Showing papers in "Siam Journal on Control and Optimization in 2019"
TL;DR: This paper studies the feedback stabilization problem of $k$-valued logical control networks (KVLCNs), and proposes a control Lyapunov function (CLF) approach for this problem.
Abstract: This paper studies the feedback stabilization problem of $k$-valued logical control networks (KVLCNs), and proposes a control Lyapunov function (CLF) approach for this problem. First, the CLF is de...
91 citations
TL;DR: A monotonicity-based method for studying input-to-state stability (ISS) of nonlinear parabolic equations with boundary inputs and shows that the PDE backstepping controller which stabilizes linear reaction-diffusion equations from the boundary is robust with respect to additive actuator disturbances.
Abstract: We introduce a monotonicity-based method for studying input-to-state stability (ISS) of nonlinear parabolic equations with boundary inputs. We first show that a monotone control system is ISS if an...
81 citations
TL;DR: The aim of this paper is to study systematically the problem of consistent discretization of the so-called generalized homogeneous non-linear systems, where the discretized model is consistent if it preserves the stability property of the original continuous-time system.
Abstract: Algorithms of implicit discretization for generalized homogeneous systems having discontinuity only at the origin are developed They are based on the transformation of the original system to an equivalent one which admits an implicit or a semi-implicit discretization schemes preserving the stability properties of the continuous-time system Namely, the discretized model remains finite-time stable (in the case of negative homogeneity degree), and practically fixed-time stable (in the case of positive homogeneity degree) The theoretical results are supported with numerical examples 1 Introduction Discretization issues are important for a digital implementation of estimation and control algorithms Construction of a consistent stable discretization is complex for essentially non-linear ordinary differential equations (ODEs), which do not satisfy some classical regularity assumptions For example, the sliding mode algorithms are known to be difficult in practical realization [1], [2], [3] due to discontinuous (set-valued) nature, which may invoke chattering caused by the discretization The mentioned papers have discovered that the implicit discretization technique is useful for practical implementation of non-smooth and discontinuous control and estimation algorithms In particular, chattering suppression in both input and output, as well as a good closed-loop performance has been confirmed experimentally in [1], [4], [5] Finite-time stability is a desirable property for many control and estimation algorithms [6], [7], [8], [9], [10], [11] It means that system trajectories reach a stable equilibrium (or a set) in a finite time, in contrast to asymptotic stability allowing this only for the time tending to infinity If the settling (reaching) time is globally bounded for all initial conditions then the origin is fixed-time stable (see, eg [12]) The corresponding ODE models do not satisfy Lipschitz condition (at least at the origin) In the general case, an application of the conventional implicit or explicit discretization schemes does not guarantee that finite-time or fixed-time stability properties will be preserved (see, eg [13], [14], [15]) The latter means that the discrete-time model may be inconsistent with the continuous-time one However, the discretized systems may remain globally finite-time stable in some cases (see [1], [2], [16], [17]) The aim of this paper is to study systematically the problem of consistent discretization of the so-called generalized homogeneous non-linear systems The discretized model is consistent if it preserves the stability property (eg exponential, finite-time or fixed-time stability) of the original continuous-time system Homogeneity is a certain form of symmetry studied in systems and control theory [9], [18], [19], [20],[21], [22], [23] The standard homogeneity (introduced originally by L Euler in 17th century) is the symmetry of a mathematical object f (eg function, vector field, operator, etc) with respect to the uniform dilation of the argument x → λx, namely, f (λx) = λ 1+ν f (x), λ > 0
77 citations
TL;DR: In this paper, the authors studied mean field stochastic control problems where the cost function and the state dynamics depend upon the joint distribution of the controlled state and the control process.
Abstract: We study mean field stochastic control problems where the cost function and the state dynamics depend upon the joint distribution of the controlled state and the control process. We prove suitable ...
56 citations
TL;DR: This work analyzes the sensitivity of the extremal equations that arise from the first order optimality conditions for time dependent optimization problems and considers parabolic PDEs.
Abstract: We analyze the sensitivity of the extremal equations that arise from the first order optimality conditions for time dependent optimization problems. More specifically, we consider parabolic PDEs wi...
47 citations
TL;DR: A backstepping method is developed for boundary stabilization of first-order inhomogeneous quasi-linear hyperbolic systems and its main result supplements the main result.
Abstract: This paper deals with the problem of boundary stabilization of first-order $n\times n$ inhomogeneous quasi-linear hyperbolic systems. A backstepping method is developed. The main result supplements...
44 citations
TL;DR: In this paper, the authors consider a mean field game with continuous time over a finite horizon, where the position of each agent belongs to a constant value of the cost of the game.
Abstract: We consider $N$-player and mean field games in continuous time over a finite horizon, where the position of each agent belongs to $\{-1,1\}$. If there is uniqueness of mean field game solutions, e....
40 citations
TL;DR: For opinion dynamics in social networks with antagonisms, distributed processes lead to challenging difficulties to characterize them, especially under changing network topologies.
