Related papers: The generalised continuous algebraic Riccati equat…
The paper establishes the exponential turnpike property for a class of mean-field stochastic linear-quadratic (LQ) optimal control problems with periodic coefficients. It first introduces the concepts of stability, stabilizability, and…
This paper deals with some reachability issues for piecewise linear switched systems with time-dependent coefficients and multiplicative noise. Namely, it aims at characterizing data that are almost reachable at some fixed time T > 0…
This paper investigates a conditional mean-field type linear quadratic (LQ) optimal control problem with partial observation and regime switching, where the conditional expectations of the state and control given the history of Markov chain…
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…
A novel method of an adaptive linear quadratic (LQ) regulation of uncertain continuous linear time-invariant systems is proposed. Such an approach is based on the direct self-tuning regulators design framework and the exponentially stable…
This note concerns a class of matrix Riccati equations associated with stochastic linear-quadratic optimal control problems with indefinite state and control weighting costs. A novel sufficient condition of solvability of such equations is…
Finite-time linear-quadratic control of partial differential-algebraic equations (PDAEs) is considered. The discussion is restricted to those that are radial with index $0$; this corresponds to a nilpotency degree of 1. We establish the…
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…
The concept of turnpike connects the solution of long but finite time horizon optimal control problems with steady state optimal controls. A key ingredient of the analysis of the turnpike is the linear quadratic regulator problem and the…
The optimal stochastic control problem with a quadratic cost functional for linear partial differential equations (PDEs) driven by a state-and control-dependent white noise is formulated and studied. Both finite-and infinite-time horizons…
This paper proposes a reduction technique for the generalised Riccati difference equation arising in optimal control and optimal filtering. This technique relies on a study on the generalised discrete algebraic Riccati equation. In…
We deduce a sufficient condition of the exponential (integral) turnpike property for infinite dimensional generalized linear-quadratic optimal control problems in terms of structural properties of the control system, such as exponential…
This paper mainly investigates the optimal control and stabilization problems for linear discrete-time Markov jump systems. The general case for the finite-horizon optimal controller is considered, where the input weighting matrix in the…
The control algebraic Riccati equation is studied for a class of systems with unbounded control and observation operators. Using a dichotomy property of the associated Hamiltonian operator matrix, two invariant graph subspaces are…
This paper is concerned with uniform stabilization and social optimality for general mean field linear quadratic control systems, where subsystems are coupled via individual dynamics and costs, and the state weight is not assumed with the…
We present high order explicit geometric integrators to solve linear-quadratic optimal control problems and $N$-player differential games. These problems are described by a system coupled non-linear differential equations with boundary…
Spacecraft attitude control using only magnetic torques is a periodic time-varying system as the Earth magnetic field in the spacecraft body frame changes periodically while the spacecraft circles around the Earth. The optimal controller…
A general time-inconsistent optimal control problem is considered for stochastic differential equations with deterministic coefficients. Under suitable conditions, a Hamilton-Jacobi-Bellman type equation is derived for the equilibrium value…
In this paper, we study the irregular output feedback linear quadratic (LQ) control problem, which is a continuous work of previous works for irregular LQ control [33] where the state is assumed to be exactly known priori. Different from…
In this paper, we consider the inverse optimal control problem for the discrete-time linear quadratic regulator, over finite-time horizons. Given observations of the optimal trajectories, and optimal control inputs, to a linear…