We present and solve a Linear Quadratic Regulator (LQR) for the boundary control of beam equation. use simple technique completing square to get an explicit solution. By decoupling spatial frequencies we are able reduce infinite dimensional LQR family two LQRs each which can be solved explicitly.

This paper investigates a linear quadratic mean field leader-follower team problem, where the model involves one leader and large number of weakly-coupled interactive followers. The followers cooperate to optimize social cost. Specifically, for any strategy provided first by leader, would like choose minimize cost functional. Using variational analysis person-by-person optimality, we construct ...

Stochastic linear quadratic control problems are considered from the viewpoint of risks. In particular, a worst-case conditional value-at-risk (CVaR) objective function is minimized subject to additive disturbances whose first two moments distribution known. The study focuses on three finding optimal feedback gain that minimizes cost of: stationary distribution, one-step, and infinite time hori...

‎In this paper‎, ‎Haar wavelets are performed for solving continuous time-variant linear-quadratic optimal control problems‎. ‎Firstly‎, ‎using necessary conditions for optimality‎, ‎the problem is changed into a two-boundary value problem (TBVP)‎. ‎Next‎, ‎Haar wavelets are applied for converting the TBVP‎, ‎as a system of differential equations‎, ‎in to a system of matrix algebraic equations‎...