In this paper, we consider robust output tracking for an Euler–Bernoulli beam equation under the guidance of the internal model principle, where the disturbances in all possible channels are considered. Three typical cases are investigated in terms of different regulated outputs. The first case is based on boundary displacement output, for which only asymptotic convergence can be achieved due to the

Stochastic control problems with delay are challenging due to the path-dependent feature of the system and thus its intrinsic high dimensions. In this paper, we propose and systematically study deep neural network-based algorithms to solve stochastic control problems with delay features. Specifically, we employ neural networks for sequence modeling (e.g., recurrent neural networks such as long short-term

The article “A local input-to-state stability result w.r.t. attractors of nonlinear reaction–diffusion equations” written by Sergey Dashkovskiy, Oleksiy Kapustyan, and Jochen Schmid, was originally published online on 6 May 2020, without Open Access.

This paper deals with the stabilization of a coupled system composed by an infinite-dimensional system and an ODE. Moreover, the control, which appears in the dynamics of the ODE, is subject to a general class of nonlinearities. Such a situation may arise, for instance, when the actuator admits a dynamics. The open-loop ODE is exponentially stable and the open-loop infinite-dimensional system is dissipative

In this paper, we will deal with a linear quadratic optimal control problem with unknown dynamics. As a modeling assumption, we will suppose that the knowledge that an agent has on the current system is represented by a probability distribution \(\pi \) on the space of matrices. Furthermore, we will assume that such a probability measure is opportunely updated to take into account the increased experience

We study control properties of a linearized fluid–structure interaction system, where the structure is a rigid body and where the fluid is a viscoelastic material. We establish the approximate controllability and the exponential stabilizability for the velocities of the fluid and of the rigid body and for the position of the rigid body. In order to prove this, we prove a general result for this kind

In this paper we study a class of semilinear wave-type equations with viscoelastic damping and delay feedback with time variable coefficient. By combining semigroup arguments, careful energy estimates and an iterative approach we are able to prove, under suitable assumptions, a well-posedness result and an exponential decay estimate for solutions corresponding to small initial data. This extends and

This paper investigates the question of strong stabilizability of non-dissipative linear systems in Hilbert spaces with input saturation. It is proved under some verifiable conditions that the origin is asymptotically stable for the closed-loop semilinear systems. The contribution is then applied to the Schrödinger equation.

Under a regularity assumption we prove that reachability in fixed time for nonlinear control systems is robust under control sampling.

It is well known that there is a correspondence between convolutional codes and discrete-time linear systems over finite fields. In this paper, we employ the linear systems representation of a convolutional code to develop a decoding algorithm for convolutional codes over the erasure channel. In this kind of channel, which is important due to its use for data transmission over the Internet, the receiver

We extend the approach based on the linearization of triangular systems to new classes of non-linearizable control systems that are almost linearizable. This means that there exists a change of variables and control mapping all but one equations of the initial nonlinear system to a linear system. We show how this property can be used for solving the problem of constructive controllability, i.e., finding

We investigate genericity of various controllability and stabilizability concepts of linear, time-invariant differential-algebraic systems. Based on well-known algebraic characterizations of these concepts (see the survey article by Berger and Reis (in: Ilchmann A, Reis T (eds) Surveys in differential-algebraic equations I, Differential-Algebraic Equations Forum, Springer, Berlin, pp 1–61. https://doi

The main concern of this article is to investigate the boundary controllability of some \(2\times 2\) one-dimensional parabolic systems with both the interior and boundary couplings: The interior coupling is chosen to be linear with constant coefficient while the boundary one is considered by means of some Kirchhoff-type condition at one end of the domain. We consider here the Dirichlet boundary control

This paper considers dynamical systems over finite fields (DSFF) defined by a map in a vector space over a finite field. An associated linear dynamical system is constructed over the space of functions. This system constitutes the well known Koopman linear system framework of dynamical systems, hence called the Koopman linear system (KLS). It is first shown that several structural properties of solutions

Positive dynamical or control systems have all their variables nonnegative. Euler discretization transforms a continuous-time system into a system on a discrete time scale. Some structural properties of the system may be preserved by discretization, while other may be lost. Four fundamental properties of positive systems are studied in the context of discretization: positivity, positive stability,

In this paper, a dynamic regressor extension and mixed estimator is proposed with finite-time convergence and freedom to choose its time-varying adaptation gain and its derivation order. This freedom is exploited to enhance the transient and robustness performance of the estimation by analytically establishing the effects of both variables. The proposed estimator is used to design adaptive controllers

