Safety requirements in dynamical systems are commonly enforced with set invariance constraints over a safe region of the state space. Control barrier functions, which are Lyapunov-like functions for guaranteeing set invariance, are an effective tool to enforce such constraints and guarantee safety when the system is represented as a point in the state space. In this paper, we introduce extent-compatible

In this paper, multi-agent dynamic optimization with a coupling constraint is studied. The aim is to minimize a strongly convex social cost function, by considering a linear stochastic dynamics for each agent and also coupling constraints among the agents. In order to handle the coupling constraint and also, to avoid high computational cost imposed by a centralized method for large scale systems, the

One proves that the moving interface of a two-phase Stefan problem on Ω⊂Rd, d=1,2,3, is controllable at the end time T by a Neumann boundary controller u. The phase-transition region is a mushy region {σtu;0≤t≤T} of a modified Stefan problem and the main result amounts to saying that, for each Lebesgue measurable set Ω∗ with positive measure, there is u∈L2((0,T)×∂Ω) such that Ω∗⊂σTu. To this aim, one

We provide novel reduced-order observer designs for continuous-time nonlinear systems with measurement error. Our first result applies to systems with continuous output measurements, and provides observers that converge in a fixed finite time that is independent of the initial state when the measurement error is zero. Our second result applies under discrete measurements, and provides observers that

Two-phase flows are frequently modelled and simulated using the Two-Fluid Model (TFM) and the Drift Flux Model (DFM). This paper proposes Stokes–Dirac structures with respect to which port-Hamiltonian representations for such two-phase flow models can be obtained. We introduce a non-quadratic candidate Hamiltonian function and present dissipative Hamiltonian representations for both models. We then

This paper deals with the robust stability of Volterra differential–algebraic equations. We consider the solvability of the equation and then the preservation of exponential stability under small perturbations. The so-called Bohl–Perron type theorem is also studied.

A class of nonautonomous linear ordinary differential equations is considered. The coefficient matrices are Metzler matrices with zero column sums such that their directed graphs have a common directed spanning tree. It is shown that if the off-diagonal elements of the coefficients are uniformly positive along the common directed spanning tree, then under mild additional assumptions the convergence

In this paper, an attitude synchronization problem of multiple rigid-body systems is investigated by using an event-based approach. The leader and followers are described by unit quaternions. A nonlinear distributed observer with event-triggered observations is proposed to estimate the attitude and angular velocity of the leader without continuous information exchange. The triggering mechanism is intermittent

In this paper, we show that a linear system with distributed state delay can be approximated by a linear delay-free system that has the same state dimension as the original system if a so-called smallness condition holds. The smallness condition is an inequality which the maximum lag and norms of the system matrices have to satisfy. The eigenvalues of the approximate system correspond to the dominant

Although adaptive parameter estimation (APE) has been studied for decades, quantifying the transient estimation error convergence performance (e.g., overshoot and convergence rate) that is essential for system safety and reliability is more difficult than the steady-state convergence analysis. To address this issue, a new APE method with prescribed convergence performance is proposed in this paper

This paper is concerned with boundary control for a class of coupled time fractional order reaction–advection–diffusion (FRAD) systems with non-constant coefficients (space-dependent coefficients) by state feedback. Partial differential equation (PDE) backstepping makes available to stabilize coupled time FRAD systems modeled by fractional PDEs. With boundary controller design and discussion on well-posedness

Given a linear time-periodic control system in a Hilbert space with a bounded control operator, we present a characterization of periodic stabilization in terms of a detectability inequality. Similar characterization was built up in Trélat et al. (2020), for time-invariant systems.

This paper deals with the H2 suboptimal output synchronization problem for heterogeneous linear multi-agent systems. Given a multi-agent system with possibly distinct agents and an associated H2 cost functional, the aim is to design output feedback based protocols that guarantee the associated cost to be smaller than a given upper bound while the controlled network achieves output synchronization.

