has been shown that the solution has a remarkable structure: It is given by the sum of two contributions; a state feedback, which coincides with the unperturbed optimal control law, and a purely feedforward term in charge of compensating the effect of the exogenous signal. The objective of this article is to extend the above result to nonlinear input-affine systems. It is shown that, while some of the relevant features of the linear case indeed rely heavily on linearity and are not preserved in the nonlinear setting, several structural claims can be proved also in the nonlinear case. [ABSTRACT FROM AUTHOR]

In this article, we rely on the theoretical foundations of radial basis function neural networks to form an adaptive parameter estimation problem, which we solve using the recently introduced prescribed performance control methodology. Such combination results in a compact user-configurable adaptive nonlinear system identification methodology that can be used to retrieve the open-loop nonlinear plant dynamics in any compact region of interest. [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]

In this article, a new time-varying adaptivedynamic programming (ADP) algorithm is developed to solve finite-horizon optimal control problems for a class of discrete-time affine nonlinear systems. Inspired by the pseudolinear method, the nonlinear system can be approximated by a series of time-varying linear systems. In each iteration of the time-varying ADP algorithm, the optimal control law for the time-varying linear system is obtained. For an arbitrary initial state, it is proven that states of the time-varying linear systems converge to the states of discrete-time affine nonlinear systems. It is also shown that the iterative value functions and the iterative control laws converge to the optimal value function and the optimal control law, respectively. Finally, numerical results are presented to verify the effectiveness of the present method. [ABSTRACT FROM AUTHOR]

Set-membership filter (SMF) has been extensively studied for state estimation in the presence of bounded noises with unknown statistics. Since it was first introduced in the 1960s, the studies on SMF have used the set-based description as its mathematical framework. One important issue that has been overlooked is the optimality of SMF. In this article, we put forward a new mathematical framework for SMF using concepts of uncertain variables. We first establish two basic properties of uncertain variables, namely, the law of total range (a nonstochastic version of the law of total probability) and the equivalent Bayes’ rule. This enables us to put forward a general SMFing framework with established optimality. Furthermore, we obtain the optimal SMF under a nonstochastic Markov condition, which is shown to be fundamentally equivalent to the Bayes filter. Note that the classical SMF in the literature is only equivalent to the optimal SMF we obtained under the nonstochastic Markov condition. When this condition is violated, we show that the classical SMF is not optimal and it only gives an outer bound on the optimal estimate. [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]

Using the notion of exponential QSR-dissipativity (i.e., dissipativity with respect to a quadratic supply rate given in terms of real matrices Q, S,R), this article presents necessary and sufficient conditions for exponential stabilizability of nonlinear systems by linear static output feedback (SOF). It is shown that, under mild assumptions, the exponential stabilization of the closed-loop system around the origin is equivalent to the exponential QSR-dissipativity of the plant. Furthermore, whereas strict QSR-dissipativity is only sufficient for SOF asymptotic stabilization, it is proved to be necessary and sufficient for full state feedback control. New necessary and sufficient conditions for SOF stabilizability of linear systems are presented as well, along with a linear and noniterative semidefinite strategy for controller design. Necessary linear matrix inequality conditions for stabilization are also introduced. Some examples illustrate the usefulness of the proposed approach. [ABSTRACT FROM AUTHOR]

This article considers the problem of output feedback stabilization for a class of nonlinear planar systems with unknown structures and measurements, which prevent the construction of conventional state observers. By taking advantage of the stability-increasing capability of a lead compensator, we propose a dynamic output feedback controller to globally stabilize the uncertain planar systems. For the special case of linear planar systems with unknown coefficients, a finite-time output feedback stabilizer based on a nonlinear compensator is constructed for a faster convergence rate. [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]

The event-triggered control problem for stochastic nonlinear systems is addressed in the presence of stochastic transmission protocols. A stochastic event-triggered transmission strategy is first proposed, which implies that the triggering condition is detected at stochastically distributed detecting instants. The entire system is modeled as a stochastic hybrid system and a new Lyapunov function is constructed to analyze stability of the resulting system. Stability conditions are derived and explicit design of the parameters is also presented. Examples of linear systems and a nonlinear system are provided to illustrate the effectiveness. [ABSTRACT FROM AUTHOR]

