In this paper we consider the problem of position tracking and error boundedness for a master–slave teleoperation system when the communication channel is characterized by a time-varying stochastic delay. In particular, we assume the delay to be a time-varying Markov regime switching process. Our solution is based on a suitable proportional–derivative (PD) like controller. Exploiting a Lyapunov–Krasovskii

The well-posedness of abstract boundary control systems with dynamic boundary conditions (i.e., boundary conditions evolving according to an operator semigroup acting on the boundary space) is established . Here, the boundary feedback operator is unbounded which makes the investigation more interesting in many applications. The positivity of such problem is well studied. By exploiting the positivity

We here show that the family of finite-dimensional, continuous-time, passive, linear, time-invariant systems can be characterized through the structure of maximal matrix-convex cones, closed under inversion. Moreover, this observation unifies three setups: (i) differential inclusions, (ii) matrix-valued rational functions, (iii) realization arrays associated with rational functions. It turns out that

Consider a set of single-input, single-output nonlinear systems whose input–output maps are described only in terms of convergent Chen–Fliess series without any assumption that finite dimensional state space models are available. It is shown that any additive or multiplicative interconnection of such systems always has a Chen–Fliess series representation that can be computed explicitly in terms of

This paper investigates the time-varying formation tracking (TVFT) control problem considering a constant input delay and unknown external disturbances for the general linear multi-agent system (MAS) under a directed communication graph containing a spanning tree. To achieve that, a new time-varying shape format is firstly proposed. Then, a disturbance observer (DO) is introduced to compensate the

This paper presents an efficient algorithm based on the alternating direction method of multipliers (ADMM) for an ℓ1-norm minimization problem with linear equality and box constraints. In the ADMM iterations, sub-problems, called proximal minimizations, are solved to obtain the next updating points by exploiting closed formulae. Furthermore, the local R-linear convergence is established by analysis

The problem of orbital stabilization of underactuated mechanical systems with one passive degree-of-freedom (DOF) is revisited. Virtual holonomic constraints are enforced using a continuous controller; this results in a dense set of closed orbits on a constraint manifold. A desired orbit is selected on the manifold and a Poincaré section is constructed at a fixed point on the orbit. The corresponding

In this paper we study approximations to the infinite-horizon quadratic optimal control problem for linear systems that may be only asymptotically stabilizable. For linear systems, this issue only arises with infinite-dimensional systems. We provide sufficient conditions which guarantee when approximations to the optimal feedback result in the cost converging to the optimal cost. One technique for

In this paper, we study the boundary feedback stabilization of a quasilinear hyperbolic system with partially dissipative structure. Thanks to this structure, we construct a suitable Lyapunov function which leads to the exponential stability to the equilibrium of the H2 solution. As an application, we also obtain the feedback stabilization for the Saint-Venant-Exner model under physical boundary conditions

We address the state feedback stabilization of linear systems with input delay using the so-called act-and-wait control strategy. The latter approach induces an analysis of the closed-loop stability based on a finite-dimensional monodromy operator, and rendering this matrix nilpotent results in fixed-time stability. We show that any controllable planar system can be stabilized in a fixed time, and

This paper deals with partially-observed optimal control problems for the state governed by stochastic differential equation with delay. We develop a stochastic maximum principle for this kind of optimal control problems using a variational method and a filtering technique. Also, we establish a sufficient condition without assumption of the concavity. Two examples that shed light on the theoretical

This paper presents a maximum principle-based approach in the establishment of ISS-like estimates for a class of nonlinear parabolic partial differential equations (PDEs) with variable coefficients and different types of nonlinear boundary conditions on higher dimensional domains. Comparing with the existing literature, the ISS-like estimates established in this paper are independent of the nonlinear

We develop a hybrid boundary feedback law for a class of scalar, linear, first-order hyperbolic PDEs, for which the state measurements or the control input are subject to quantization. The quantizers considered are Lipschitz functions, which can approximate arbitrarily closely typical piecewise constant, taking finitely many values, quantizers. The control design procedure relies on the combination

In this brief note we pose, and solve, the problem of robustification of controller designs where the actuator dynamics was neglected. This situation is very common in applications where, to validate the assumption that the actuator dynamics can be neglected, a high-gain inner-loop that enforces a time-scale separation between the actuator and the plant dynamics is implemented. Of course, the injection

Adaptive synchronization protocols for heterogeneous multi-agent network are investigated. The interaction between each of the agents is carried out through a directed graph. We highlight the lack of communication between agents and the presence of uncertainties in each system among the conventional problems that can arise in cooperative networks. Two methodologies are presented to deal with the uncertainties:

