1,797 research outputs found
Linear Quadratic Stochastic Optimal Control Problems with Operator Coefficients: Open-Loop Solutions
An optimal control problem is considered for linear stochastic differential
equations with quadratic cost functional. The coefficients of the state
equation and the weights in the cost functional are bounded operators on the
spaces of square integrable random variables. The main motivation of our study
is linear quadratic optimal control problems for mean-field stochastic
differential equations. Open-loop solvability of the problem is investigated,
which is characterized as the solvability of a system of linear coupled
forward-backward stochastic differential equations (FBSDE, for short) with
operator coefficients. Under proper conditions, the well-posedness of such an
FBSDE is established, which leads to the existence of an open-loop optimal
control. Finally, as an application of our main results, a general mean-field
linear quadratic control problem in the open-loop case is solved.Comment: to appear in ESAIM Control Optim. Calc. Var. The original publication
is available at www.esaim-cocv.org (https://doi.org/10.1051/cocv/2018013
Optimal control of nonlinear partially-unknown systems with unsymmetrical input constraints and its applications to the optimal UAV circumnavigation problem
Aimed at solving the optimal control problem for nonlinear systems with
unsymmetrical input constraints, we present an online adaptive approach for
partially unknown control systems/dynamics. The designed algorithm converges
online to the optimal control solution without the knowledge of the internal
system dynamics. The optimality of the obtained control policy and the
stability for the closed-loop dynamic optimality are proved theoretically. The
proposed method greatly relaxes the assumption on the form of the internal
dynamics and input constraints in previous works. Besides, the control design
framework proposed in this paper offers a new approach to solve the optimal
circumnavigation problem involving a moving target for a fixed-wing unmanned
aerial vehicle (UAV). The control performance of our method is compared with
that of the existing circumnavigation control law in a numerical simulation and
the simulation results validate the effectiveness of our algorithm
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