Showing papers in "Siam Journal on Control and Optimization in 2018"
TL;DR: A novel technique is provided for the global stability analysis of Boolean control networks under aperiodic sampled-data control (ASDC) and the sampling period is allowed to be taken from a limerick.
Abstract: A novel technique is provided for the global stability analysis of Boolean control networks (BCNs) under aperiodic sampled-data control (ASDC). The sampling period is allowed to be taken from a lim...
136 citations
TL;DR: It is shown that integral input- to-state stability can be characterized in terms of input-to- state stability with respect to Orlicz spaces, and since this work considers linear systems, the results can also be formulated in Terms of admissibility.
Abstract: In this work, the relation between input-to-state stability and integral input-to-state stability is studied for linear infinite-dimensional systems with an unbounded control operator. Although a special focus is laid on the case $L^{\infty}$, general function spaces are considered for the inputs. We show that integral input-to-state stability can be characterized in terms of input-to-state stability with respect to Orlicz spaces. Since we consider linear systems, the results can also be formulated in terms of admissibility. For parabolic diagonal systems with scalar inputs, both stability notions with respect to $L^\infty$ are equivalent.
101 citations
TL;DR: In this article, the steady-state (or periodic) exponential turnpike property of optimal control problems in Hilbert spaces was studied, which is essentially due to the hyperbolic feature of the Hamiltonian system resulting from the Pontryagin maximum principle, reflecting the fact that, in large control time horizons, the optimal state and control and adjoint state remain most of the time close to an optimal steady state.
Abstract: In this work, we study the steady-state (or periodic) exponential turnpike property of optimal control problems in Hilbert spaces. The turnpike property, which is essentially due to the hyperbolic feature of the Hamiltonian system resulting from the Pontryagin maximum principle, reflects the fact that, in large control time horizons, the optimal state and control and adjoint state remain most of the time close to an optimal steady-state. A similar statement holds true as well when replacing an optimal steady-state by an optimal periodic trajectory. To establish the result, we design an appropriate dichotomy transformation, based on solutions of the algebraic Riccati and Lyapunov equations. We illustrate our results with examples including linear heat and wave equations with periodic tracking terms.
82 citations
Journal Article•
TL;DR: In this paper, the authors studied the problem of learning the parameters of a high-dimensional Gaussian in the presence of noise and gave robust estimators that achieve estimation error O(varepsilon) in the total variation distance, which is optimal up to a universal constant.
Abstract: We study the fundamental problem of learning the parameters of a high-dimensional Gaussian in the presence of noise -- where an $\\varepsilon$-fraction of our samples were chosen by an adversary. We give robust estimators that achieve estimation error $O(\\varepsilon)$ in the total variation distance, which is optimal up to a universal constant that is independent of the dimension.
In the case where just the mean is unknown, our robustness guarantee is optimal up to a factor of $\\sqrt{2}$ and the running time is polynomial in $d$ and $1/\\epsilon$. When both the mean and covariance are unknown, the running time is polynomial in $d$ and quasipolynomial in $1/\\varepsilon$. Moreover all of our algorithms require only a polynomial number of samples. Our work shows that the same sorts of error guarantees that were established over fifty years ago in the one-dimensional setting can also be achieved by efficient algorithms in high-dimensional settings.
81 citations
TL;DR: This paper studies distributed algorithms for the nonsmooth extended monotropic optimization problem, which is a general convex optimization problem with a certain separable structure.
Abstract: This paper studies distributed algorithms for the nonsmooth extended monotropic optimization problem, which is a general convex optimization problem with a certain separable structure. The consider...
68 citations
TL;DR: The connection between turnpike behaviors and strict dissipativity properties for discrete time finite dimensional linear quadratic optimal control problems is analyzed and the consideration of state and input constraints is considered.
Abstract: We analyze the connection between turnpike behaviors and strict dissipativity properties for discrete time finite dimensional linear quadratic optimal control problems. We first use strict dissipativity as a sufficient condition for the turnpike property. Next, we characterize strict dissipativity and the newly introduced property of strict pre-dissipativity in terms of the system matrices related to the linear quadratic problem. These characterizations then lead to new necessary conditions for the turnpike properties under consideration, and thus eventually to necessary and sufficient conditions in terms of spectral criteria and matrix inequalities. One of the key novelties which distinguishes the results in the present paper from earlier ones on linear quadratic optimal control problems is the consideration of state and input constraints.
67 citations
TL;DR: This paper introduces a new solution concept of the Markov--Nash equilibrium, under which a policy is player-by-player optimal in the class of all Markov policies.
Abstract: In this paper, we consider discrete-time dynamic games of the mean-field type with a finite number $N$ of agents subject to an infinite-horizon discounted-cost optimality criterion. The state space...
64 citations
TL;DR: An optimal input-state transfer graph (OISTG) is defined for BCNs with cost in every stage for optimal control problem of Boolean control networks.
Abstract: In this paper, we study the optimal control problem of Boolean control networks (BCNs). An optimal input-state transfer graph (OISTG) is defined for BCNs with cost in every stage. Optimal controlle...