Poset-causal systems form a class of decentralized systems introduced by Shah and Parrilo (47th IEEE conference on decision and control, IEEE, 2008) and studied mainly in the context of optimal decentralized control. In this paper, we develop part of the realization theory for poset-causal systems. More specifically, we investigate several notions of controllability and observability, and their relation

In this paper the turnpike phenomenon is studied for problems of optimal control where both pointwise-in-time state and control constraints can appear. We assume that in the objective function, a tracking term appears that is given as an integral over the time-interval \([0,\, T]\) and measures the distance to a desired stationary state. In the optimal control problem, both the initial and the desired

This paper is devoted to a studying of the controllability properties for the Coleman–Gurtin-type equation, which is a class of multidimensional integral–differential equations. The goal is to prove the existence of a control function which steers the state variable and the integral term to the neighborhood of two given final configurations at the same time, respectively. This new approximate controllability

Tracking of reference signals is addressed in the context of a class of nonlinear controlled systems modelled by r-th-order functional differential equations, encompassing inter alia systems with unknown “control direction” and dead-zone input effects. A control structure is developed which ensures that, for every member of the underlying system class and every admissible reference signal, the tracking

This manuscript presents a notion of parallelizability of control systems. Parallelizability is a well-known concept of dynamical systems that associates with complete instability and dispersiveness. The concept of dispersiveness has been successfully interpreted in the setup of control systems. This naturally asks about the meaning of a parallelizable control system. The answer can be given in the

The following corrections should be made to this article.

We propose a class of locally Lipschitz functions with piecewise structure for use as Lyapunov functions for hybrid dynamical systems. Subject to some regularity of the dynamics, we show that Lyapunov inequalities can be checked only on a dense set and thus we avoid checking them at points of nondifferentiability of the Lyapunov function. Connections to other classes of locally Lipschitz or piecewise

In this paper, we study variational point-obstacle avoidance problems on complete Riemannian manifolds. The problem consists of minimizing an energy functional depending on the velocity, covariant acceleration and a repulsive potential function used to avoid an static obstacle given by a point in the manifold, among a set of admissible curves. We derive the dynamical equations for stationary paths

We consider here the problem of constructing a general recursive algorithm to interpolate a given set of data with a rational function. While many algorithms of this kind already exist, they are either providing non-minimal degree solutions (like the Schur algorithm) or exhibit jumps in the degree of the interpolants (or of the partial realization, as the problem is called when the interpolation is

This paper considers the problem of controlled invariance of involutive regular distribution, both for smooth and real analytic cases. After a review of some existing work, a precise formulation of the problem of local and global controlled invariance of involutive regular distributions for both affine control systems and affine distributions is introduced. A complete characterization for local controlled

Boundary feedback control design for systems of linear hyperbolic conservation laws in the presence of boundary measurements affected by disturbances is studied. The design of the controller is performed to achieve input-to-state stability (ISS) with respect to measurement disturbances with a minimal gain. The closed-loop system is analyzed as an abstract dynamical system with inputs. Sufficient conditions

The probability hypothesis density (PHD) filter, which is used for multi-target tracking based on sensor measurements, relies on the propagation of the first-order moment, or intensity function, of a point process. This algorithm assumes that targets behave independently, an hypothesis which may not hold in practice due to potential target interactions. In this paper, we construct a second-order PHD

This paper aims to develop a system-theoretic approach to ordinary differential equations which deterministically describe dynamics of prevalence of epidemics. The equations are treated as interconnections in which component systems are connected by signals. The notions of integral input-to-state stability (iISS) and input-to-state stability (ISS) have been effective in addressing nonlinearities globally

A distributional solution framework is developed for systems consisting of linear hyperbolic partial differential equations and switched differential-algebraic equations (DAEs) which are coupled via boundary conditions. The unique solvability is then characterize in terms of a switched delay DAE. The theory is illustrated with an example of electric power lines modelled by the telegraph equations which

Achieving a simplified model is a major issue in the field of fractional-order nonlinear systems, especially large-scale systems. So that in addition to simplifying the model, the outstanding features of the fractional-order modeling, such as memory feature, are preserved. This paper presented the homotopy singular perturbation method (HSPM) to reduce the complexity of the model and use the advantages

