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This paper aims to apply Negative Imaginary (NI) systems theory to non-square LTI systems, for example, flexible structure systems with redundant sensors and actuators. The paper proposes static pre- and post-compensation schemes to transform stable fat (i.e. no. of inputs more than the no. of outputs) and tall (i.e. no. of outputs more than the no. of inputs) LTI plants into the class of Strongly Strict Negative Imaginary (SSNI) systems, a subset of the Strictly Negative Imaginary (SNI) systems. The proposed compensators can also stabilise a non-square or a non-NI square plant in a positive feedback loop . Moreover, the compensators can be utilised to design a simple constant reference tracking scheme exploiting the integral controllability propoerty of SSNI systems. Subsequently, observer-based pre- and post-compensators are developed to handle the cases when some of the system states are not available for direct measurement. Then, the compensation schemes are extended to stable, non-square or non-NI square systems with polytopic uncertainty . Finally, the post-compensation technique is applied to stabilise a class of tall/square uncertain LTI plants preceded by a slope-restricted nonlinearity.

This paper considers identification of nonlinear rational systems defined as the ratio of two nonlinear functions of past inputs and outputs. Despite its long history, a globally consistent identification algorithm remains illusive. This paper proposes a globally convergent identification algorithm for such nonlinear rational systems. To the best of our knowledge, this is the first globally convergent algorithm for the nonlinear rational systems. The technique employed is a two-step estimator. Though two-step estimators are known to produce consistent nonlinear least squares estimates if a N consistent estimate can be determined in the first step, how to find such a N consistent estimate in the first step for nonlinear rational systems is nontrivial and is not answered by any two-step estimators. The technical contribution of the paper is to develop a globally consistent estimator for nonlinear rational systems in the first step. This is achieved by involving model transformation, bias analysis, noise variance estimation, and bias compensation in the paper. Two simulation examples and a practical example are provided to verify the good performance of the proposed two-step estimator.

[EN] This paper addresses the problem of bounding the trajectories of nonlinear systems (transient and ultimate bounds) from initial conditions in given sets, when subject to possibly nonvanishing disturbances constrained by some finite-interval integral bounds, with a suitable controller. The so-called robustly inescapable sets are determined from such initial conditions and disturbance bounds. In order to get numerical results, the approach considers embedding the nonlinear dynamics in a convex combination of polynomials, and solving sum-of-squares (SOS) problems on them, optimising some inescapable-set size parameters. Determination of approximate (locally) optimal solutions usually requires an iterative evaluation of SOS problems, because of products of decision variables. (C) 2016 Elsevier Ltd. All rights reserved., The research leading to these results has received funding from the European Union (FP7/2007-2013 no 604068) and from the Spanish Government (MINECO/FEDER DPI2015-70975-P, DPI2016-81002). The material in this paper was not presented at any conference. This paper was recommended for publication in revised form by Associate Editor Graziano Chesi under the direction of Editor Richard Middleton.

International audience; In this paper we investigate the stability analysis of nonlinear sampled-data systems, which are affine in the input. We assume that a stabilizing controller is designed using the emulation technique. We intend to provide sufficient stability conditions for the resulting sampled-data system. This allows to find an estimate of the upper bound on the asynchronous sampling intervals, for which stability is ensured. The main idea of the paper is to address the stability problem in a new framework inspired by the dissipativity theory. Furthermore, the result is shown to be constructive. Numerically tractable criteria are derived using linear matrix inequality for polytopic systems and using sum of squares technique for the class of polynomial systems.

This paper considers the problem of using noisy output data to estimate unknown time-delays and unknown system parameters in a general nonlinear time-delay system. We formulate the problem as a dynamic optimization problem in which the unknown quantities are decision variables to be chosen optimally, with the cost function penalizing the mean and variance of the least-squares error between actual and predicted system output. Since the time-delays and system parameters influence the cost function implicitly through the governing time-delay system, the cost function's gradient-which is required to solve the problem using gradient-based optimization techniques-cannot be computed analytically using standard differentiation rules. We instead develop two computational methods for evaluating this gradient: one involves solving an auxiliary time-delay system forward in time; the other involves solving an auxiliary time-advance system backward in time. On this basis, we propose an efficient optimization algorithm for determining optimal estimates for the time-delays and system parameters. We conclude the paper by examining the performance of this algorithm on a dynamic model of a continuously-stirred tank reactor.