64 citations
TL;DR: The Riesz basis approach and the fractional Lyapunov method is used to prove the existence and uniqueness and the Mittag--Leffler stability for the closed-loop systems.
Abstract: In this paper, we consider boundary feedback stabilization for unstable time fractional reaction diffusion equations. New state feedback controls with actuation on one end are designed by the backstepping method for both Dirichlet and Neumann boundary controls. By the Riesz basis approach and the fractional Lyapunov method, we prove the existence and uniqueness and the Mittag--Leffler stability for the closed-loop systems. For both cases, the observers and the observer-based output feedback are designed to stabilize the systems.
56 citations
TL;DR: In this article, the numerical approximation of mean field games with local couplings was studied for power-like Hamiltonians and a stationary system and also a system involving density constraints, respectively.
Abstract: We address the numerical approximation of mean field games with local couplings. For power-like Hamiltonians, we consider a stationary system and also a system involving density constraints modelin...
52 citations
TL;DR: The value function of each of the players can be approximated by the solution of a partial differential equation called the master equation and it is shown that it is governed by a solution to a stochastic differential equation.
Abstract: We consider an $n$-player symmetric stochastic game with weak interactions between the players. Time is continuous, and the horizon and the number of states are finite. We show that the value funct...
TL;DR: In this article, a real-time motion planning problem is proposed for real time motion planning with obstacles in the environment, which is highly nonconvex and makes it diffi...
Abstract: With the development of robotics, there are growing needs for real time motion planning. However, due to obstacles in the environment, the planning problem is highly nonconvex, which makes it diffi...
TL;DR: In this paper, the convergence properties of continuous-time best-response dynamics from game theory were studied and shown to be poorly under-stoo-sto-stable, despite their fundamental role in game theory.
Abstract: The paper studies the convergence properties of (continuous-time) best-response dynamics from game theory. Despite their fundamental role in game theory, best-response dynamics are poorly understoo...
TL;DR: A global stochastic maximum principle is established by introducing the first-order and second-order variational equations which is a fully-coupled FBSDEs, and employing thefirst-and second- order adjoint equations.
Abstract: We study a stochastic optimal control problem for fully coupled forward-backward stochastic control systems with a nonempty control domain. For our problem, the first-order and second-order variati...
TL;DR: It is revealed that almost sure strong consensus and mean square strong consensus are equivalent under general digraphs, and almost sure weak consensus implies mean square weak consensus under undirected graphs.
Abstract: This work is concerned with the consensus problem of multi-agent systems with additive and multiplicative measurement noises. By developing general stochastic stability lemmas for nonautonomous stochastic differential equations, stochastic weak and strong consensus conditions are investigated under fixed and time-varying topologies, respectively. For the case with fixed topologies and additive noises, the necessary and sufficient conditions for almost sure strong consensus are given. It is revealed that almost sure strong consensus and mean square strong consensus are equivalent under general digraphs, and almost sure weak consensus implies mean square weak consensus under undirected graphs; if multiplicative noises appear, then small noise intensities do not affect the control gain to guarantee stochastic strong consensus. For the case with time-varying topologies, sufficient consensus conditions are given under the periodically connected condition of the topology flow.
TL;DR: In this paper, a stochastic game of mean field type where the agents solve optimal stopping problems and interact through the proportion of players that have already stopped is formulated, and the agents interact with each other.
Abstract: We formulate a stochastic game of mean field type where the agents solve optimal stopping problems and interact through the proportion of players that have already stopped. Working with a continuum...
TL;DR: This paper considers a dynamic optimization problem for a class of switched systems characterized by two key attributes: (i) the switching mechanism is invoked automatically when the state variable is changed and (ii) the system can be switched on the fly.
Abstract: This paper considers a dynamic optimization problem for a class of switched systems characterized by two key attributes: (i) the switching mechanism is invoked automatically when the state variable...
TL;DR: In this paper, the fully nonlinear stochastic Hamilton-Jacobi-Bellman (HJB) equation was studied for the optimal control problem of stochastically differential equations with random coefficiencies.
Abstract: In this paper we study the fully nonlinear stochastic Hamilton--Jacobi--Bellman (HJB) equation for the optimal stochastic control problem of stochastic differential equations with random coefficien...
TL;DR: A variant of the classical augmented Lagrangian method for constrained optimization problems in Banach spaces, which allows the treatment of inequality constraints with infinite-dimensional image space and the convergence properties of the algorithm are discussed.
Abstract: We propose a variant of the classical augmented Lagrangian method for constrained optimization problems in Banach spaces Our theoretical framework does not require any convexity or second-order assumptions, and it allows the treatment of inequality constraints with infinite-dimensional image space Moreover, we discuss the convergence properties of our algorithm with regard to feasibility, global optimality, and KKT conditions Some numerical results are given to illustrate the practical viability of the method
TL;DR: In this article, a distributed optimal control problem for a convective viscous Cahn-Hilliard system with dynamic boundary conditions was investigated, and the optimal control of phase separation processes was shown to be NP-hard.
Abstract: In this paper, we investigate a distributed optimal control problem for a convective viscous Cahn--Hilliard system with dynamic boundary conditions. Such systems govern phase separation processes b...