This paper addresses the mean stability analysis and \(L_1\) performance of continuous-time Markov jump linear systems (MJLSs) driven by a two time-scale Markov chain, in the scenario in which the temporal scale parameter \(\epsilon \) tends to zero. The jump process considered here is bivariate, with slow and fast components. Our approach relies on a convergence analysis involving the semigroup that

In this paper, we consider the input-to-state stabilization of an ODE-wave feedback-connection system with Neumann boundary control, where the left end displacement of the wave equation enters the ODE, while the output of the ODE is fluxed into boundary of the wave equation. The disturbance is appeared as a nonhomogeneous term in the ODE. Based on the backstepping approach, a state feedback control

This paper studies a notion of topological entropy for switched systems, formulated in terms of the minimal number of trajectories needed to approximate all trajectories with a finite precision. For general switched linear systems, we prove that the topological entropy is independent of the set of initial states. We construct an upper bound for the topological entropy in terms of an average of the

We investigate input-to-state stability (ISS) of infinite-dimensional collocated control systems subject to saturated feedback. Here, the unsaturated closed loop is dissipative and uniformly globally asymptotically stable. Under an additional assumption on the linear system, we show ISS for the saturated one. We discuss the sharpness of the conditions in light of existing results in the literature

We consider forced Lur’e systems in which the linear dynamic component is an infinite-dimensional well-posed system. Numerous physically motivated delay and partial differential equations are known to belong to this class of infinite-dimensional systems. We present refinements of recent incremental input-to-state stability results (Guiver in SIAM J Control Optim 57:334–365, 2019) and use them to derive

Linear differential systems, in Willems’ behavioral system theory, are defined to be the solution sets to systems of linear constant coefficient PDEs, and they are naturally parameterized in a bijective way by means of polynomial modules. In this article, introducing appropriate topologies, this parametrization is made continuous in both directions. Moreover, the space of linear differential systems

This paper deals with the minimization of \(H_\infty \) output feedback control. This minimization can be formulated as a linear matrix inequality (LMI) problem via a result of Iwasaki and Skelton 1994. The strict feasibility of the dual problem of such an LMI problem is a valuable property to guarantee the existence of an optimal solution of the LMI problem. If this property fails, then the LMI problem

Motivated by the ubiquitous sampled-data setup in applied control, we examine the stability of a class of difference equations that arises by sampling a right- or left-invariant flow on a solvable matrix Lie group. The map defining such a difference equation has three key properties that facilitate our analysis: (1) its Lie series expansion enjoys a type of strong convergence; (2) the origin is an

In this paper, we study the hierarchic control problem for a linear system of a population dynamics model with an unknown birth rate. Using the notion of low-regret control and an adapted observability inequality of Carleman type, we show that there exist two controls such that, the first control called follower solves an optimal control problem which consists in bringing the state of the linear system

In this paper, we introduce a weak maximum principle-based approach to input-to-state stability (ISS) analysis for certain nonlinear partial differential equations (PDEs) with certain boundary disturbances. Based on the weak maximum principle, a classical result on the maximum estimate of solutions to linear parabolic PDEs has been extended, which enables the ISS analysis for certain nonlinear parabolic

Model order reduction (MOR) techniques are often used to reduce the order of spatially discretized (stochastic) partial differential equations and hence reduce computational complexity. A particular class of MOR techniques is balancing related methods which rely on simultaneously diagonalizing the system Gramians. This has been extensively studied for deterministic linear systems. The balancing procedure

We establish the local input-to-state stability of a large class of disturbed nonlinear reaction–diffusion equations w.r.t. the global attractor of the respective undisturbed system.

Classical discrete-time adaptive controllers provide asymptotic stabilization and tracking; neither exponential stabilization nor a bounded noise gain is typically proven. In our recent work, it is shown, in both the pole placement stability setting and the first-order one-step-ahead tracking setting, that if the original, ideal, projection algorithm is used (subject to the common assumption that the

This article presents a new method for computing sharp bounds on the solutions of nonlinear dynamic systems subject to uncertain initial conditions, parameters, and time-varying inputs. Such bounds are widely used in algorithms for uncertainty propagation, robust state estimation, system verification, global dynamic optimization, and more. Recently, it has been shown that bounds computed via differential

This article considers the problem of optimally recovering stable linear time-invariant systems observed via linear measurements made on their transfer functions. A common modeling assumption is replaced here by the related assumption that the transfer functions belong to a model set described by approximation capabilities. Capitalizing on recent optimal recovery results relative to such approximability