This paper proposes a generalized weak rigidity theory, and aims to apply the theory to formation control problems with a gradient descent flow law. The generalized weak rigidity theory is utilized in order to characterize desired rigid formations by a general set of pure inter-agent distances and subtended angles, where the rigid formation shape with distances and subtended angles is determined up

Often only some aspect of the state needs to be estimated, not the whole state. This problem is referred to as output estimation Also, there may be disturbances other than Gaussian noise. In such situations a Kalman filter may not be the most appropriate estimator. Two alternative approaches are to reduce the H2 or H∞ output estimation error. A derivation of both types of estimators for output estimation

This paper focuses on a class of stochastic systems describing tumor-immune dynamics. The underlying systems are given by stochastic differential equations. Our study concentrates on longtime behavior. A sharp threshold-type condition is obtained, which characterizes the dynamic systems, and pinpoints sufficient and nearly necessary conditions for persistence and extinction. Examples and numerical

We present a formation control algorithm for agents with extended unicycle dynamics that include orientation kinematics on SO(m), first-order uncertain speed dynamics, and hard constraints on speed. The desired interagent positions are expressed in a leader-fixed coordinate frame. Thus, the desired interagent positions vary in time as the leader-fixed frame rotates. We assume that each agent has relative-position

Dwell-time based stability conditions for a class of LPV systems with piecewise constant parameters under time-varying delay are derived using clock-dependent Lyapunov–Krasovskii functional. Sufficient synthesis conditions for clock-dependent gain-scheduled state-feedback controllers ensuring L2-performance are also provided. Several numerical and practical examples, to illustrate the efficacy of the

In this paper, we formulate and investigate the leader-following almost output consensus problem for linear multi-agent systems with disturbance affected unstable zero dynamics. Conditions on the communication topology, agent dynamics and the way the disturbances affect the zero dynamics are established under which low-and-high gain based consensus protocols are designed. These protocols are shown

We present an algorithm for the time-inversion of diffusion–advection equations, based on the adjoint methodology. Given a final state distribution our main aim is to recover sparse initial conditions, constituted by a finite combination of Kronecker deltas, identifying their location and mass. We discuss the strengths of the adjoint machinery and the difficulties that are to be faced, in particular

We consider a class of nonlinear optimal control problems in which the aim is to minimize control variation subject to an upper bound on the system cost. This idea of sacrificing some cost in exchange for less control volatility—thereby making the control signal easier and safer to implement—is explored in only a handful of papers in the literature, and then mainly for piecewise-constant (discontinuous)

Motivated by the goal of having a building block in the design of direct data-driven controllers for nonlinear systems, we show how, for an unknown discrete-time bilinear system, the data collected in an offline open-loop experiment enable us to design a feedback controller and provide a guaranteed underapproximation of its basin of attraction. Both can be obtained by solving a linear matrix inequality

Opacity is a privacy property which aims to determine whether the “secret” of a system can be deduced by an outside intruder. In this paper, we investigate the enforcement of opacity using insertion functions which insert additional events if necessary to modify the output of the system. Inspired by the existing insertion mechanisms, we propose a mechanism named k-memory-embedded insertion mechanism

In natural resource management, decision-makers often aim at maintaining the state of the system within a desirable set for all times. For instance, fisheries management procedures include keeping the spawning stock biomass over a critical threshold. Another example is given by the peak control of an epidemic outbreak that encompasses maintaining the number of infected individuals below medical treatment

This paper considers the decentralized control of vehicle platoons and gives necessary and sufficient conditions for the existence of such controllers. Specifically, we consider a predecessor–follower control structure in which a vehicle is responsible for tracking of a desired spacing policy with respect to its predecessor, regardless of the control action of the latter. By building on geometric control

We consider operator-valued positive-real functions H and show that the intersections of the point, continuous and residual spectra of H(s) with the imaginary axis do not depend on s. In particular, if H is positive real and H(z) is invertible for some z in the open right-half plane, then H(s) is invertible for all s in the open right-half plane. Furthermore, we prove that the eigenspace of H(s) corresponding

Reducible state variables are important for the study of reduced-order observer and control design of logical control networks (LCNs). This paper studies the number of reducible state variables of LCNs. Based on the upper bound of reducible state variables, several sufficient/necessary conditions are presented for the number of reducible state variables. In addition, using the regular subspace theory

While the asymptotic output tracking property has been proven for many nonlinear adaptive control systems, their higher-order output tracking property has not been reported. In this paper, the higher-order derivative convergence of the output tracking error e(t) is studied for nonlinear adaptive control systems using the feedback linearization design. It is proven that not only each error component