The super-twisting algorithm (STA) has become the prototype of second-order sliding mode algorithm. It achieves finite time convergence by means of a continuous action, without using information about derivatives of the sliding constraint. Thus, chattering associated to traditional sliding-mode observers and controllers is reduced. The stability and finite-time convergence analysis have been jointly addressed from different points of view, most of them based on the use of scaling symmetries (homogeneity), or non-smooth Lyapunov functions. Departing from these approaches, in this contribution we decouple the stability analysis problem from that of finite-time convergence. A nonlinear change of coordinates and a time-scaling are used. In the new coordinates and time¿space, the transformed system is stabilized using any appropriate standard design method. Conditions under which the combination of the nonlinear coordinates transformation and the time-scaling is a stability preserving map are given. Provided convergence in the transformed space is faster thanO(1/¿ )¿where ¿ is the transformed time¿ convergence of the original system takes place in finite-time. The method is illustrated by designing a generalized super-twisting observer able to cope with a broad class of perturbations., This work was supported by the National University of La Plata (Project 11-1127), ANPCyT (PICT2007-005359), and CONICET (PIP112-200801-01052) of Argentina; and grants FPI-UPV/2009-21, and Cicyt-FEDER DPI2011-28112-004-01 from Spain. The material in this paper was not presented at any conference. This paper was recommended for publication in revised form by Associate Editor Zhihua Qu under the direction of Editor Andrew R. Teel.

In this paper, we consider a challenging optimal control problem in which the terminal time is determined by a stopping criterion. This stopping criterion is defined by a smooth surface in the state space; when the state trajectory hits this surface, the governing dynamic system stops. By restricting the controls to piecewise constant functions, we derive a finite-dimensional approximation of the optimal control problem. We then develop an efficient computational method, based on nonlinear programming, for solving the approximate problem. We conclude the paper with four numerical examples.

This paper describes a new algorithm for initializing and estimating Wiener-Hammerstein models which consist of two linear parts with a static nonlinearity in between. The algorithm makes use of the best linear model of the system, which is a consistent estimate of the systems dynamics for Gaussian excitations. The linear model is split in all possible ways into two sub-models. For all possible splits, a Wiener-Hammerstein model is initialized which means that a nonlinearity is introduced in between the two sub-models. The linear parameters of this nonlinearity can be estimated using least-squares. All initialized models can then be ranked depending on the fit. Typically, one is only interested in the best one, for which all parameters are fitted using prediction error minimization. The paper explains the algorithm in detail and consistency of the initialization is proven. Computational aspects are investigated, showing that in most realistic cases, the number of splits of the initial linear model remains low enough to make the algorithm useful. The algorithm is illustrated on an example where it is shown that the initialization is a tool to avoid many local minima.

In this paper, the robust H"~ finite-horizon filtering problem is investigated for discrete time-varying stochastic systems with polytopic uncertainties, randomly occurred nonlinearities as well as quantization effects. The randomly occurred nonlinearity, which describes the phenomena of a nonlinear disturbance appearing in a random way, is modeled by a Bernoulli distributed white sequence with a known conditional probability. A new robust H"~ filtering technique is developed for the addressed Ito-type discrete time-varying stochastic systems. Such a technique relies on the forward solution to a set of recursive linear matrix inequalities and is therefore suitable for on-line computation. It is worth mentioning that, in the filtering process, the information of both the current measurement and the previous state estimate is employed to estimate the current state. Finally, a simulation example is exploited to show the effectiveness of the method proposed in this paper.

Boundary control of nonlinear parabolic PDEs is an open problem with applications that include fluids, thermal, chemically-reacting, and plasma systems. In this paper we present stabilizing control designs for a broad class of nonlinear parabolic PDEs in 1-D. Our approach is a direct infinite dimensional extension of the finite-dimensional feedback linearization/backstepping approaches and employs spatial Volterra series nonlinear operators both in the transformation to a stable linear PDE and in the feedback law. The control law design consists of solving a recursive sequence of linear hyperbolic PDEs for the gain kernels of the spatial Volterra nonlinear control operator. These PDEs evolve on domains T"n of increasing dimensions n+1 and with a domain shape in the form of a ''hyper-pyramid'', 0@?@x"n@?@x"n"-"1...@?@x"1@?x@?1. We illustrate our design method with several examples. One of the examples is analytical, while in the remaining two examples the controller is numerically approximated. For all the examples we include simulations, showing blow up in open loop, and stabilization for large initial conditions in closed loop. In a companion paper we give a theoretical study of the properties of the transformation, showing global convergence of the transformation and of the control law nonlinear Volterra operators, and explicitly constructing the inverse of the feedback linearizing Volterra transformation; this, in turn, allows us to prove L^2 and H^1 local exponential stability (with an estimate of the region of attraction where possible) and explicitly construct the exponentially decaying closed loop solutions.