In this article, we consider controllability of discrete-time bilinear systems. A classical sufficient condition was obtained in this journal in 1973, which, unfortunately, is not algebraically verifiable, and the required control inputs to achieve state transition are unknown. However, based on a recently established notion, near-controllability, we propose a seeking nonzero entries approach to derive fully algebraically verifiable controllability criteria for discrete-time bilinear systems. More specifically, by our approach, the verification of controllability of the systems is transformed into the problem of seeking nonzero entries of a sequence of matrices generated by the two system matrices. In addition, the control inputs steering the controllable systems between any given pair of states can be easily computed by proposing two algorithms based on near-controllability. As applications, the seeking nonzero entries approach is generalized to construct arbitrary-finite-dimensional controllable discrete-time bilinear systems and also to prove positive-controllability of discrete-time bilinear systems, where algebraic criteria are obtained by the root locus theory and positive-near-controllability that is a new notion introduced in this article. Examples are provided to illustrate the obtained algebraic controllability criteria and algorithms. [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]

The goal of this article is to show that the observation scheme recently proposed for linear systems by Menini et al. in 2019, achieving good performance in the presence of a high-frequency measurement disturbance, can be adapted to be used for nonlinear autonomous systems. The design is based on the use of the time-integrals of the measured output and requires the availability of a state observer able to provide a rough estimate of the state; the proposed scheme can be then understood as an observer postprocessing algorithm. For the implementation of the proposed scheme, the time-integrals of the output are required to express as functions of the state of the system. Such functions are called directional antiderivatives; in the article, conditions to guarantee their existence and methods for their computation, in closed-form or by approximation, are resumed. The performance of the proposed observation scheme is illustrated through an example. [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]

This article studies the problem of prescribed-time global stabilization of a class of nonlinear systems, where the nonlinear functions are unknown but satisfy a linear growth condition. By using solutions to a class of parametric Lyapunov equations containing a time-varying parameter that goes to infinity as the time approaches the prescribed settling time, linear time-varying feedback is designed explicitly to solve the considered problem, with the help of a Lyapunov-like function. It is shown moreover that the control signal is uniformly bounded by a constant depending on the initial condition. Both linear state feedback and linear observer-based output feedback are considered. The effectiveness of the proposed approach is illustrated by a numerical example borrowed from the literature. [ABSTRACT FROM AUTHOR]

This article presents new mathematical results for exact and approximate relaxations of nonconvex optimal control problems defined on disconnected control sets. The exact relaxations are based upon extreme point relaxations wherein the relaxed control set is constructed so that its extreme points belong to the original set. A system property required for exactness is normality. In the absence of normality, control set approximations and system dynamic perturbations are introduced so that normality holds. The results hold for linear dynamical systems and nonlinear systems affine in the control. It is shown that the convex relaxations enable the efficient solution of problems in aerospace engineering, sparsity-promoting optimization, overactuated systems, and multiplexing systems. The computational guarantees associated with convex optimization make the relaxation techniques suitable for real-time control. [ABSTRACT FROM AUTHOR]

Model reduction by moment-matching relies upon the availability of the so-called moment. If the system is nonlinear, the computation of moments depends on an underlying specific invariance equation, which can be difficult or impossible to solve. This article presents four technical contributions related to the theory of moment matching: first, we identify a connection between moment-based theory and weighted residual methods. Second, we exploit this relation to provide an approximation technique for the computation of nonlinear moments. Third, we extend the definition of nonlinear moment to the case in which the generator is described in explicit form. Finally, we provide an approximation technique to compute the moments in this scenario. The results are illustrated by means of two examples. [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]

The stabilization problem for a class of nonlinear systems is solved via a novel method inspired by back-stepping. The method, that we call underactuated back-stepping, is introduced by solving the stabilization problem for an inertia wheel pendulum and it is then developed for a class of underactuated mechanical systems. The properties of the resulting closed-loop systems are studied in detail and case studies are given to show the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

Relaxed conditions are given for stability of a feedback system consisting of an exponentially stable multi-input multi-output nonlinear plant and an integral controller. Roughly speaking, it is shown that if the composition of the plant equilibrium input–output map and the integral feedback gain is infinitesimally contracting, then the closed-loop system is exponentially stable if the integral gain is sufficiently low. The main result is illustrated with an application arising in frequency control of ac power systems. We demonstrate how the contraction condition can be checked computationally via semidefinite programming, and how integral gain matrices can be synthesized via convex optimization to achieve robust L2 performance in the presence of nonlinearity and uncertainty. [ABSTRACT FROM AUTHOR]