TL;DR: In this paper, the authors extend the class of pedestrian crowd models introduced by Lachapelle and Wolfram to allow for nonlocal crowd aversion and arbitrarily but finitely many interacting crowds, and derive the model from a particle picture and treat it as a mean-field type game.
Abstract: We extend the class of pedestrian crowd models introduced by Lachapelle and Wolfram [Transp. Res. B: Methodol., 45 (2011), pp. 1572--1589] to allow for nonlocal crowd aversion and arbitrarily but finitely many interacting crowds. The new crowd aversion feature grants pedestrians a “personal space” where crowding is undesirable. We derive the model from a particle picture and treat it as a mean-field type game. Solutions to the mean-field type game are characterized via a Pontryagin-type maximum principle. The behavior of pedestrians acting under nonlocal crowd aversion is illustrated by a numerical simulation.
TL;DR: The aim of this paper is to consider a sensitivity analysis of optimal control problems for a class of systems governed by differential hemivariational inequalities on Banach spaces.
Abstract: The aim of this paper is to consider a sensitivity analysis of optimal control problems for a class of systems governed by differential hemivariational inequalities (DHVIs) on Banach spaces. The fi...
TL;DR: A kind of coupled forward-backward stochastic differential equations with multilevel self-similar domination-monotonicity structure is proposed, and this kind of FBSDEs is used to characterize the unique equilibrium of a linear-quadratic generalized Stackelberg game in a closed form.
Abstract: A multilevel self-similar domination-monotonicity structure is proposed, and a kind of coupled forward-backward stochastic differential equations (FBSDEs) with such structure is proved to be unique...
TL;DR: The scheme is based on second order Volterra--Fliess approximations, and on an augmentation of the control variable in a control set of higher dimension, which has the advantage of providing a higher order accuracy, which may make it more efficient when aiming for a certain precision.
Abstract: This paper presents a discretization scheme for Mayer's type optimal control problems of linear systems. The scheme is based on second order Volterra--Fliess approximations, and on an augmentation of the control variable in a control set of higher dimension. Compared with the existing results, it has the advantage of providing a higher order accuracy, which may make it more efficient when aiming for a certain precision. Error estimations (depending on the controllability index of the system at the solution) are proved by using a recent result about stability of the optimal solution with respect to disturbances. Numerical results are provided which show the sharpness of the error estimations.
TL;DR: In this paper, the authors show that the first entry time into the stopping set is optimal for each initial state of the process, and that this is consistent with standard Markovian optimal stopping problems.
Abstract: Standard Markovian optimal stopping problems are consistent in the sense that the first entrance time into the stopping set is optimal for each initial state of the process. Clearly, the usual conc...
TL;DR: This work studies the output feedback exponential stabilization of a one-dimensional unstable wave equation, where the boundary input, given by the Neumann trace at one end of the domain, is the sum of the coefficients of the wave equation.
Abstract: We study the output feedback exponential stabilization of a one-dimensional unstable wave equation, where the boundary input, given by the Neumann trace at one end of the domain, is the sum of the ...
TL;DR: The technique is based on adiabatic approximation theory and on the presence of curves of conical eigenvalue intersections of the controlled Hamiltonian and shows that the assumptions guaranteeing ensemble controllability are structurally stable with respect to perturbations of the parametrized family of systems.
Abstract: In this article we discuss how to control a parameter-dependent family of quantum systems. Our technique is based on adiabatic approximation theory and on the presence of curves of conical eigenvalue intersections of the controlled Hamiltonian. As particular cases, we recover chirped pulses for two-level quantum systems and counter-intuitive solutions for three-level stimulated Raman adiabatic passage (STIRAP). The proposed technique works for systems evolving both in finite-dimensional and infinite-dimensional Hilbert spaces. We show that the assumptions guaranteeing ensemble controllability are structurally stable with respect to perturbations of the parametrized family of systems.
TL;DR: An infinite-horizon optimal control problem subject to an infinite-dimensional state equation with state and control variables appearing in a bilinear form is investigated.
Abstract: An infinite-horizon optimal control problem subject to an infinite-dimensional state equation with state and control variables appearing in a bilinear form is investigated. A sensitivity analysis w...
TL;DR: A global form stochastic maximum principle is developed for a Markov regime switching mean-field model driven by Brownian motions and Poisson jumps.
Abstract: In this paper, we develop a global form stochastic maximum principle for a Markov regime switching mean-field model driven by Brownian motions and Poisson jumps The form of the maximum principle t
TL;DR: Taking different structures in different modes into account, a new theory on the structured robust stability and boundedness for nonlinear hybrid stochastic differential delay equations (SDDEs) without the linear growth condition is developed.
Abstract: Taking different structures in different modes into account, the paper has developed a new theory on the structured robust stability and boundedness for nonlinear hybrid stochastic differential delay equations (SDDEs) without the linear growth condition. A new Lyapunov function is designed in order to deal with the effects of different structures as well as those of different parameters within the same modes. Moreover, a lot of effort is put into showing the almost sure asymptotic stability in the absence of the linear growth condition.