Related papers: Characterization of the solution to a constrained …
This paper addresses the inverse optimal control problem of finding the state weighting function that leads to a quadratic value function when the cost on the input is fixed to be quadratic. The paper focuses on a class of infinite horizon…
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…
An optimal control problem with an infinite horizon quadratic cost functional for a linear system with a known additive disturbance is considered. The feature of this problem is that a weight matrix of the control cost in the cost…
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…
In this paper, we show the optimality of a certain class of disturbance-affine control policies in the context of one-dimensional, constrained, multi-stage robust optimization. Our results cover the finite horizon case, with minimax…
A Deterministic affine quadratic optimal control problem is considered. Due to the nature of the problem, optimal controls exist under some very mild conditions. Further, it is shown that under some assumptions, the value function is…
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…
In this paper, a finite-horizon optimal control problem involving a dynamical system described by a linear Caputo fractional differential equation and a quadratic cost functional is considered. An explicit formula for the value functional…
Let $T>0$ fixed. We consider the optimal control problem for analytic affine systems: $\ds{\dot{x}=f\_0(x)+\sum\_{i=1}^m u\_if\_i(x)}$, with a cost of the form: $\ds{C(u)=\int\_0^T \sum\_{i=1}^m u\_i^2(t)dt}$. For this kind of systems we…
In this article we study a finite horizon optimal control problem with monotone controls. We consider the associated Hamilton-Jacobi-Bellman (HJB) equation which characterizes the value function. We consider the totally discretized problem…
This paper is dedicated to the analysis of infinite horizon optimal control problems subject to semilinear parabolic equations with constraints on the controls and discounted cost functionals. The discount factors on the cost and the state…
We study a family of optimal control problems in which one aims at minimizing a cost that mixes a quadratic control penalization and the variance of the system, both for finitely many agents and for the mean-field dynamics as their number…
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…
This paper considers the infinite horizon optimal control problem for nonlinear systems. Under the condition of nonlinear controllability of the system to any terminal set containing the origin and forward invariance of the terminal set, we…
We consider discrete-time infinite horizon deterministic optimal control problems with nonnegative cost per stage, and a destination that is cost-free and absorbing. The classical linear-quadratic regulator problem is a special case. Our…
The present work addresses a finite-horizon linear-quadratic optimal control problem for uncertain systems driven by piecewise constant controls. The precise values of the system parameters are unknown, but assumed to belong to a finite set…
A finite horizon linear quadratic(LQ) optimal control problem is studied for a class of discrete-time linear fractional systems (LFSs) affected by multiplicative, independent random perturbations. Based on the dynamic programming technique,…
Traditional solvable optimal control theory predominantly focuses on quadratic costs due to their analytical tractability, yet they often fail to capture critical non-linearities inherent in real-world systems including water, energy,…
We study the infinite-horizon distributionally robust (DR) control of linear systems with quadratic costs, where disturbances have unknown, possibly time-correlated distribution within a Wasserstein-2 ambiguity set. We aim to minimize the…
The paper studies a class of quadratic optimal control problems for partially observable linear dynamical systems. In contrast to the full information case, the control is required to be adapted to the filtration generated by the…