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Asymptotic stability in economic receding horizon control can be obtained under a strict dissipativity assumption, related to positive-definiteness of a so-called rotated cost, and through the use of suitable terminal cost and constraints.…
We examine the minimization of a quadratic cost functional composed of the output and the final state of abstract infinite-dimensional evolution equations in view of existence of solutions and optimality conditions. While the initial value…
This paper investigates the stochastic linear-quadratic (LQ, for short) optimal control problems with non-Markovian regime switching in a finite time horizon where the state equation is multi-dimensional. Similar to the classical stochastic…
This paper studies the exponential stabilization on infinite dimensional system with impulse controls, where impulse instants appear periodically. The first main result shows that exponential stabilizability of the control system with a…
A linear control system with quadratic cost functional over infinite time horizon is considered without assuming controllability/stabilizability condition and the global integrability condition for the nonhomogeneous term of the state…
In most real cases transition probabilities between operational modes of Markov jump linear systems cannot be computed exactly and are time-varying. We take into account this aspect by considering Markov jump linear systems where the…
We investigate the asymptotic properties of a finite-time horizon linear-quadratic optimal control problem driven by a multiscale stochastic process with multiplicative Brownian noise. We approach the problem by considering the associated…
This paper is concerned with stochastic linear quadratic (LQ, for short) optimal control problems in an infinite horizon with conditional mean-field term in a switching regime environment. The orthogonal decomposition introduced in [21] has…
This paper mainly establishes the finite-horizon stochastic bounded real lemma, and then solves the $H_{\infty}$ control problem for discrete-time stochastic linear systems defined on the separable Hilbert spaces, thereby unifying the…
The paper addresses an existence problem for infinite horizon optimal control when the system under control is exponentially stabilizable or stable. Classes of nonlinear control systems for which infinite horizon optimal controls exist are…
Different from most of the previous works, this paper provides a thorough solution to the fundamental problems of linear-quadratic (LQ) control and stabilization for discrete-time mean-field systems under basic assumptions. Firstly, the…
This paper is concerned with the problems of optimal control and stabilization for networked control systems (NCSs), where the remote controller and the local controller operate the linear plant simultaneously. The main contributions are…
This paper is dedicated to the stability analysis of the optimal solutions of a control problem associated with a semilinear elliptic equation. The linear differential operator of the equation is neither monotone nor coercive due to the…
We consider the linear quadratic (LQ) optimal control problem for a class of evolution equations in infinite dimensions, in the presence of distributed and nonlocal inputs. Following the perspective taken in our previous research work on…
We consider a general linear control system and a general quadratic cost, where the state evolves continuously in time and the control is sampled, i.e., is piecewise constant over a subdivision of the time interval. This is the framework of…
This paper is concerned with a stochastic linear quadratic (LQ, for short) optimal control problem. The notions of open-loop and closed-loop solvabilities are introduced. A simple example shows that these two solvabilities are different.…
This paper studies the finite-horizon linear quadratic regulation problem where the dynamics of the system are assumed to be unknown and the state is accessible. Information on the system is given by a finite set of input-state data, where…
The minimization of energy-like cost functionals is addressed in the context of optimal control problems. For a general class of dynamical systems, with possibly unstable and nonlinear free dynamics, it is shown that a sequence of solutions…
In this work we investigate explicit and implicit difference equations and the corresponding infinite time horizon linear-quadratic optimal control problem. We derive conditions for feasibility of the optimal control problem as well as…
In this paper, we extend a classical approach to linear quadratic (LQ) optimal control via Popov operators to abstract linear differential-algebraic equations (ADAEs) in Hilbert spaces. To ensure existence of solutions, we assume that the…