This paper presents a new delay system approach to network-based control. This approach is based on a new time-delay model proposed recently, which contains multiple successive delay components in the state. Firstly, new results on stability and H"~ performance are proposed for systems with two successive delay components, by exploiting a new Lyapunov-Krasovskii functional and by making use of novel techniques for time-delay systems. An illustrative example is provided to show the advantage of these results. The second part of this paper utilizes the new model to investigate the problem of network-based control, which has emerged as a topic of significant interest in the control community. A sampled-data networked control system with simultaneous consideration of network induced delays, data packet dropouts and measurement quantization is modeled as a nonlinear time-delay system with two successive delay components in the state and, the problem of network-based H"~ control is solved accordingly. Illustrative examples are provided to show the advantage and applicability of the developed results for network-based controller design.

This paper develops a Lyapunov approach to the analysis of input-output characteristics for systems under the excitation of a class of oscillatory inputs. Apart from sinusoidal signals, the class of oscillatory inputs include multi-tone signals and periodic signals which can be described as the output of an autonomous system. The Lyapunov approach is developed for linear systems, homogeneous systems (differential inclusions) and nonlinear systems (differential inclusions), respectively. In particular, it is established that the steady-state gain can be arbitrarily closely characterized with Lyapunov functions if the output response converges exponentially to the steady-state. Other output measures that will be characterized include the peak of the transient response and the convergence rate. Tools based on linear matrix inequalities (LMIs) are developed for the numerical analysis of linear differential inclusions (LDIs). This paper's results can be readily applied to the evaluation of frequency responses of general nonlinear and uncertain systems by restricting the inputs to sinusoidal signals. Guided by the numerical result for a second order LDI, an interesting phenomenon is observed that the peak of the frequency response can be strictly larger than the L"2 gain.

This paper shows how interval arithmetic can be applied to the computation of control invariant sets. The paper reviews some concepts in invariant set theory and presents recursive algorithms to compute sequences of control invariant sets. These ideas can be used to design stable controllers subject to state and control constraints. To prove set inclusion and inversion, interval arithmetic is also used.

This paper presents a method for enlarging the domain of attraction of nonlinear model predictive control (MPC). The usual way of guaranteeing stability of nonlinear MPC is to add a terminal constraint and a terminal cost to the optimization problem such that the terminal region is a positively invariant set for the system and the terminal cost is an associated Lyapunov function. The domain of attraction of the controller depends on the size of the terminal region and the control horizon. By increasing the control horizon, the domain of attraction is enlarged but at the expense of a greater computational burden, while increasing the terminal region produces an enlargement without an extra cost. In this paper, the MPC formulation with terminal cost and constraint is modified, replacing the terminal constraint by a contractive terminal constraint. This constraint is given by a sequence of sets computed off-line that is based on the positively invariant set. Each set of this sequence does not need to be an invariant set and can be computed by a procedure which provides an inner approximation to the one-step set. This property allows us to use one-step approximations with a trade off between accuracy and computational burden for the computation of the sequence. This strategy guarantees closed loop-stability ensuring the enlargement of the domain of attraction and the local optimality of the controller. Moreover, this idea can be directly translated to robust MPC. Ministerio de Ciencia y Tecnología DPI2002-04375-c03-01

This paper considers the problem of finite-time stability for stochastic nonlinear systems. A general Lyapunov theorem of stochastic finite-time stability is proposed, and an important corollary is obtained. Some comparisons with the existing results are also given. This theorem not only generalizes the classical stochastic finite-time theorem, but also somewhat shows that Brownian noise takes an active role in stochastic finite-time stability. In addition, more general conditions on stochastic finite-time stability via multiple Lyapunov functions are given to further relax the constraint of the differential operator L V . Moreover, with the help of this criterion, it shows that an unstable deterministic system can even be finite-time stabilized by Brownian noise. Some concrete examples are constructed to show the significant features of the proposed results, and simulations are presented to verify the theoretical analysis.

This paper concerns the incremental L2-gain stability of piecewise-affine (PWA) systems. We propose sufficient conditions derived from dissipativity theory to compute an upper bound on the incremental L2-gain. This is achieved by constructing piecewise-polynomial storage functions through the use of sum of squares (SOS) relaxations. The constraints are expressed as linear matrix inequalities (LMIs), which can be solved numerically in an efficient way. The proposed conditions are verified to be less conservative than previous results found in the literature by means of a numerical example.