We solve an adaptive control problem for n+1 hyperbolic systems using collocated sensing and control, extending recent results for adaptive control of 2×2 systems and systems with non-collocated sensing and control. The boundary condition has an affine form with both unknown reflective and additive parameters and can be used to model well–reservoir interactions in oil and gas drilling where properties

In this paper, we consider exponential stabilization for a 1-D wave equation with variable coefficients and Neumann boundary actuation. A novel transformation is constructed to convert the wave equation into an equation of the same type with constant coefficient and low order term. By using the backstepping approach, we design a state observer via non-collocated boundary displacement and velocity measurement

This paper concerns the detectability problem of Boolean networks with disturbance inputs using the semi-tensor product approach. Detectability like observability describes the ability of the system state to be indirectly measured, which is an important issue to be considered in designing the controller. Four kinds of detectability, weak, weak periodical, strong and strong periodical ones, are defined

In some applications one is interested in having a state–space realization with nonnegative matrices (positive realization) of a given transfer function and it is known that such a realization may have a dimension strictly larger than the order of the transfer function itself. Moreover, in most cases, it is desirable to have a realization with minimal dimension. Unfortunately, it is not known, to date

In the paper we consider the problem of exact observability of a general class of distributed parameter systems in Hilbert spaces. We show that under some conditions on asymptotic behavior of the spectrum of the differential operator the system is not exact observable in default topologies, and find a stronger topology for state observation for which the system becomes exactly observable. We illustrate

In this study, we propose a new method to design a smooth implicit control Lyapunov function and a smooth control law for a multi-integrator system with an input constraint. The proposed controller is almost linear near the origin, and it tends to a homogeneous controller of the previous implicit Lyapunov function methods as the state goes to infinity. The proposed method can be used for the backstepping

This contribution deals with energy-based in-domain control of systems governed by partial differential equations with spatial domain up to dimension two. We exploit a port-Hamiltonian system description based on an underlying jet-bundle formalism, where we restrict ourselves to systems with 2nd-order Hamiltonian. A certain power-conserving interconnection enables the application of a dynamic control

This work studies the stationary distribution of stochastic Lotka–Volterra population dynamics in state-dependent random environments. We first use the stochastic comparison approach to handle the difficulty caused by the state-dependent regime-switching. Then the ergodic property and positive recurrence are investigated by the theory of M-matrix under small perturbation. The mean of the stationary

The present article gathers the analysis of non-asymptotic convergence rates (finite-time and fixed-time) with the property of input-to-state stability. Theoretical tools to determine this joint property are presented for the case where an explicit ISS Lyapunov function is known, and when it remains in implicit form (e.g. as a solution of an algebraic equation). For the case of finite-time input-to-state

In this paper, we propose an obstacle avoidance controller for a disk-shaped holonomic robot with double-integrator dynamics and local sensing. The control objective is for the robot to converge to a target velocity while avoiding collisions with strictly convex obstacles in an unbounded environment. We assume that the robot has no information about the location and geometry of the obstacles, has no

In this paper, we consider multiple-attackers schedule problem against remote state estimation in cyber-physical systems (CPSs). Compared with the existing results in which only one type of attacker is considered, we aim to address the case that Denial-of-Service (DoS) attacker and linear deception attacker exist in CPSs simultaneously. With limited resource, the two attackers have to, cooperatively

In the presence of unmodelled dynamics and uncertainties with no a priori constant bounds, conventional robust adaptation strategies for switched systems cannot allow the control gains of inactive subsystems to remain constant during inactive intervals: vanishing gains are typically required in order to prove bounded stability. As a consequence, these strategies, known in literature as leakage-based

We prove an inverse mapping theorem on a metric space of controls that allows to “control” final points of trajectories of a nonlinear system. More precisely, our result provides local distance estimates of arbitrary controls from feasible ones. As an application we derive second-order necessary optimality conditions for L1-local minima for the Mayer optimal control problem with a general control constraint

We study the non-autonomous version of an infinite-dimensional linear port-Hamiltonian system on an interval [a,b]. Employing abstract results on evolution families, we show C1-well-posedness of the corresponding Cauchy problem, and thereby existence and uniqueness of classical solutions for sufficiently regular initial data. Further, we demonstrate that a dissipation condition in the style of the

Primal–dual gradient dynamics that find saddle points of a Lagrangian have been widely employed for handling constrained optimization problems. Building on existing methods, we extend the augmented primal–dual gradient dynamics (Aug-PDGD) to incorporate general convex and nonlinear inequality constraints, and we establish its semi-global exponential stability when the objective function is strongly