In this paper stabilization of switched differential algebraic equations is considered, where Dirac impulses in both the input and the state trajectory are to be avoided during the stabilization process. First it is shown that stabilizability of a switched DAE and the existence of impulse-free solutions are merely necessary conditions for impulse-free stabilizability. Then necessary and sufficient

Models can be wrong and recognising their limitations is important in financial and economic decision making under uncertainty. Robust strategies, which are least sensitive to perturbations of the underlying model, take uncertainty into account. Interpreting the explicit set of alternative models surrounding the baseline model has been difficult so far. We specify alternative models via a time-consistent

This paper is concerned with one kind of stochastic optimal control problem of mean-field jump–diffusion system with moving-average as well as pointwise delays. By means of the maximum principle, both necessary and sufficient optimality conditions are established. Two kinds of adjoint equations are used, which are shown to be equivalent. That is, a unified adjoint equation is provided.

The study of logical matrix factorization provides a new insight into the matrix dimension reduction problems of biological systems. This paper develops the logical matrix factorization technique for exploring the topological structure and stability of probabilistic Boolean networks (PBNs). Firstly, the union set of distinct indices in factorized structural matrices for different modes is obtained

In this paper, we introduce regularized stochastic team problems. Under mild assumptions, we prove that there exists a unique fixed point of the best response operator, where this unique fixed point is the optimal regularized team decision rule. Then, we establish an asynchronous distributed algorithm to compute this optimal strategy. We also provide a bound that shows how the optimal regularized team

This paper aims at secure and privacy-preserving consensus algorithms of networked systems. Due to the technical challenges behind decentralized design of such algorithms, the existing results are mainly restricted to a network of systems with simplest first-order dynamics. Like many other control problems, breakthrough of the gap between first-order dynamics and higher-order ones demands for more

To address the well-known noise sensitivity problems associated with high-gain observers, we insert a low-pass filter on the measurement channel. Considering nonlinear plants in observability canonical form, we first motivate an architecture where the output error is filtered by a linear system parametrized by its arbitrary order and a scalar positive gain. Our main result establishes an exponential

This note shows how classical tools from linear control theory can be leveraged to provide a global analysis of nonlinear reaction–diffusion models. The approach is differential in nature. It proceeds from classical tools of contraction analysis and recent extensions to differential dissipativity.

Bayesian methods have been extended for the linear system identification problem in the past ten years. The traditional Bayesian identification selects a Gaussian prior and considers the tuning of kernels, i.e., the covariance matrix of a Gaussian prior. However, Gaussian priors cannot express the system information appropriately for identifying a positive finite impulse response (FIR) model. This

This paper is devoted to the controllability of a general linear hyperbolic system in one space dimension using boundary controls on one side. Under precise and generic assumptions on the boundary conditions on the other side, we previously established the optimal time for the null and the exact controllability for this system for a generic source term. In this work, we prove the null-controllability

This paper is concerned with the global attracting sets and the exponential stability in the mean square of mild solutions for stochastic functional partial differential equations. Some new sufficient conditions ensuring the existence of the global attracting sets and the exponential stability in the mean square of mild solutions for the considered equations are established by introducing approximating

This paper studies optimal sensor placement in networked control systems for improving the detectability of cyber–physical attacks. The problem is formulated as a game between an attacker and a detector. The attacker’s decision is to select a set of nodes in the network to attack, and the detector’s decision is to places sensors on a set of nodes. The detector tries to maximize the detectability of

The existence of a locally Lipschitz continuous homogeneous Lyapunov function is proven for a class of asymptotically stable homogeneous infinite dimensional systems with unbounded nonlinear operators.

Nonlinear observers based on the well-known concept of minimum energy estimation are discussed. The approach relies on an output injection operator determined by a Hamilton–Jacobi–Bellman equation whose solution is subsequently approximated by a neural network. A suitable optimization problem allowing to learn the network parameters is proposed and numerically investigated for linear and nonlinear

Agents are normally designed to be self-interested and tend to maximize their own interests in many realistic systems, such as robotics, smart grids and autonomous vehicles. In this paper, we propose a model of repeated bimatrix game to study the ubiquitous group behavior, coalescence, in multi-agent systems, where different agents form a union and keep consensus in states. We find that whether the

We consider a linear system composed of N+1 one dimensional heat equations connected by point-mass-like interface conditions. Assume an L2 Dirichlet boundary control at one end, and Dirichlet boundary condition on the other end. Given any L2-type initial temperature distribution, we show that the system is null controllable in arbitrarily small time. The proof uses known results for exact controllability