In this paper, the stability problem for time-varying nonlinear delayed systems is investigated. An infinite-dimensional version of the nested Matrosov function theorem is proposed to conclude uniform global asymptotic stability for time-varying nonlinear delayed systems. Such a stability theorem requires a weak Lyapunov functional and some auxiliary functionals and the upper bounds of the derivatives on these functionals must satisfy some nested conditions. The proposed results can be used to analyze uniform asymptotic stability of time-varying delayed systems where LaSalle’s invariance principle cannot be applied and Barbalat’s lemma is not sufficient to conclude the uniform attractivity property. An example is given to illustrate the effectiveness of the proposed stability theorem.

Additive nonlinear systems are one of the most widely used nonlinear and non-parametric models to describe nonlinear behaviors. A number of analysis and identification techniques have been developed in the literature for such systems. To apply, however, one has to make sure that the system is additive or can be approximated well by an additive system. This is a nontrivial problem and has eluded researchers for a long time. To the best of our knowledge, only scatter results are reported in the literature. The difficulties lie in the fact that the function and its structure are unknown so estimating its derivatives under an unknown multidimensional density function could be subject to the curse of dimensionality. In this paper, we present two methods to check if a system is additive. The first one estimates the squared derivative average via the Fourier transform. The other one directly estimates the squared derivative average in a reproducing kernel Hilbert space (RKHS) setting. For both methods, convergence results are established and practical numerical algorithms are developed.

A matrix is called totally nonnegative (TN) [totally positive (TP)] if all its minors are nonnegative [positive]. Multiplying a vector by a TN matrix does not increase the number of sign variations in the vector. In a largely forgotten paper, Binyamin Schwarz (1970) considered matrices whose exponentials are TN or TP. He also analyzed the evolution of the number of sign changes in the vector solutions of the corresponding linear system. His work, however, considered only linear systems. In a seemingly different line of research, Smillie (1984), Smith (1991), and others analyzed the stability of nonlinear tridiagonal cooperative systems by using the number of sign variations in the derivative vector as an integer-valued Lyapunov function. We show that these two research topics are intimately related. This allows to derive important generalizations of the results by Smillie (1984) and Smith (1991) while simplifying the proofs. These generalizations are particularly relevant in the context of control systems. Also, the results by Smillie and Smith provide sufficient conditions for analyzing stability based on the number of sign changes in the vector of derivatives and the connection to the work of Schwarz allows to show in what sense these results are also necessary. We describe several new and interesting research directions arising from this new connection.

The exponential stability problem of the nonlinear Saint-Venant equations is addressed in this paper. We consider the general case where an arbitrary friction and space-varying slope are both included in the system, which lead to non-uniform steady-states. An explicit quadratic Lyapunov function as a weighted function of a small perturbation of the steady-states is constructed. Then we show that by a suitable choice of boundary feedback controls, that we give explicitly, the local exponential stability of the nonlinear Saint-Venant equations for the H 2-norm is guaranteed.

This paper extends the finite-time input-to-state stability (FTISS ) property to nonlinear impulsive systems. By the Lyapunov method , several sufficient conditions are provided to obtain ISS property of nonlinear impulsive systems in the framework of finite time, where external inputs are considered in both the continuous dynamics and impulsive dynamics. Considering destabilizing impulsive actions, a relation of the impulsive frequency, the system structure, and exogenous disturbances is given to guarantee the FTISS and the uniform FTISS of impulsive systems. Examples are given to illustrate the effectiveness of the proposed results.

This paper is concerned with the envelope-constrained H ∞ filtering problem for a class of discrete nonlinear stochastic systems subject to quantization effects over a finite horizon. The system under investigation involves both deterministic and stochastic nonlinearities. The stochastic nonlinearity described by statistical means is quite general that includes several well-studied nonlinearities as its special cases. The output measurements are quantized by a logarithmic quantizer. Two performance indices, namely, the finite-horizon H ∞ specification and the envelope constraint criterion, are proposed to quantify the transient dynamics of the filtering errors over the specified time interval. The aim of the proposed problem is to construct a filter such that both the prespecified H ∞ requirement and the envelope constraint are guaranteed simultaneously over a finite horizon. By resorting to the recursive matrix inequality approach, sufficient conditions are established for the existence of the desired filters. A numerical example is finally proposed to demonstrate the effectiveness of the developed filtering scheme.

In controlling nonlinear uncertain systems, compensating for infinite number of actuator failures/faults based on the well-known tuning function approach is an important, yet challenging problem in the field of adaptive control. In fact, it has been illustrated through simulation examples that instability is observed when an existing tuning function based scheme designed for compensating finite number of actuator failures is applied to an infinite number case. So far, there is still no solution to this problem. In this paper, we address this issue by proposing a novel adaptive scheme. Technically, our scheme is developed from a new piecewise Lyapunov function analysis, the parameter projection and a modified tuning function method. It is proved that all closed-loop signals are ensured bounded by the control scheme even there is a possibility that the actuator failures take place infinitely, provided that the minimum time interval between two successive failures is bounded below by any positive scalar. Moreover, the ultimate bound of tracking error can be reduced arbitrarily small even for relatively frequent failures. In addition, a guideline for improving transient performance in terms of L 2 -norm of tracking error is also established. Perfect asymptotic tracking is obtained when the total number of actuator failures becomes finite.

