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

We propose a method to outer bound forward reachable sets on finite horizons for uncertain nonlinear systems with polynomial dynamics. This method makes use of time-dependent polynomial storage functions that satisfy appropriate dissipation inequalities that account for time-varying uncertain parameters, L2 disturbances, and perturbations Δ characterized by integral quadratic constraints (IQCs) with

We introduce and study the turnpike property for time-varying shapes, within the viewpoint of optimal control. We focus here on second-order linear parabolic equations where the shape acts as a source term and we seek the optimal time-varying shape that minimizes a quadratic criterion. We first establish existence of optimal solutions under some appropriate sufficient conditions. We then provide necessary

We study discrete-time (m,n)-multirate systems on separable Hilbert spaces, solving the problem of approximating such a system by one which has a shorter multirate period (m∕q,n∕q), optimally in the Hilbert–Schmidt norm. We work in the state–space setting, providing two state–space representations of the optimal approximant which are expressed in terms of a state–space representation of the original

In this work, we mainly study the exact controllability of stochastic differential equations with memory. For time invariant systems, by applying forward backward stochastic differential equations, some rank criteria ensuring systems’ exact controllability are provided. For time variant systems, equivalent conditions guaranteeing systems’ exact controllability are given. For deterministic systems,

In this paper, we study a containment control problem for second-order multi-agent systems in the presence of convex position constraints and switching graphs. A distributed algorithm with a nonlinear projection operator is proposed to guarantee that each agent eventually converges into the convex hull spanned by some given multiple static points, while the position of each agent is kept lying in a

Dynamical systems driven by two or multi-timescales arise in systems science, natural and social sciences quite naturally. Work done by Vivek S. Borkar (1997) on stochastic approximation driven by two timescales and later by others pave the pathway for wide applications of such systems. In this article we provide weak convergence of such systems for the linear case.

A general theorem is proved on the stability of an equilibrium point of a nonlinear delay differential equation, in the critical case when zero is a simple root of the characteristic equation for linearized equation. It extends the classical theorem of Malkin from the case of ordinary differential equations. An application to the case of a electrohydraulic governor with delay in control is given.

We consider abstract second order evolution equations with unbounded feedback with delay. If the delay term is small enough, we rigorously prove the fact that the system with delay has the same decay rate than the one without delay. Some old and new results easily follow.

Fully probabilistic design (FPD) of control strategies models both the closed control loop and control objectives by joint probabilities of involved variables. It selects the optimal strategy as the minimiser of Kullback–Leibler (KL) divergence of the closed-loop model to its ideal counterpart expressing the control objectives. Since its proposal (Kárný, 1996) and general algorithmisation (Kárný and

In this paper, we propose an online alternating minimization (OAM) algorithm to estimate the sparse coefficients of stochastic regression models from time-series data. We apply the alternating minimization (AM) directly to the penalty function of the variant of the least absolute shrinkage and selection operator (Lasso), which leads to convex subproblems, and thereby can be solved efficiently. Moreover

We study the stabilization of two vibrating strings with variable physical coefficients joined by a feedback control at a common endpoint and subject to non-symmetrical boundary conditions. We prove that this system is exponentially stable under sufficient conditions on the physical coefficients. For this result, we show that the system has a sequence of the generalized eigenvectors which forms a Riesz

A design of a distributed observer is proposed for continuous-time systems with nonlinear observer nodes such that the estimation errors converge in a finite time to zero. By taking advantage of individual observability decompositions, the designs for the locally observable and the unobservable substate are made independent from each other. For the observable substate of each node, standard centralized

We consider the stability region of monic polynomials in the coefficient space. Starting from specially chosen stable points we define polytopes, whose edges are either stable or belong to the stability boundary. Therefore by the Edge Theorem the interiors are stable. Stable polytopes, in the reverse directions which are directed to infinity have been studied in the work (Dzhafarov et al., 2019). Some

This paper concerns a class of uncertain linear quantum systems subject to quadratic perturbations in the system Hamiltonian. In order to obtain improved control performance, we propose two methods to design coherent robust controllers for the system. One is to formulate a static quantum controller by adding a controller Hamiltonian to the given system, and the other is to build a dynamic quantum controller

This paper proposes a quadratic programming based cooperative-distributed model predictive control strategy, with stability and feasibility guarantees. Its feasibility is achieved by considering slacked terminal constraints of the optimization problem without the assessment of an invariant terminal set. The stability proof uses Lyapunov arguments and is carried out by properly setting the move suppression

This article addresses a fixed-time tracking problem of uncertain nonlinear system. Firstly, a sufficient condition for practical fixed-time stability is given. Secondly, on the basis of the sufficient condition, a novel adaptive control strategy is proposed. The designed parameter adaptive law is expressed as a nonlinear differential equation, which is different from the existing adaptive design method

