Related papers: On Exact Solutions to the Linear Bellman Equation
In this paper we derive a necessary optimality condition for a local optimal solution of some control problems. These optimal control problems are governed by a semi-linear Vettsel boundary value problem of a linear elliptic equation. The…
In this paper, we study the conditions to be satisfied by a discrete-time linear system to ensure output controllability using sparse control inputs. A set of necessary and sufficient conditions can be directly obtained by extending the…
This paper is concerned with a stochastic linear-quadratic optimal control problem in a finite time horizon, where the coefficients of the control system are allowed to be random, and the weighting matrices in the cost functional are…
In this paper, we focus on formal synthesis of control policies for finite Markov decision processes with non-negative real-valued costs. We develop an algorithm to automatically generate a policy that guarantees the satisfaction of a…
The numerical realization of the dynamic programming principle for continuous-time optimal control leads to nonlinear Hamilton-Jacobi-Bellman equations which require the minimization of a nonlinear mapping over the set of admissible…
Optimal control problems for semilinear elliptic equations with control costs in the space of bounded variations are analysed. BV-based optimal controls favor piecewise constant, and hence 'simple' controls, with few jumps. Existence of…
The DPG method with optimal test functions for solving linear quadratic optimal control problems with control constraints is studied. We prove existence of a unique optimal solution of the nonlinear discrete problem and characterize it…
The aim of this notes is to give a concise introduction to control theory for systems governed by stochastic partial differential equations. We shall mainly focus on controllability and optimal control problems for these systems. For the…
Optimal control theory is usually formulated as an indirect method requiring the solution of a two-point boundary value problem. Practically, the solution is obtained by iterative forward and backward propagation of quantum wavepackets.…
This paper presents a data-driven model predictive control framework for mobile robots navigating in dynamic environments, leveraging Koopman operator theory. Unlike the conventional Koopman-based approaches that focus on the linearization…
We consider integer-restricted optimal control of systems governed by abstract semilinear evolution equations. This includes the problem of optimal control design for certain distributed parameter systems endowed with multiple actuators,…
In this work, we explore finite-dimensional linear representations of nonlinear dynamical systems by restricting the Koopman operator to an invariant subspace. The Koopman operator is an infinite-dimensional linear operator that evolves…
We consider the optimal control of linear systems over wireless MIMO fading channels, where the MIMO wireless fading and random access of the remote controller may cause intermittent controllability or uncontrollability of the closed-loop…
The fundamental problem of the calculus of variations on time scales concerns the minimization of a delta-integral over all trajectories satisfying given boundary conditions. This includes the discrete-time, the quantum, and the…
Linearized models of power systems are often desirable to formulate tractable control and optimization problems that still reflect real-world physics adequately under various operating conditions. In this paper, we propose an approach that…
We derive an explicit solution to the operator Riccati equation solving the Linear-Quadratic (LQ) optimal control problem for a class of boundary controlled hyperbolic partial differential equations (PDEs). Different descriptions of the…
The purpose of this work is to study an optimal control problem for a semilinear elliptic partial differential equation with a linear combination of Dirac measures as a forcing term; the control variable corresponds to the amplitude of such…
We consider the approximation of some optimal control problems for the Navier-Stokes equation via a Dynamic Programming approach. These control problems arise in many industrial applications and are very challenging from the numerical point…
This paper build on our recent work where we presented a dual stochastic optimal control formulation of the nonlinear filtering problem [1]. The constraint for the dual problem is a backward stochastic differential equations (BSDE). The…
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…