This paper addresses the dynamic properties of a class of continuous-time switched nonlinear systems with perturbations and delays. With the assumption that the nominal system is exponentially stable, it is shown that the trajectory of the perturbed system exponentially decays to or asymptotically approaches origin provided that the perturbation exponentially decays to or asymptotically approaches origin. These properties are then applied to cascade systems for their stability analysis. It is proven that a delayed switched nonlinear cascade system is exponentially stable if and only if all subsystems obtained from the cascade system by deleting the coupling terms are exponentially stable. A sufficient condition ensuring asymptotic stability of a cascade system is also proposed.

A new LMI design technique is developed to address the problem of circle criterion-based $\mathcal{H}_{\infty}$ observer design for nonlinear systems. The developed technique applies to both locally Lipschitz as well as monotonic nonlinear systems, and allows for nonlinear functions in both the process dynamics and output equations. The LMI design condition obtained is less conservative than all previous results proposed in the literature for these classes of nonlinear systems. By judicious use of a modified Young’s relation, additional degrees of freedom are included in the observer design. These additional decision variables enable improvements in the feasibility of the obtained LMI. Several recent results in the literature are shown to be particular cases of the more general observer design methodology developed in this paper. Illustrative examples are given to show the effectiveness of the proposed methodology. The application of the method to slip angle estimation in automotive applications is discussed and experimental results are presented.

This paper analyzes the robust feedback stability of a single-input-single-output stable linear time-invariant (LTI) system against three different classes of nonlinear systems using the Zames–Falb multipliers. The contribution is threefold. Firstly, we identify a class of uncertain systems over which the robust feedback stability is equivalent to the existence of an appropriate Zames–Falb multiplier. Secondly, when restricted to be static (a.k.a. memoryless), such a class of systems coincides with the class of sloped-restricted monotone nonlinearities , and the classical result of using the Zames–Falb multipliers to ensure feedback stability is recovered. Thirdly, when restricted to be LTI, the first class is demonstrated to be a subset of the second, and the existence of a Zames–Falb multiplier is shown to be sufficient but not necessary for the robust feedback stability.

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

This paper studies consensus problems for multi-agent systems defined on directed graphs where the consensus dynamics involves general nonlinear and discontinuous functions. Sufficient conditions, only involving basic properties of the nonlinear functions and the topology of the underlying graph, are derived for the agents to converge to consensus.

This paper studies exponential stability properties of a class of two-dimensional (2D) systems called differential repetitive processes (DRPs). Since a distinguishing feature of DRPs is that the problem domain is bounded in the "time" direction, the notion of stability to be evaluated does not require the nonlinear system defining a DRP to be stable in the typical sense. In particular, we study a notion of exponential stability along the discrete iteration dimension of the 2D dynamics, which requires the boundary data for the differential pass dynamics to converge to zero as the iterations evolve. Our main contribution is to show, under standard regularity assumptions, that exponential stability of a DRP is equivalent to that of its linearized dynamics. In turn, exponential stability of this linearization can be readily verified by a spectral radius condition. The application of this result to Picard iterations and iterative learning control (ILC) is discussed. Theoretical findings are supported by a numerical simulation of an ILC algorithm., 13 pages, 3 figures. Technical report accompanying "Exponential Stability of Nonlinear Differential Repetitive Processes with Applications to Iterative Learning Control" published in Automatica Volume 81, July 2017 (Pages 369-376, URL: http://www.sciencedirect.com/science/article/pii/S0005109817301772)

High-gain observers proved to be a useful tool in the design of output feedback control of nonlinear systems. However, the observer faces a numerical challenge when its dimension is high. For an observer of dimension ρ and a high-gain parameter k , the observer gain is of the order of k ρ and the observer variables could be of the order of k ρ − 1 during the transient period. This paper presents a new high-gain observer that is based on cascading lower-dimensional observers with saturation functions in between them. The observer gain in the new observer is of the order of k and its variables are limited to be of the order of k during the transient period. It is shown that the cascade observer has properties similar to the standard one. In particular, a nonlinear separation principle is proved.