This paper is concerned with the problems of stability analysis and stabilization synthesis for a class of discrete-time semi-Markov jump linear systems. The novel sufficient stability conditions for such systems are obtained, in which the sojourn times are allowed to be unbounded, and thus these conditions are applicable to discrete-time Markov jump linear systems. Moreover, by truncating the sojourn

This paper studies the formation control problem in clustered network systems composing of linear agents that are subjected to state constraints. In each cluster, there exists an agent called a leader who can communicate with other leaders outside of its cluster at some specific discrete instants. Moreover, the continuous-time communication structure in each cluster is represented by a fixed and undirected

We consider distributed control of a class of 1-D parabolic PDEs under distributed in-domain point actuation and measurements in the presence of control constraints. This class includes unstable diffusion-reaction equations as well as stable Burgers’ equations, where we aim to locally improve the convergence. We suggest an observer-based control law that employs the averaged values of the observer

This paper is devoted to study the pth moment exponential stability problem for a class of stochastic delay nonlinear systems (SDNSs) driven by G-Brownian motion. The delays considered in this paper are time-varying delays τi(t)∈[0,τ] (1≤i≤3) and they are not required to be differentiable. Different from the traditional methods, we use a new approach: stochastic delay feedback controls. We firstly

In this paper, we study a time inconsistent asset–liability management problem of an insurance firm, where the liability is controllable, the surplus is partially observable. We introduce the open-loop equilibrium premium operator (OLEPO), by which the open-loop equilibrium premium strategy (OLEPS) can be represented. We give the characterization and explicit forms of OLEPO, and also obtain the existence

It is known that Kalman–Bucy filter is stable with respect to initial conditions under the assumptions of uniform complete controllability and uniform complete observability. In this paper, we prove the stability of Kalman-Bucy filter for the case of noise free dynamical system, i.e., for deterministic processes. The earlier stability results cannot be applied for this case, as the system is not controllable

We consider output trajectory tracking for a class of uncertain nonlinear systems whose internal dynamics may be modelled by infinite-dimensional systems which are bounded-input, bounded-output stable. We describe under which conditions these systems belong to an abstract class for which funnel control is known to be feasible. As an illustrative example, we show that for a system whose internal dynamics

This paper studies the problem of global asymptotic stabilization for a class of upper-triangular systems with large delays in the state and input. Using the idea of feedback domination, we develop a Lyapunov-Krasovskii method for the design of time-invariant, memoryless linear state and output feedback controllers, achieving global asymptotic stabilization of the closed-loop systems under a linear

The objective of containment control in multi-agent systems is to design control algorithms for the followers to converge to the convex hull spanned by the leaders. Sampled-data based containment control algorithms are suitable for the cases where the power supply and sensing capacity are limited, due to their low-cost and energy-saving features resulting from discrete sensing and interactions. In

We consider the tracking problem of a point moving in a three-dimensional space using only measurements of distance from a set of reference points. The approach followed in this paper is to derive a linear map with multiplicative noise through a quadratic transformation of the distance measurements. A suitable rewriting by means of an output injection term makes the multiplicative noise of the linear

For control systems, the local regularity of the minimum time function τmin in the absence of state constraints has been extensively studied and related both to inward-pointing conditions and to small-time controllability in the neighborhood of a closed target C. In the presence of state constraints, assessing this regularity is crucial to ensure the existence of solutions when perturbing the initial

This paper considers L2 and BIBO stability and stabilization issues for systems with time-varying delays which can be of retarded or neutral type. An important role is played by a nominal system with fixed delays which are close to the time-varying ones. Under stability or stabilizability conditions of this nominal system, sufficient conditions are given in order to ensure similar properties for the

We consider the strong stabilization of small amplitude gravity water waves in a two dimensional rectangular domain. The control acts on one lateral boundary, by imposing the horizontal acceleration of the water along that boundary, as a multiple of a scalar input function u, times a given function h of the height along the active boundary. The state z of the system consists of two functions: the water

In this paper we propose a novel stochastic consensus seeking algorithm based on the introduction of a nonlinear transformation aimed at robustification with respect to noise influence. The introduced nonlinear transformation is selected according to the methodology of stochastic approximation and robust statistics. The proposed algorithm represents a general nonlinear stochastic consensus seeking

In this note we reflect on the work and life of Ruth Curtain. This article is strongly based on the article (Zwart, 2019), which was written in Dutch.

