In this paper, we consider the infinite time horizon LQR optimal control problem for linearized Boussinesq system. The goal is to justify approximation by penalization of free divergence condition in context. We establish convergence results controls, solutions and Riccati operators when parameter goes zero. These are obtained under two different assumptions. first one treats linearization arou...

We investigate steering and distance computations based on linearizations about zero-control trajectories for RRT-like motion planning of highly dynamic systems. With planning constrained to dynamically feasible trajectories, the concept of “straight” is no longer Euclidean but instead determined as the path with least cost to transfer from one state to another. This additional complexity trans...

When designing a control system for structural control, the Linear Quadratic Regulation (LQR) approach is usually taken. While this centralized control approach optimally controls structural deflections during earthquakes, it is not well suited for systems employing a large number of sensors and actuators. As an alternative to LQR, a market-based control system is proposed. Market-based control...

This paper presents the ndings of a study devoted to a comparison of the eeective-ness of Linear Quadratic Regulator (LQR) and H 1 control for structures subjected to earthquake loadings. Research in the eld of active structural control has received much attention over the past few years, with the majority of eeorts focusing on formulation and application of the LQR-based control algorithms. Be...

This paper describes the method for trajectory tracking and balancing the Self Erecting Single Inverted Pendulum (SESIP) using Linear Quadratic Regulator (LQR). A robust LQR controller for stabilizing the SESIP is proposed in this paper. The first part of the controller is a Position Velocity (PV) controller to swing up the pendulum from its hanging position by moving the pendulum left and righ...

The problem of designing an Extended Regulator is defined as designing an algorithm that can adjust the optimal regulator gains for a time-variant linear system appropriately to match the variations in system parameters with time. Due to conditions of positive definiteness on the unknown variable in the Riccati equation for quadratic optimal control it is possible to show that repetitive iterat...

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.

We consider the problem of controlling a Linear Quadratic Regulator (LQR) system over finite horizon $T$ with fixed and known cost matrices $Q,R$, but unknown non-stationary dynamics $\{A_t, B_t\}$. The sequence can be arbitrary, total variation, $V_T$, assumed to $o(T)$ controller. Under assumption that stabilizing, potentially sub-optimal controllers is available for all $t$, we present an al...

Graphon control has been proposed and developed in [1]-[3] to approximately solve problems for very large-scale networks (VLSNs) of linear dynamical systems based on graphon limits. This paper provides a solution method invariant subspace decompositions class quadratic regulation (LQR) where the local dynamics share homogeneous parameters but couplings may be heterogeneous among coupled agents....