In this paper, we study the leader-following consensus problem for a class of uncertain nonlinear multi-agent systems under jointly connected directed switching networks. The uncertainty includes constant unbounded parameters and external disturbances. We first extend the recent result on the adaptive distributed observer from global asymptotical convergence to global exponential convergence. Then, by integrating the conventional adaptive control technique with the adaptive distributed observer, we present our solution by a distributed adaptive state feedback control law. Our result is illustrated by the leader-following consensus problem for a group of van der Pol oscillators., 21 pages, 5 figures. In this replacement version, the higher-order case is considered instead of the second-order case. Also, the main difference of this version from the reference [16] is that Appendix B is added to show the existence of the limit of the function V(t) defined in the equation (33) as t tends to infinity

This paper deals with an extended framework of the distributed asymptotic agreement problem by allowing the presence of unilateral interactions (optimistic or pessimistic) in place of bilateral ones, for a large class of nonlinear monotone time-varying networks. In this original setup we firstly introduce notions of unilateral optimistic and/or pessimistic interaction, of associated bicolored edge in the interaction graph and a suitable graph-theoretical connectedness property. Secondly, we formulate a new assumption of integral connectivity and show that it is sufficient to guarantee exponential convergence towards the agreement subspace. Finally, we show that the proposed conditions are also necessary for consensuability and discuss how the new notions of bicolored graph and related connectivity concepts encompass the usual criteria in the standard case of bilateral interactions. Theoretical advances are emphasized through illustrative examples given both to support the discussion and to highlight how the proposed framework extends all existing conditions for consensus of monotone networks.

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

In this paper, continuous observer is designed for a class of multi-output nonlinear systems with multi-rate sampled and delayed output measurements. The time delay may be larger or less than the sampling intervals. The sampled and delayed measurements are used to update the observer whenever they are available. Sufficient conditions are presented to ensure global exponential stability of the observation errors by constructing a Lyapunov-Krasovskii function. A numerical example is given to illustrate the effectiveness of the proposed methods.

International audience; We consider the problem of state observation for systems having a well-defined observability canonical form (Gauthier and Kupka (2004)) by means of high-gain observers. The main goal is to show that, for this class of systems, observers can be designed with the high-gain parameter powered just up to the order 2 regardless the dimension of the state system. In this way we substantially overtake the main limitations of standard design procedures in which the high-gain parameter is powered up to the order of the system. The observer structure, which generalizes the ideas presented in Astolfi and Marconi (2015), can be used in all those contexts where fast state observation is required, such as in the design of output feedback stabilizers by means of the nonlinear separation principle that is also specifically addressed in the paper.

In this paper, the relationship between notions of observability for continuous-time nonlinear system related to distinguishability, observability rank condition and K-function has been investigated. It is proved that an autonomous nonlinear system that is observable in both distinguishability and rank condition sense permits an observation window of finite width, and it is possible to construct a K-function related to observability for such system., Comment: This work was supported by the Japan Society for the Promotion of Science under Grant-in-Aid for Scientific Research (C) 23560535. Copyright 2018. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/

In this paper a special type of nonlinear marking specifications called stair generalized mutual exclusion constraints (stair-GMECs) is defined. A stair-GMEC can be represented by an inequality whose left-hand is a linear combination of floor functions. Stair-GMECs have higher modeling power than classical GMECs and can model legal marking sets that cannot be defined by OR-AND GMECs. We propose two algorithms to enforce a stair-GMEC as a closed-loop net, in which the control structure is composed by a residue counter, remainder counters, and duplicate transitions. We also show that the proposed control structure is maximally permissive since it prevents all and only the illegal trajectories of a plant net. This approach can be applied to both bounded and unbounded nets. Several examples are proposed to illustrate the approach.

In this paper, a general event-triggered framework is set up to deal with the variance-constrained H ∞ control problem for a class of discrete time-varying systems with randomly occurring saturations, stochastic nonlinearities and state-multiplicative noises. Based on the relative error with respect to the measurement signal, an event indicator variable is introduced and the corresponding event-triggered scheme is proposed in order to determine whether the measurement output is transmitted to the controller or not. The stochastic nonlinearities under consideration are characterized by statistical means which can cover several classes of well-studied nonlinearities. A set of unrelated random variables is exploited to govern the phenomena of randomly occurring saturations, stochastic nonlinearities and state-dependent noises. The purpose of the addressed multiobjective control problem is to design a set of time-varying output feedback controller such that, over a finite horizon, the closed-loop system achieves both the prescribed H ∞ noise attenuation level and the state covariance constraints. A recursive matrix inequality approach is developed to derive the sufficient conditions for the existence of the desired finite-horizon controllers, and the analytical characterization of such controllers is also given. Simulation studies are conducted to demonstrate the effectiveness of the developed controller design scheme.