In this article, we propose two new iterative algorithms to solve the frequency-limited Riemannian optimization model order reduction problems of linear and bilinear systems. Different from the existing Riemannian optimization methods, we design a new Riemannian conjugate gradient scheme based on the Riemannian geometry notions on a product manifold, and then generate a new search direction. Theoretical analysis shows that the resulting search direction is always descent with depending neither on the line search used, nor on the convexity of the cost function. The proposed algorithms are also suitable for generating reduced systems over a frequency interval in bandpass form. Finally, two numerical examples are simulated to demonstrate the efficiency of our algorithms. [ABSTRACT FROM AUTHOR]

Network inference has been attracting increasing attention in several fields, notably systems biology and biomedicine. Indeed, one of our biggest challenges is to uncover and understand complex molecular networks behind cells and organisms. A network is mainly characterized by its topology and internal dynamics. In particular, sparse topologies with stable dynamics are properties present in most real-world networks. Moreover, experiments typically measure a partial set of nodes. Linear systems have been used as approximations of complex nonlinear systems in a wide range of applications. Although they exhibit simpler dynamics, they can easily model unmeasured nodes, e.g., via transfer functions, which is not possible for nonlinear systems. This article explores these properties and considers general linear network models. It develops a method, based on reversible jump Markov chain Monte Carlo, to estimate the confidence of all links and produce the most likely topology. Monte Carlo simulations indicate that our approach consistently produces more accurate networks compared with other state-of-the-art methods, including kernel-based methods, nonlinear ordinary-differential-equation-based methods (iCheMA), and machine-learning-based methods (dynGINIE3). We show that this is also true on a well-known biological nonlinear model. The proposed method can be used in a wide range of applications, such as systems biology and biomedicine, and fault detection and diagnosis. [ABSTRACT FROM AUTHOR]

This article considers the problem of output feedback funnel control for a class of uncertain nonlinear systems with arbitrary known relative degree. By utilizing the funnel control approach with a barrier Lyapunov function, a novel adaptive output feedback controller is constructed recursively, which accomplishes the output tracking with prescribed transient behavior. The developed control scheme features that the precise knowledge of system nonlinearities, including generally required bounding functions, is not needed. A physical example is performed to verify the effectiveness of the proposed theoretical findings. [ABSTRACT FROM AUTHOR]

In this article, we study the robust output regulation problem of linear systems by an event-triggered output feedback control law. We first summarize the solvability of the linear robust output regulation problem by the internal model design. Then, we implement this continuous-time control law by an event-triggered output feedback control law together with an output-based triggering mechanism. We show that, under almost the same solvability conditions as those for the linear robust output regulation problem, the robust output regulation problem can also be solved by an event-triggered output feedback control law without incurring Zeno phenomenon. Furthermore, we show that, it is possible to solve the robust output regulation problem practically while preventing the interevent time from approaching zero as time tends to infinity. [ABSTRACT FROM AUTHOR]

This article investigates global practical output tracking via adaptive output feedback for a class of uncertain nonlinear systems. Remarkably, the control problem under investigation is in the context of unknown control directions and output feedback, which severely restricts the system nonlinearities. Nevertheless, the growth on the unknown system nonlinearities in this article is extended from polynomial (of output) to arbitrary function, and meanwhile no further a priori information is required on the reference signal to be tracked. Specifically, sufficiently smooth pseudosign and pseudo-dead-zone functions are introduced acting as substitutions of sign and dead-zone functions in the literature, respectively. Typically, based on the pseudo-dead-zone function, a delicate estimate on the unknown system nonlinearities is established and a novel Lyapunov function is proposed. This, together with the elegant system performance analysis, is quite critical to remove the polynomial constraint and overcome the technical obstacle stemming from the essential extension. Additionally owing to the two refined functions, the use of smooth domination/treatment is moderately avoided in control design that enables the established control strategy to be tighter and less conservative. It turns out that under the proposed adaptive output-feedback controller, all the closed-loop system states are globally bounded, while the system tracking error enters a prescribed λ neighborhood of the origin in finite time and remains inside thereafter. A simulation example illustrates the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

The Lyapunov–Krasovskii functional (LKF) method is an effective tool to obtain delay-dependent stability criteria of time-varying delay systems. However, in the method, the requirement that there must exist an appropriate LKF for a system with a delay varying in a delay interval is too strict and may lead to considerable conservativeness. In order to get less conservative stability criteria, a novel stability analysis method called a delay-mode-based LKF (DMBLKF) method is first presented for nonlinear delay systems. Compared with the LKF method, the main advantage of the DMBLKF method lies in relaxing the aforementioned requirement and leading to a less conservative criterion in stability analysis. Then, with the help of the novel method, new stability criteria of linear delay systems are derived. Finally, the effectiveness of the proposed method and the obtained criteria is illustrated through two numerical examples. [ABSTRACT FROM AUTHOR]