Abstract: For opinion dynamics in social networks with antagonisms, distributed processes lead to challenging difficulties to characterize them, especially under changing network topologies. There may appear...
38 citations
TL;DR: It is shown that for optimal boundary control problems with integer constraints for the controls the turnpike phenomenon occurs, and a numerical verification is given for a control problem in gas pipeline operations.
Abstract: We study problems of optimal boundary control with systems governed by linear hyperbolic partial differential equations. The objective function is quadratic and given by an integral over the finite...
35 citations
TL;DR: This article summarizes recent results on a priori error estimates for space-time finite element discretizations of linear-quadratic parabolic optimal control problems and considers three cases: problems without inequality constraints, problems with pointwise control constraints, and problems with state constraints pointwise in time.
Abstract: In this article we summarize recent results on a priori error estimates for space-time finite element discretizations of linear-quadratic parabolic optimal control problems. We consider the following three cases: problems without inequality constraints, problems with pointwise control constraints, and problems with state constraints pointwise in time. For all cases, error estimates with respect to the temporal and to the spatial discretization parameters are derived. The results are illustrated by numerical examples.
34 citations
TL;DR: Considering economic Agents in competition with relative performance concerns, this model derives the optimal contracts in both first best and moral hazard settings and relies heavily on the connection between Nash equilibria and multidimensional quadratic BSDEs.
Abstract: In a framework close to the one developed by Holmstrom and Milgrom [44], we study the optimal contracting scheme between a Principal and several Agents. Each hired Agent is in charge of one project, and can make efforts towards managing his own project, as well as impact (positively or negatively) the projects of the other Agents. Considering economic agents in competition with relative performance concerns, we derive the optimal contracts in both first best and moral hazard settings. The enhanced resolution methodology relies heavily on the connection between Nash equilibria and multidimensional quadratic BSDEs. The optimal contracts are linear and each agent is paid a fixed proportion of the terminal value of all the projects of the firm. Besides, each Agent receives his reservation utility, and those with high competitive appetence are assigned less volatile projects, and shall even receive help from the other Agents. From the principal point of view, it is in the firm interest in our model to strongly diversify the competitive appetence of the Agents.
TL;DR: In this article, the controllability of a general linear hyperbolic system of the form ∆ ∆ w w (t, x) = \Sigma(x) \partial_x w(t, X) + \gamma C(x, w(T, x)) w( t, x), w(n, x).
Abstract: We are concerned about the controllability of a general linear hyperbolic system of the form $\partial_t w (t, x) = \Sigma(x) \partial_x w (t, x) + \gamma C(x) w(t, x) $ ($\gamma \in \mathbb{R}$) i...
TL;DR: In this paper, the controllability of the space-time fractional diffusive equation was studied in a bounded domain with a Lipschitz continuous boundary, and the authors showed that it is controllable.
Abstract: Let $\Omega\subset\mathbb{R}^N$ be a bounded domain with a Lipschitz continuous boundary. We study the controllability of the space-time fractional diffusive equation $\{\mathbb D_t^\alpha u+(-\Del...
TL;DR: The Nash equilibrium (NE) is obtained explicitly by deriving and analyzing a system of Hamilton--Jacobi--Bellman equations and by establishing the existence of a unique strong solution to the associated Skorokhod problem on an unbounded polyhedron with an oblique reflection.
Abstract: In this paper we formulate and analyze an $N$-player stochastic game of the classical fuel follower problem and its mean field game (MFG) counterpart. For the $N$-player game, we obtain the Nash eq...
TL;DR: This paper considers the functional Ito calculus framework to find a path-dependent version of the Hamilton--Jacobi-Bellman equation for stochastic control problems that feature dynamics and running costs that depend on the path of the control.
Abstract: In this paper we consider the functional Ito calculus framework to find a path-dependent version of the Hamilton--Jacobi-Bellman equation for stochastic control problems that feature dynamics and r...
TL;DR: The robust consensus problem for a set of discrete-time linear agents to coordinate over an uncertain communication network, which is to achieve consensus against the transmission errors and noises resulted from the information exchange between the agents, is studied.
Abstract: In this paper, we study the robust consensus problem for a set of discrete-time linear agents to coordinate over an uncertain communication network, which is to achieve consensus against the transm...
TL;DR: The proposed method consists of building a hierarchy of relaxations for an infinite-dimensional moment problem of approximating the reachable set of a discrete-time polynomial system from a semialgebraic set of initial conditions under general semial geometry set constraints.
Abstract: We consider the problem of approximating the reachable set of a discrete-time polynomial system from a semialgebraic set of initial conditions under general semialgebraic set constraints. Assuming ...
TL;DR: This chapter deals with the internal observability for some coupled systems of partial differential equations with constant or time-dependent coupling terms by means of a reduced number of observed components.
Abstract: We deal with the internal observability for some coupled systems of partial differential equations with constant or time-dependent coupling terms by means of a reduced number of observed components...