This paper studies the adaptive and optimal output-feedback problem for continuous-time uncertain systems with nonlinear dynamic uncertainties. Data-driven output-feedback control policies are developed by approximate/adaptive dynamic programming (ADP) based on both policy iteration and value iteration methods. The obtained adaptive and optimal output-feedback controllers differ from the existing literature on the ADP in that they are derived from sampled-data systems theory and are guaranteed to be robust to dynamic uncertainties. A small-gain condition is given under which the overall system is globally asymptotically stable at the origin. An application to power systems is given to test the effectiveness of the proposed approaches.

This paper considers the observability of nonlinear systems from a Koopman operator theoretic perspective – and in particular – the effect of symmetry on observability. We first examine an infinite-dimensional linear system (constructed using independent Koopman eigenfunctions) and relate its observability properties to the observability of the original nonlinear system. Next, we derive an analytic relation between symmetry and nonlinear observability; it is shown that symmetry in the nonlinear dynamics is reflected in the symmetry of the corresponding Koopman eigenfunctions, as well as presence of repeated Koopman eigenvalues. We then proceed to show that loss of observability in symmetric nonlinear systems can be traced back to the presence of these repeated eigenvalues. In the case where we have a sufficient number of measurements, the nonlinear system remains unobservable when these functions have symmetries that mirror those of the dynamics. The proposed observability framework provides insights into the minimum number of measurements needed to make an unobservable nonlinear system, observable. The proposed results are then applied to a network of nano-electromechanical oscillators coupled via a symmetric interaction topology.

This paper studies the linear dynamic errors-in-variables (EIV) problem in a fairly general condition where the input–output disturbing noises are colored and the input is quasi-stationary. A novel formulation of the extended frequency domain maximum likelihood (ML) estimator is developed which reduces the number of nonlinear normal equations to be solved. Sufficient conditions are provided to achieve local identifiability of the EIV model for specified noise cases of interest. The parameter estimates are calculated via a numerically stable Gauss–Newton minimization scheme started by an initial value generation strategy. Also, both the consistency and accuracy of the extended ML estimate are analyzed in detail. The performance of the proposed method is finally demonstrated on simulated dynamic systems.

Many large-scale and distributed optimization problems can be brought into a composite form in which the objective function is given by the sum of a smooth term and a nonsmooth regularizer. Such problems can be solved via a proximal gradient method and its variants, thereby generalizing gradient descent to a nonsmooth setup. In this paper, we view proximal algorithms as dynamical systems and leverage techniques from control theory to study their global properties. In particular, for problems with strongly convex objective functions, we utilize the theory of integral quadratic constraints to prove the global exponential stability of the equilibrium points of the differential equations that govern the evolution of proximal gradient and Douglas-Rachford splitting flows. In our analysis, we use the fact that these algorithms can be interpreted as variable-metric gradient methods on the suitable envelopes and exploit structural properties of the nonlinear terms that arise from the gradient of the smooth part of the objective function and the proximal operator associated with the nonsmooth regularizer. We also demonstrate that these envelopes can be obtained from the augmented Lagrangian associated with the original nonsmooth problem and establish conditions for global exponential convergence even in the absence of strong convexity., 8 pages; 1 figure

In recent work it is shown that importance sampling can be avoided in the particle filter through an innovation structure inspired by traditional nonlinear filtering combined with Mean-Field Game formalisms. The resulting feedback particle filter (FPF) offers significant variance improvements; in particular, the algorithm can be applied to systems that are not stable. The filter comes with an up-front computational cost to obtain the filter gain. This paper describes new representations and algorithms to compute the gain in the general multivariable setting. The main contributions are, (i) Theory surrounding the FPF is improved: Consistency is established in the multivariate setting, as well as well-posedness of the associated PDE to obtain the filter gain. (ii) The gain can be expressed as the gradient of a function, which is precisely the solution to Poisson's equation for a related MCMC diffusion (the Smoluchowski equation). This provides a bridge to MCMC as well as to approximate optimal filtering approaches such as TD-learning, which can in turn be used to approximate the gain. (iii) Motivated by a weak formulation of Poisson's equation, a Galerkin finite-element algorithm is proposed for approximation of the gain. Its performance is illustrated in numerical experiments., In Proc. of 51st IEEE Conference on Decision and Control

In this paper, incremental exponential asymptotic stability of a class of switched Carathéodory nonlinear systems is studied based on the novel concept of measure of switched matrices via multiple norms and the transaction coefficients between these norms. This model is rather general and includes the case of staircase switching signals as a special case. Sufficient conditions are derived for incremental stability allowing for the system to be incrementally exponentially asymptotically stable even if some of its modes are unstable in some time periods. Numerical examples on switched linear systems with periodic switching and on the synchronization of switched networks of nonlinear systems are used to illustrate the theoretical results.