In this paper we study the global exponential stability in the L2 norm of semilinear 1-d hyperbolic systems on a bounded domain, when the source term and the nonlinear boundary conditions are Lipschitz. We exhibit two sufficient stability conditions: an internal condition and a boundary condition. This result holds also when the source term is nonlocal. Finally, we show its robustness by extending

For a class of SISO non-affine systems, we address the problem of how semiglobal asymptotic stabilization (SGAS) can be achieved by n-dimensional sampled-data output feedback. The new result of this paper gives a partial answer to the open question in the recent work Lin (2020), where (2n−1)-dimensional output feedback controllers were designed based on the dynamic extension method.

In this paper, we develop a completely model-free moving target defense framework for the detection and mitigation of sensor and/or actuator attacks in cyber–physical systems with dynamics that evolve in discrete-time. We incorporate an intrusion detection mechanism based on an approximate dynamic programming technique that learns the policies for optimal regulation and optimal tracking while simultaneously

Resistive–capacitive (RC) networks are used to model various processes in engineering, physics or biology. We consider the problem of recovering the network connection structure from measured input–output data. We address this problem as a structured identification one, that is, we assume to have a state-space model of the system (identified with standard techniques, such as subspace methods) and find

Data-driven, model-free control strategies leverage statistical or learning techniques to design controllers based on data instead of dynamic models. We have previously introduced the dissipativity learning control (DLC) method, where the dissipativity property is learned from the input–output trajectories of a system, based on which L2-optimal P/PI/PID controller synthesis is performed. In this work

In this manuscript we study the problem of finding incremental L2-gain of a class of nonlinear systems obtained by combining a linear plant and a general dynamic controller and a nonlinear actuator. The proposed method allows for the existence of possible nonlinear imperfections in the actuator. The justification of the proposed approach is provided through a compelling example.

This paper focuses on a prediction-based control for a class of convolution systems subject to constant input delays, also known as the reduction approach. We propose here a characterization of the D-invariance property of polytope sets for continuous-time systems. Our motivations come from production management, where a general model for a production network is considered. The system is subject to

In this work, the generalized value iteration with a discount factor is developed for optimal control of discrete-time nonlinear systems, which is initialized with a positive definite value function rather than zero. The convergence analysis of the discounted value function sequence is provided. The condition for the discount factor is given to guarantee the stability of the controlled plants. With

We extend a sliding mode control methodology to linear evolution equations with uncertain but bounded inputs and noise in observations. We first describe the reachability set of the state equation in the form of an infinite-dimensional ellipsoid, and then steer the minimax center of this ellipsoid toward a finite-dimensional sliding surface in finite time by using the standard sliding mode output-feedback

In this paper, we propose a framework to study the resistance to bribery of nodes in a network via average consensus. We extend the proposed bribery resistance measure to sets of nodes, and networks. The proposed framework evaluates quantitatively how much an external entity needs to drive the state of an agent away from its current state, to change the final consensus value. Subsequently, we illustrate

This paper is concerned with the stabilization and optimal control of discrete-time systems with multiplicative noise and multiple input delays. First, it is shown that the systems are stabilizable if and only if some algebraic Riccati-type equations have a solution which satisfies a given condition. To the best of our knowledge, this is the first time to propose a necessary and sufficient stabilizing

In this paper, we investigate differential–algebraic equations (DAEs) subject to stochastic perturbations. We introduce the index-ν concept and establish a formula of solution for these equations. After that the stability is studied by using the method of Lyapunov functions. Finally, the robust stability of DAEs with respect to stochastic perturbations is considered. Formulas of the stability radii

This paper investigates a completely distributed adaptive formation control protocol for networked quadrotors under switching communication topologies, where the dynamics of each quadrotor involves seriously nonlinearity and uncertainty simultaneously. For the switching communication topologies case, the adaptive formation control protocol is proposed to guarantee that the translational and rotational

This paper is devoted to the stability analysis of a class of switched nonlinear positive systems with nonlinearities of a sector type. A special construction of common Lyapunov function is proposed for the family of subsystems associated with a switched system and conditions of the existence of such a function are derived. The obtained results are used for the absolute stability investigation of switched

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