We study the sample-data control problem of output tracking and disturbance rejection for unstable well-posed linear infinite-dimensional systems with constant reference and disturbance signals. We obtain a sufficient condition for the existence of finite-dimensional sampled-data controllers that are solutions of this control problem. To this end, we study the problem of output tracking and disturbance

The purpose of this work is to obtain restrictions on the asymptotic structure of two-dimensional hybrid dynamical systems. Previous results have been achieved by the authors concerning hybrid dynamical systems with a single impact surface and a single state space. Here, this work is extended to hybrid dynamical systems defined on a directed graph; each vertex corresponds to a state space and each

This paper shows that within the space of all LTI systems, equipped with the Zariski topology, the set of impulse controllable systems contains an open dense set of systems; in other words, impulse controllable systems are generic. This genericity persists for many closed subsets of LTI systems of interest, such as the class of singular descriptor systems.

This work revisits the constant stepsize stochastic approximation algorithm for tracking a slowly moving target and obtains a bound for the tracking error that is valid for the entire time axis, using the Alekseev nonlinear variation of constants formula. It is the first non-asymptotic bound for the entire time axis in the sense that it is not based on the vanishing stepsize limit and associated limit

We establish characterizations of weak input-to-state stability for abstract dynamical systems with inputs, which are similar to characterizations of uniform and of strong input-to-state stability established in a recent paper by A. Mironchenko and F. Wirth. We also investigate the relation of weak input-to-state stability to other common stability concepts, thus contributing to a better theoretical

Symmetries, e.g. rotational and translational invariances for the class of mechanical systems, allow to characterize solution trajectories of nonlinear dynamical systems. Thus, the restriction to symmetry-induced dynamics, e.g. by using the concept of motion primitives, may be considered as a quantization of the system. Symmetry exploitation is well established in both motion planning and control.

In a recent paper by Bourdin and Trélat, a version of the Pontryagin maximum principle (in short, PMP) has been stated for general nonlinear finite-dimensional optimal sampled-data control problems. Unfortunately, their result is only concerned with fixed sampling times, and thus, it does not take into account the possibility of free sampling times. The present paper aims to fill this gap in the literature

We provided a detailed study of the Schur–Cohn stability algorithm for Schur stable polynomials of one complex variable. Firstly, a real analytic principal \(\mathbb {C}\times \mathbb {S}^1\)-bundle structure in the family of Schur stable polynomials of degree n is constructed. Secondly, we consider holomorphic \(\mathbb {C}\)-actions \(\mathscr {A}\) on the space of polynomials of degree n. For each

This paper deals with the analysis of the internal control of a parabolic PDE with nonlinear diffusion, nonlocal in space. In our main result, we prove the local exact controllability to the trajectories with distributed controls, locally supported in space. The main ingredients of the proof are a compactness–uniqueness argument and Kakutani’s fixed-point theorem in a suitable functional setting. Some

In this paper, we investigate connectedness and convexity properties of the subspace \(\mathbf {L}_{n,m}^c(\mathbb {R})\) of controllable input pairs \((A,B)\in \mathbf {L}_{n,m}(\mathbb {R}):= \mathbb {R}^{n\times n}\times \mathbb {R}^{n\times m}\). We introduce three restricted convexity properties (“dense”, “almost sure” and “generic” convexity). In order to prove that the space \(\mathbf {L}_{n

We study a sequence of many-agent exit time stochastic control problems, parameterized by the number of agents, with risk-sensitive cost structure. We identify a fully characterizing assumption, under which each such control problem corresponds to a risk-neutral stochastic control problem with additive cost, and sequentially to a risk-neutral stochastic control problem on the simplex that retains only

In this paper, the problem of robust stability for linear time-varying implicit dynamic equations is generally studied. We consider the effect of uncertain structured perturbations on all coefficient matrices of equations. A formula of stability radius with respect to dynamic structured perturbations acting on the right-hand side coefficients is obtained. In case where structured perturbations affect

The Grassmann manifold\(Gr_m({\mathbb {R}}^n)\) of all m-dimensional subspaces of the n-dimensional space \({\mathbb {R}}^n\)\((m

This paper deals with some reachability issues for piecewise linear switched systems with time-dependent coefficients and multiplicative noise. Namely, it aims at characterizing data that are almost reachable at some fixed time \(T>0\) (belong to the closure of the reachable set in a suitable \({\mathbb {L}}^2\)-sense). From a mathematical point of view, this provides the missing link between approximate