We consider a finite-horizon continuous-time optimal control problem with nonlinear dynamics, an integral cost, control constraints and a time-varying parameter which represents perturbations or uncertainty. After discretizing the problem we employ a Model Predictive Control (MPC) approach by first solving the problem over the entire remaining time horizon and then applying the first element of the

This paper investigates the cooperative output regulation problem of heterogeneous linear multi-agent systems under singular dynamics and adaptive distributed protocol. Considering the followers do not know the matrix information of the leader, two novel adaptive distributed protocols are developed based on the state and measurement output. Then, as the technology basis of the cooperative output regulation

A new formulation of the fault-tolerant control (FTC) problem in presence of disturbances is given, based on fault estimation (FE). Two solutions/controllers to this problem are given. The first one is a new controller that includes a fault estimator, a nominal controller and a fault accommodation block. This controller requires the strict conditions that the nominal controller is stable, and that

This paper studies the problem of synchronization in a dynamical network, where we identify the nodes of the undirected graph as identical Lur’e-type nonlinear systems and the edges as heterogeneous and asymptotically stable linear systems, i.e., both of the nodes and edges are dynamical systems. It is shown that sufficiently fast convergence rate of each edge guarantees the dynamic edges degenerate

In this work, we establish different control design approaches for discrete-time systems, which build upon the notion of finite-step control Lyapunov functions (fs-CLFs). The design approaches are formulated as optimization problems and solved in a model predictive control (MPC) fashion. In particular, we establish contractive multi-step MPC with and without reoptimization and compare it to classic

Sadeghi et al. considered a bottleneck system with periodic arrival rate, and proved that a constant-rate arrival maximizes the time-averaged output rate among all periodic arrival rates. Here we provide a short and elementary proof of this result, without use of optimal control theory. The new approach developed here allows us to prove an extension of the result to the case of a general non-periodic

The paper is concerned with distributed optimal resource allocation problems on multi-agent systems that each agent has single-integrator dynamics. For the single-integrator multi-agent system, a local feasible set constraint is introduced and a distributed algorithm with projection operator is proposed. Compared with the algorithms in the existing literature on the single-integrator multi-agent systems

This paper promotes an idea of describing singularities of non-holonomic robotic systems by normal forms under feedback of associated control systems. In order to increase the explanatory power of the presentation this idea has been applied to the dynamics of a planar free-floating space robot composed of a base (a spacecraft) and a k-DOF (Degrees Of Freedom) on board manipulator. A general Lagrangian

In this paper, the problem of distributed estimation in linear discrete-time large-scale stochastic systems is explored. The objective is to estimate the states as well as the unknown inputs of the system under partial observation of the system states by utilizing a number of estimators. The main assumption is that the estimator at each node of the system can exchange its estimated state with the neighboring

This article presents the dynamic interpolation problem for locomotion systems evolving on a trivial principal bundle Q. Given an ordered set of points in Q, we wish to generate a trajectory which passes through these points by synthesizing suitable controls. The global product structure of the trivial bundle is used to obtain an induced Riemannian product metric on Q. The squared L2-norm of the covariant

This paper addresses the stability analysis of infinite-dimensional sampled-data systems under unbounded perturbations. We present two classes of unbounded perturbations preserving the exponential stability of sampled-data systems. To this end, we investigate the continuity of strongly continuous semigroups with respect to their generators, considering the uniform operator topology.

This paper deals with the exponential input-to-state stabilization with respect to boundary disturbances of a class of diagonal infinite-dimensional systems via delay boundary control. The considered input delays are uncertain and time-varying. The proposed control strategy consists of a constant-delay predictor feedback controller designed on a truncated finite-dimensional model capturing the unstable

In our previous work, we investigated detectability of discrete event systems, which is defined as the ability to determine the current and subsequent states of a system based on observation. For different applications, we defined four types of detectabilities: (weak) detectability, strong detectability, (weak) periodic detectability, and strong periodic detectability. In this paper, we extend our

This paper studies monotone tridiagonal systems with negative feedback. These systems possess the Poincaré-Bendixson property, which implies that, if orbits are bounded, if there is a unique steady state and this unique steady state is asymptotically stable, and if one can rule out periodic orbits, then the steady state is globally asymptotically stable. Two different approaches are discussed to rule

Our previous work considers detectability of discrete event systems which is to determine the current state and subsequent states of a system based on event observation. We assume that event observation is static, that is, if an event is observable, then all its occurrences are observable. However, in practical systems such as sensor networks, event observation often needs to be dynamic, that is, the

After stimulation by chemoattractant, Dictyostelium cells exhibit a rapid response. The concentrations of several intracellular proteins rise rapidly reaching their maximum levels approximately 5-10 seconds, after which they return to prestimulus levels. This response, which is found in many other chemotaxing cells, is an example of a step disturbance rejection, a process known to biologists as perfect