In this article, we aim to investigate the synchronization problem of dynamical systems, which can be of generic linear or Lipschitz nonlinear type, communicating over directed switching network topologies. A mild connectivity assumption on the switching topologies is imposed, which allows them to be directed and jointly connected. We propose a novel analysis framework from both algebraic and geometric perspectives to justify the attractiveness of the synchronization manifold. Specifically, it is proven that the complementary space of the synchronization manifold can be spanned by certain subspaces constructed from the network structure. This allows to project the states of the dynamical systems onto these subspaces and transform the synchronization problem under consideration equivalently into a convergence one of the projected states in each subspace. Then, assuming the joint connectivity condition on the communication topologies, we are able to work out a unified convergence analysis for both types of dynamical systems. More specifically, for partial-state coupled generic linear systems, it is proven that synchronization can be reached if an extra condition, which is easy to verify in several cases, on the system dynamics is satisfied. For Lipschitz nonlinear systems with positive-definite inner coupling matrix, synchronization is realized if the coupling strength is strong enough to stabilize the evolution of the projected states in each subspace under certain conditions. The above claims generalize the existing results concerning both types of dynamical systems to so far the most general framework. Some illustrative examples are provided to verify our theoretical findings. [ABSTRACT FROM AUTHOR]

To study optimal control and disturbance attenuation problems, two prominent—and somewhat alternative—strategies have emerged in the last century: dynamic programming (DP) and Pontryagin's minimum principle (PMP). The former characterizes the solution by shaping the dynamics in a closed loop (a priori unknown) via the selection of a feedback input, at the price, however, of the solution to (typically daunting) partial differential equations. The latter, instead, provides (extended) dynamics that must be satisfied by the optimal process, for which boundary conditions (a priori unknown) should be determined. The results discussed in this article combine the two approaches by matching the corresponding trajectories, i.e., combining the underlying sources of information: knowledge of the complete initial condition from DP and of the optimal dynamics from PMP. The proposed approach provides insights for linear as well as nonlinear systems. In the case of linear systems, the derived conditions lead to matrix algebraic equations, similar to the classic algebraic Riccati equations (AREs), although with coefficients defined as polynomial functions of the input gain matrix, with the property that the coefficient of the quadratic term of such equation is sign definite, even if the corresponding coefficient of the original ARE is sign indefinite, as it is typically the case in the H∞ control problem. This feature is particularly appealing from the computational point of view, since it permits the use of standard minimization techniques for convex functions, such as the gradient algorithm. In the presence of nonlinear dynamics, the strategy leads to algebraic equations that allow us to (locally) construct the optimal feedback by considering the behavior of the closed-loop dynamics at a single point in the state space. [ABSTRACT FROM AUTHOR]

This article addresses the problem of robust observer design for nonlinear systems with transformed output. We first assume that there exists an observer design for a given nonlinear system. The structure of the system output is often crucial for estimating the system states. Therefore, we consider the problem that arises when the output is only available under a nonlinear transformation (affected by noise). This formulation is especially useful in engineering applications, where nonlinear sensors are frequent. We propose a new interconnected observer that estimates both the unavailable output and the system states, and we establish small-gain type conditions ensuring the asymptotic convergence of the overall error dynamics. To explicit our design parameters, we study the particular cases of state-affine systems up to output injection and systems with additive triangular nonlinearities. Finally, we provide corresponding numerical examples and comparisons with known observers. [ABSTRACT FROM AUTHOR]

Quadratic boundedness is adopted to construct state observers for linear, piecewise linear, and Lipschitz nonlinear systems subject to bounded disturbances. Upper bounds on the estimation error are derived by exploiting quadratic boundedness and a design method based on linear matrix inequalities is proposed to minimize such bounds. Simulation results are provided to show the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

In this article, by coupling sliding-mode differentiators with a tool capable of inverting, in finite time, the suspension of the observability map, a local finite-time observer for nonlinear control systems is proposed. Differently from other approaches, this observer does not rely on a change of coordinates and provides the state estimates in the original coordinates. [ABSTRACT FROM AUTHOR]

A systematic stabilization approach is provided for systems whose regulation error dynamics is subject to rational nonlinearities given prior knowledge of the system zero-error steady-state condition and a proper internal model. The error dynamics is cast in a differential-algebraic form so as to address the synthesis of controller parameters by a numerical optimization problem subject to bilinear matrix inequality constraints. A particular case is also explored where the resulting constraints are linear matrix inequalities. [ABSTRACT FROM AUTHOR]