We present a new design methodology of sampled-data observers that unifies and generalizes many existing design methodologies. The approach is based on continuous-time observers that feature two characteristics: (i) exhibit exponential convergence in the noiseless case with respect to a given Observer Lyapunov Function, and (ii) satisfy an Input-to-Output Stability property with respect to output measurement

We consider the problem of distributed secondary frequency regulation in power networks such that stability and an optimal power allocation are guaranteed. This is a problem that has been widely studied in the literature, where two main control schemes have been proposed, usually referred to as ’Primal-Dual’ and ’distributed averaging proportional–integral (DAPI)’ respectively. However, each has its

In this note, an effort is put forward to make two revisions with respect to mistakes in the derivations of Khan et al. (2019). The main result of Khan et al. (2019) claimed that the Laplacian matrix L is a symmetric matrix. However, the paper only assumed that the jointly connected graph contains a spanning tree. Clearly, L is a symmetric matrix if and only if the joint graph is strongly connected

We consider a central bank strategy for maintaining a two-sided currency target zone, in which an exchange rate of two currencies is forced to stay between two thresholds. To keep the exchange rate from breaking the prescribed barriers, the central bank is generating permanent price impact and thereby accumulating inventory in the foreign currency. Historical examples of failed target zones illustrate

It is well known that stability is one of most important topics in economy and control. In this paper, we focus on the practical stability problem for a class of stochastic age-dependent (vintage) capital system with Lévy noise. Compared with the classical Lyapunov stability theory, practical stability can depict not only qualitative behavior but also quantitative properties, such as specific trajectory

Models are of great importance for many purposes, including control design. However, most real systems are complex, frequently nonlinear and first principle models tend to be too complicated, or even unknown, for control-oriented modeling. Therefore, data-based models are often used; however, since most likely the true system is not an element of any assumed model class, the available model is an approximation

The state feedback regulation of nonlinear systems of order n in parametric strict-feedback form is considered. A simple, easy to tune, adaptive control with projected parameter estimates is proposed. The uncertain parameter vector is estimated by n parallel vector estimates whose differences are constrained to tend asymptotically to zero. When the uncertain parameter vector is identifiable, the closed

This paper discusses the stability properties of a robust nonlinear model predictive control (NMPC) scheme that is based on a multi-stage optimization formulation. The use of a scenario tree to represent the uncertainty makes it possible to formulate a closed-loop robust approach with recourse which improves the open-loop approach in terms of performance and domain of attraction. We show that a straightforward

In the literature, existence of mean-field equilibria has been established for discrete-time mean field games under both the discounted cost and the average cost optimality criteria. In this paper, we provide a value iteration algorithm to compute stationary mean-field equilibrium for both the discounted cost and the average cost criteria, whose existence proved previously. We establish that the value

In this paper, we study the identification problem of strictly passive systems from frequency response data. We present a simple construction approach based on the Mayo–Antoulas generalized realization theory that automatically yields a port-Hamiltonian realization for every strictly passive system with simple spectral zeros. Furthermore, we discuss the construction of a frequency-limited port-Hamiltonian

This paper is concerned with the existence and uniqueness, the almost sure stability with general decay rate (including almost sure exponential stability, almost sure polynomial stability and almost sure logarithmic stability) for the global solution of nonlinear neutral stochastic functional hybrid differential equations with Lévy noise. The key technique used is the method of Lyapunov function, nonnegative

This paper is concerned with the linear quadratic regulation (LQR) problem for discrete-time systems involving input delay and colored multiplicative noise. Due to the correlation of the adjoining state, this problem will be more complicated than the case of white noise. In this paper, the necessary and sufficient condition for the solvability of optimal control problem is presented by solving the

We develop a convex analysis approach for solving LQG optimal control problems and apply it to major–minor (MM) LQG mean–field game (MFG) systems. The approach retrieves the best response strategies for the major agent and all minor agents that attain an ϵ-Nash equilibrium. An important and distinctive advantage to this approach is that unlike the classical approach in the literature, we are able to

This paper proposes a novel method to compute an upper bound on the induced L2-gain for a linear parameter varying (LPV) system with rational parameter dependence. The proposed method relies on a standard dissipation inequality condition. The storage function is a quadratic function of the state and a rational function of the parameters. The specific parameter dependence is restricted to involve (fixed)

We investigate the stabilizability of discrete-time linear switched systems, when the sole control action of the controller is the switching signal, and when the controller has access to the state of the system in real time. Despite their apparent simplicity, determining if such systems are stabilizable appears to be a very challenging problem, and basic examples have been known for long, for which