SIAM Journal on Control and Optimization

We consider the simplest optimal control problem with one nonregular mixed constraint $G(x,u)\le0,$ i.e., such a constraint that the gradient $G_u(x, u)$ can vanish on the surface $G = 0.$ Using the Dubovitskii--Milyutin theorem on the approximate separation ...

In this paper, we consider a mean field game model inspired by crowd motion in which several interacting populations evolving in $\mathbbm R^d$ aim at reaching given target sets in minimal time. The movement of each agent is described by a control system ...

This paper focuses on a time-varying constrained nonconvex optimization problem, and considers the synthesis and analysis of online regularized primal-dual gradient methods to track a Karush--Kuhn--Tucker (KKT) trajectory. The proposed regularized primal-...

This paper studies an infinite horizon optimal control problem for discrete-time linear systems and quadratic criteria, both with random parameters which are independent and identically distributed with respect to time. A classical approach is to solve an ...

Stochastic flows of an advective-diffusive nature are ubiquitous in biology and the physical sciences. Of particular interest is the problem of reconciling observed marginal distributions with a given prior posed by Schrödinger in 1932 and known as the ...

We present several characterizations, via some weak observability inequalities, on the complete stabilizability for a control system $[A,B]$, i.e., $y'(t)=Ay(t)+Bu(t)$, $t\geq 0$, where $A$ generates a $C_0$-semigroup on a Hilbert space $X$ and $B$ is a ...

Infinite horizon open loop optimal control problems for semilinear parabolic equations are investigated. The controls are subject to a cost functional which promotes sparsity in time. The focus is put on deriving first order optimality conditions. This ...

We present a novel variant of fictitious play dynamics combining classical fictitious play with $Q$-learning for stochastic games and analyze its convergence properties in two-player zero-sum stochastic games. Our dynamics involves players forming ...

We consider the singular optimal control problem of minimizing the energy supply of linear dissipative port-Hamiltonian descriptor systems. We study the reachability properties of the system and prove that optimal states exhibit a turnpike behavior with ...

This article is largely concerned with the time-discretization of differential-algebraic equations (DAEs) with complementarity constraints, which we name differential-algebraic linear complementarity systems (DALCSs). Specifically, the Euler implicit ...

This paper investigates the robust social optimum problem for linear quadratic mean field control systems by the direct approach, where model uncertainty appears in both drift and diffusion terms of each agent. We take a zero-sum game approach by ...

An adaptive feedback control scheme is proposed for stabilizing a class of forced nonlinear positive difference equations. The adaptive scheme is based on so-called high-gain adaptive controllers and contains substantial robustness with respect to model ...

We analyze the maximal growth of trajectories of discrete-time linear switching system, i.e., controlled linear systems with the control set being an arbitrary compact set of matrices. This is done by applying the optimal convex Lyapunov function called ...

In this work, we deal with the global well-posedness and stability of the linear and nonlinear Korteweg-de Vries equations on a finite star-shaped network by acting with saturated controls. We obtain the global well-posedness by using the Kato ...

We investigate the problem of finding the optimal shape and topology of a system of acoustic lenses in a dissipative medium. The sound propagation is governed by a general semilinear strongly damped wave equation. We introduce a phase-field formulation of ...

The paper deals with stochastic control problems associated with $H_2$ performance indices such as energy or power norms or energy measurements. The control applies to a class of systems for which a stochastic process conveys the underlying uncertainties, ...

This paper is devoted to a study of an observability estimate for the wave equation with variable coefficients $(h^{jk}(x))_{n\times n}$ ($n\in{{\mathop{\rm l\negthinspace N}}})$. We consider the observation point lying both outside the domain and inside ...

There has been an increased interest in the variation diminishing properties of controlled linear time-invariant (LTI) systems and time-varying linear systems without inputs. In controlled LTI systems, these properties have recently been studied from the ...

In this article, a class of backward stochastic Volterra integro-differential equations (BSVIDEs) is introduced and studied. It is worthy mentioning that the proposed BSVIDEs cannot be covered by the existing backward stochastic Volterra integral ...

This paper is devoted to analyzing the explicit slow decay rate and turnpike in infinite-horizon linear quadratic optimal control problems for hyperbolic systems. Under suitable weak observability or controllability conditions, lower and upper bounds of ...

The paper investigates the accuracy of the model predictive control (MPC) method for finding on-line approximate optimal feedback control for Bolza-type problems on a fixed finite horizon. The predictions for the dynamics, the state measurements, and the ...

This paper deals with control of partially observable discrete-time stochastic systems. It introduces and studies Markov Decision Processes with Incomplete Information and with semiuniform Feller transition probabilities. The important feature of these ...

This work proposes a detectability condition for linear time-varying systems based on the exponential dichotomy spectrum. The condition guarantees the existence of an observer, whose gain is determined only by the unstable modes of the system. This allows ...

We study a class of sampled stochastic optimization problems, where the underlying state process has diffusive dynamics of the mean-field type. We establish the existence of optimal relaxed controls when the sample set has finite size. The core of our ...

This paper studies system theoretic properties of the class of difference inclusions of convex processes. We will develop a framework considering eigenvalues and eigenvectors, weakly and strongly invariant cones, and a decomposition of convex processes. ...

In this paper, we study feedback linearization of multi-input control-affine systems via a particular class of nonregular feedback transformations, namely by reducing the number of controls by one. A complete geometric characterization of systems of that ...