This article addresses stability and stabilization of infinite delay systems, which are more general but also more challenging to deal with than bounded delay systems. Based on a general model of infinite delay systems and a newly approved key technical lemma, several new Lyapunov theorems for uniform asymptotical stability and exponential stability, respectively, are established. The stability results are more general than existing stability results, and the corresponding conditions are more easily satisfied than existing ones. Therefore, the new stability results are expected to be more widely applicable. These new Lyapunov theorems are then applied to the problems of stabilizing both time-invariant and time-varying linear systems with distributed infinite input delays, and the corresponding stabilizing controllers are developed. Key to obtaining the stabilizing controllers is to construct appropriate Lyapunov functionals for these systems via introduction of a regulation term into the Lyapunov functional. A distinctive advantage of the Lyapunov-based time-domain method proposed in this article over the existing frequency domain method is that the former can be adopted to deal with more general systems, such as time-varying linear systems or even nonlinear systems. Several examples are provided to illustrate the effectiveness of our results. [ABSTRACT FROM AUTHOR]

This article deals with the problem of output regulation in a “nonequilibrium” context for a special class of multivariable nonlinear systems stabilizable by high-gain feedback. A postprocessing internal model design suitable for the multivariable nature of the system, which might have more inputs than regulation errors, is proposed. Uncertainties in the system and exosystem are dealt with by assuming that the ideal steady-state input belongs to a certain “class of signals,” by which an appropriate model set for the internal model can be derived. The adaptation mechanism for the internal model is then cast as an identification problem, and a least-squares solution is specifically developed. In line with recent developments in the field, the vision that emerges from this article is that approximate, possibly asymptotic, regulation is the appropriate way of approaching the problem in a multivariable and uncertain context. New insights about the use of identification tools in the design of adaptive internal models are also presented. [ABSTRACT FROM AUTHOR]

In this article, we consider the estimation problem of continuous-time stochastic systems with discrete measurements, having linear drift and nonlinear diffusion term. We build the infinite-dimensional linear system equivalent to this class of systems by means of a Carleman linearization approach. Based on this embedding, we investigate the properties of the moment equations of the original system, and we show that it is possible to write the optimal linear filter, for which a finite-dimensional approximation can be implemented. We validate the approach by showing that the resulting algorithm may outperform widely used continuous-discrete filters without increasing the computational burden. [ABSTRACT FROM AUTHOR]

This article proposes an extension of the well-known concept of Granger causality, called GB–Granger causality. GB–Granger causality is designed to relate the internal structure of bilinear state-space systems and statistical properties of their output processes. That is, if such a system generates two processes, where one does not GB–Granger cause the other, then it can be interpreted as the interconnection of two subsystems: one that sends information to the other, and one which does not send information back.This result is an extension of earlier obtained results on the relationship between Granger causality and the internal structure of linear time-invariant state-space representations. [ABSTRACT FROM AUTHOR]

The notions of eigenvalue, pole and moment at a pole of a continuous-time, nonlinear, time-invariant system are studied. Eigenvalues and poles are first characterized in terms of invariant subspaces. Tools from geometric control theory are used to define nonlinear enhancements of these notions and to study their relationship with the solution of certain partial differential equations, cascade decompositions and steady-state impulse responses. The theory is illustrated by means of worked-out examples and its significance is demonstrated by solving the model reduction problem by moment matching at poles for nonlinear systems. [ABSTRACT FROM AUTHOR]

In this paper, we study incremental stability of monotone nonlinear systems through contraction analysis. We provide sufficient conditions for incremental asymptotic stability in terms of the Lie derivatives of differential one-forms or Lie brackets of vector fields. These conditions can be viewed as sum- or max-separable conditions, respectively. For incremental exponential stability, we show that the existence of such separable functions is both necessary and sufficient under standard assumptions for the converse Lyapunov theorem of exponential stability. As a by-product, we also provide necessary and sufficient conditions for exponential stability of positive linear time-varying systems. The results are illustrated through examples. [ABSTRACT FROM AUTHOR]

This note proposes a new extended-state observer-based framework for an adaptive nonlinear regulator design of a class of nonlinear systems, in the general nonequilibrium theory. By augmenting an adaptive extended-state observer with an internal model, one is able to obtain an estimate of the term containing uncertain parameters, which then makes it possible to design an adaptive internal model in the presence of a general nonlinearly parameterized immersion condition. [ABSTRACT FROM AUTHOR]