In this paper, we propose a new adaptive output-feedback tracking control scheme for a class of uncertain nonlinear systems with input quantized by a newly-proposed quantizer. This quantizer is a combination of a logarithmic (or a hysteresis) quantizer and a uniform quantizer, and it has the advantages of both logarithmic and uniform quantizers in ensuring reducible communication expenses and acceptable quantization errors for better system performances. Compared with existing results in adaptive control, the proposed scheme provides a way to relax certain restrictive conditions, in addition to solving the problem of adaptive output-feedback control with input quantization. It is shown that the designed adaptive controller ensures global boundedness of all the signals in the closed-loop system and enables the tracking error to exponentially converge towards a compact set which is adjustable. Accepted version

Traditional model-based approaches are based on periodic iterations, where the continuous-time model is discretized with a fixed period. Despite the easiness in analysis and design, such periodic approximation model may be undesirable from the computation-efficiency point of view. This paper presents the Lebesgue-approximation model (LAM) of continuous-time nonlinear systems, where the iteration is activated on an "as-needed" basis, but not periodically. We show that the proposed LAM behaves exactly the same as a specific event-triggered feedback system, through which the properties of the LAM can be studied. We provide a sufficient condition to ensure asymptotic stability of the LAM and derive theoretical bounds on the difference between the states of the LAM and the original continuous-time system. The LAM is then integrated in the particle-filtering approach for fault prognosis. Simulation results show that the LAM can dramatically reduce the number of iterations in prognosis without sacrificing accuracy and precision.

This paper establishes identifiability and informativity conditions for a class of deterministic linearly parametrized scalar rational models. The class considered is rational in the state and polynomial in the input. The standard definitions of identifiability and informativity for linear systems are expanded to account for the situation, common for nonlinear deterministic systems, where the identification is achieved either through the application of an informative input or via the response to an informative initial condition. We provide necessary and sufficient conditions for identifiability from the initial state, respectively from the input, as well as necessary and sufficient conditions on the initial state to produce an informative experiment. We also provide sufficient conditions on the input to be informative when the initial condition is unknown and could therefore potentially destroy the transfer of information from the input to the regressor.

It has been shown that quantifying the unstable in linear systems is important for establishing the existence of stabilizing feedback controllers in the presence of communications constraints. In this context, the instability measure is defined as the sum of the real parts (continuous-time case) or the product of the magnitudes (discrete-time case) of the unstable eigenvalues. This paper addresses the problem of quantifying the unstable in linearized systems obtained from nonlinear systems for a family of constant inputs, i.e., quantifying the largest instability measure over all admissible equilibrium points and all admissible constant inputs. It is supposed that the dynamics of the nonlinear system is polynomial in both state and input, either continuous-time or discrete-time, and that the set of constant inputs is a semialgebraic set. Two cases are considered: first, when the equilibrium points are known polynomial functions of the input, and, second, when the equilibrium points are unknown (polynomial or non-polynomial) functions of the input. It is shown that upper bounds of the sought instability measure can be established through linear matrix inequalities (LMIs) by searching for polynomially-dependent Lyapunov function candidates. Moreover, it is shown that these upper bounds are nonconservative for a sufficiently large degree of the Lyapunov function candidates under some conditions. Lastly, necessary and sufficient conditions are provided for establishing whether the obtained upper bounds are nonconservative. Some numerical examples also show the advantages of the proposed method with respect to grid techniques.

This paper considers local asymptotic stabilization of a class of uncertain upper-triangular systems. It shows that, by appropriately increasing the powers of the states in a linear controller, an uncertain upper-triangular system can be locally asymptotically stabilized. A nested nonlinear controller is designed by introducing the notion of homogeneity with strictly decreasing degrees. For the stability analysis, a common Lyapunov/Chetaev function is constructed and a necessary and sufficient condition for the local asymptotic stability is established.

This paper studies a class of random nonlinear systems with time-varying delay, in which the r -order moment of the random disturbance is finite. Firstly, some general conditions are proposed to guarantee the existence and uniqueness of the global solution to random nonlinear time-delay systems. Secondly, some criteria on noise-to-state stability in the moment sense and in probability sense are given by Lyapunov method respectively. Finally, an adaptive output feedback regulation controller is constructed for a class of random nonlinear time-delay systems and the effectiveness of the proposed recursive procedure is demonstrated by a simulation example.