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A general bilinear optimal control problem subject to an infinite-dimensional state equation is considered. Polynomial approximations of the associated value function are derived around the steady state by repeated formal differentiation of…
In this paper we study optimal control problems governed by a semilinear elliptic equation. The equation is nonmonotone due to the presence of a convection term, despite the monotonocity of the nonlinear term. The resulting operator is…
It is well known that highly volatile control laws, while theoretically optimal for certain systems, are undesirable from an engineering perspective, being generally deleterious to the controlled system. In this article we are concerned…
In this paper, the open-loop, closed-loop, and weak closed-loop solvability for discrete-time linear-quadratic (LQ) control problem is considered due to the fact that it is always open-loop optimal solvable if the LQ control problem is…
Current research suggests the use of a liner quadratic performance index for optimal control of regulators in various applications. Some examples include correcting the trajectory of rocket and air vehicles, vibration suppression of…
In this paper, we consider the problem of multi-objective optimal control of a dynamical system with additive and multiplicative noises with given second moments and arbitrary probability distributions. The objectives are given by quadratic…
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…
A discrete-time stochastic LQ problem with multiplicative noises and state transmission delay is studied in this paper, which does not require any definiteness constraint on the cost weighting matrices. From some abstract representations of…
This paper proposes an optimal control problem for a parabolic equation with a nonlocal nonlinearity. The system is described by a parabolic equation involving a nonlinear term that depends on the solution and its integral over the domain.…
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…
We present a novel class of minimax optimal control problems with positive dynamics, linear objective function and homogeneous constraints. The proposed problem class can be analyzed with dynamic programming and an explicit solution to the…
Necessary optimality conditions and numerical methods for solving an optimal control problem for a linear continuous-time dynanical system with controlled coefficients and quadratic goal functional are discussed.
We consider an optimal control problem for a system of local continuity equations on a space of probability measures. Such systems can be viewed as macroscopic models of ensembles of non-interacting particles or homotypic individuals,…
We study the minimum energy null-controllability problem for differential equations with point-wise delays. For the equations of both neutral and retarded type we reduce the problem of finding the optimal control to a Volterra integral…
We consider a stochastic control problem where the set of strict (classical) controls is not necessarily convex and the the variable control has two components, the first being absolutely continuous and the second singular. The system is…
In this paper, we are concerned with a stochastic optimal control problem of mean-field type under partial observation, where the state equation is governed by the controlled nonlinear mean-field stochastic differential equation, moreover…
We consider a stochastic control problem where the set of controls is not necessarily convex and the system is governed by a nonlinear backward stochastic differential equation. We establish necessary as well as sufficient conditions of…
In this paper we give feedback laws for a class of parametrized infinite horizon control problems under state constraints. We provide a two-player representation assuming time dependent dynamics and Lagrangian and the set constraints merely…
We consider a system that is exactly controllable. For given initial state, terminal state and objective function, an optimal control is often well-defined. Such an optimal control has the disadvantage that although it works perfectly well…
This work deals with the existence of optimal solution and the maximum principle for optimal control problem governed by Navier-Stokes equations with state constraint in 3-D. Strong results in 2-D also are given.