TL;DR: In order to promote declustering, instead of using the classical variance that does not capture well the phenomenon of dispersion, an entropy-type functional is introduced that is adapted to measuring pairwise distances between agents.
Abstract: This paper elaborates control strategies to prevent clustering effects in opinion formation models. This is the exact opposite of numerous situations encountered in the literature where, on the contrary, one seeks controls promoting consensus. In order to promote declustering, instead of using the classical variance that does not capture well the phenomenon of dispersion, we introduce an entropy-type functional that is adapted to measuring pairwise distances between agents. We then focus on a Hegselmann-Krause-type system and design declustering sparse controls both in finite-dimensional and kinetic models. We provide general conditions characterizing whether clustering can be avoided as function of the initial data. Such results include the description of black holes (where complete collapse to consensus is not avoidable), safety zones (where the control can keep the system far from clustering), basins of attraction (attractive zones around the clustering set) and collapse prevention (when convergence to the clustering set can be avoided).
TL;DR: In this paper, a distributed stochastic optimization problem without gradient/subgradient information for local objective functions and subject to local convex constraints is considered.
Abstract: In this paper we consider a distributed stochastic optimization problem without gradient/subgradient information for local objective functions and subject to local convex constraints. Objective fun...
TL;DR: In this article, a robust dynamic programming theory for continuous-time dynamical systems is presented, which is different from traditional dynamic programming (DP) methods, and is based on a new theory known as robust dynamical programming.
Abstract: This paper presents a new theory, known as robust dynamic programming, for a class of continuous-time dynamical systems. Different from traditional dynamic programming (DP) methods, this new theory...
TL;DR: In this paper, the authors design and analyze solution techniques for a linear-quadratic optimal control problem involving the integral fractional Laplacian and derive existence and uniqueness results for first-order optimal control.
Abstract: We design and analyze solution techniques for a linear-quadratic optimal control problem involving the integral fractional Laplacian. We derive existence and uniqueness results, first-order optimal...
TL;DR: In this article, the authors studied an infinite-horizon discrete-time optimal stopping problem under nonexponential discounting and developed an iterative approach to find subgame perfect Nash equilibria.
Abstract: We study an infinite-horizon discrete-time optimal stopping problem under nonexponential discounting. A new method, which we call the iterative approach, is developed to find subgame perfect Nash e...
TL;DR: A novel methodology for the design of boundary feedback stabilizers for one-dimensional, semilinear, parabolic PDEs based on the use of small-gain arguments is presented.
Abstract: This paper presents a novel methodology for the design of boundary feedback stabilizers for one-dimensional, semilinear, parabolic PDEs. The methodology is based on the use of small-gain arguments ...
TL;DR: This paper considers the feedback stabilization problem for N-level quantum angular momentum systems undergoing continuous-time measurements using stochastic and geometric control tools and designs a class of feedback control laws satisfying the above-mentioned conditions.
Abstract: In this paper, we consider the feedback stabilization problem for $N$-level quantum angular momentum systems undergoing continuous-time measurements. By using stochastic and geometric control tools...
TL;DR: In this article, the controllability of a Partial Differential Equation of transport type with Lipschitz control was studied in crowd models and it was shown that one can steer approximately one to another in a crowd when the uncontrolled dynamics allows to cross the control set.
Abstract: We study controllability of a Partial Differential Equation of transport type, that arises in crowd models. We are interested in controlling it with a control being a vector field, representing a perturbation of the velocity, localized on a fixed control set. We prove that, for each initial and final configuration, one can steer approximately one to another with Lipschitz controls when the uncontrolled dynamics allows to cross the control set. We also show that the exact controllability only holds for controls with less regularity, for which one may lose uniqueness of the associated solution.
TL;DR: This paper provides a method for designing robust state observers for a class of time-delay systems where unknown exogenous disturbances and time delays appear in both the states and the output mea...
Abstract: This paper provides a method for designing robust state observers for a class of time-delay systems where unknown exogenous disturbances and time delays appear in both the states and the output mea...
TL;DR: This work addresses the question of the exponential stability for the $C^{1}$ norm of general one-dimensional quasilinear systems with source terms under boundary conditions with a focus on the LaSalle-Bouchut inequality.
Abstract: We address the question of the exponential stability for the $C^{1}$ norm of general one-dimensional quasilinear systems with source terms under boundary conditions. To reach this aim, we introduce...
TL;DR: It is demonstrated by means of a counterexample that the solution map of an EVI with a unilateral constraint is typically not (weakly) directionally differentiable or Lipschitz continuous in any of the spaces.
Abstract: This paper is concerned with the differential sensitivity analysis and the optimal control of evolution variational inequalities (EVIs) of obstacle type. We demonstrate by means of a counterexample...
TL;DR: This paper aims to find the time-consistent equilibrium strategy for a mean-variance portfolio selection problem under a non-Markovian regime-switching model, in which the coefficients are adapted to the Markovians.
Abstract: This paper aims to find the time-consistent equilibrium strategy for a mean-variance portfolio selection problem under a non-Markovian regime-switching model, in which the coefficients are adapted ...