Optimal control problems with convex costs, for which Hamiltonians have Lipschitz continuous gradients, are considered. Examples of such problems, including extensions of the linear-quadratic regulator with hard and possibly state-dependent control constraints, and piecewise linear-quadratic penalties are given. Lipschitz continuous differentiability and strong convexity of the terminal cost ar...

This paper shows for a class of differential games that the global Stackelberg equilibrium (GSE) coincides with feedback (FSE), although GSE assumes leader/regulator announces at initial time regulatory instrument rule she will follow rest game, while in FSE, regulator any chooses optimal level rate. coincidence is based on fact FSE calculated using dynamic programming what implies rate maximiz...

In this paper, state-derivative and especially output-derivative feedbacks for linear time-invariant systems are derived using control approach similar to linear quadratic regulator (LQR). The optimal feedback gain matrices are derived for the desired performance. This problem is always solvable for any controllable system if the open-loop system matrix is nonsingular. Explicit expression of th...

By parametrizing input and state trajectories with basis functions different approximations to the constrained linear quadratic regulator problem are obtained. These notes present and discuss technical results that are intended to supplement a corresponding journal article. The results can be applied in a model predictive control context.

In this paper we consider the convergence of the infinite dimensional version of the Kleinman–Newton algorithm for solving the algebraic Riccati operator equation associated with the linear quadratic regulator problem in a Hilbert space. We establish mesh independence for this algorithm and apply the result to systems governed by delay equations. Numerical examples are presented to illustrate t...

The problem of stabilizing the double inverted pendulum has been solved using two different techniques which were the Pole Placement and Linear Quadratic Regulator techniques to design controls for the system. Copyright c ©2003 Yang’s Scientific Research Institute, LLC. All rights reserved.

In this paper we describe a control methodology for the navigation of an autonomous lighter-than-air vehicle based on visual input. The control system consists in a Linear Quadratic Regulator (LQR) and a Linear Quadratic Gaussian observer (LQG). Due to non-linearities in the actuators and in the radio frequency control system, some non-linear control terms are added. The additional terms lead t...

A reduced-order method based on approximate inertial manifolds is applied to optimal control problems in infinite-dimensional state spaces. A detailed analysis of the method is given for the linear quadratic regulator problem. The method can also be applied to higher-order control systems with an appropriate decomposition of the state space in terms of slow and fast exponential decay.

The linear quadratic regulator problem for the second order evolution system with boundary controls is studied. Case that the input-to-state map is non-admissible is treated assuming that the system is exponentially stabilizable by the passive feedback. It is shown that the optimal control is of feedback form in terms of solution to the operator Riccati equation.

In this study, modeling and LQR control of a reaction wheel inverted pendulum system is described. The model created by using 3D CAD platform exported to Simscape Multibody. multibody linearized derive state-space representation. A (Linear-quadratic regulator) controller designed applied for balance the pendulum. results show that deriving representation from an easy effective way dynamic syste...