This chapter will consider two discrete time mixed LQR/ H∞ control problems. One is the discrete time state feedback mixed LQR/ H∞ control problem, another is the non-fragile discrete time state feedback mixed LQR/ H∞ control problem. Motivation for mixed LQR/ H∞ control problem is to combine the LQR and suboptimal H∞ controller design theories, and achieve simultaneously the performance of the...

The goal of this paper is to study a connection between the finite-horizon Kalman filtering and the LQR problems for discrete-time LTI systems. Motivated from the recent duality results on the LQR problem, a Lagrangian dual relation is used to prove that the Kalman filtering problem is a Lagrange dual problem of the LQR problem.

This paper is concerned with the linear quadratic regulation (LQR) problem for linear discrete-time systems with multiple delays in a single input channel. Although the LQR problem for discrete-time systems with single delay in each of the multiple input channels has been studied in existing literature, the problem to be addressed in this paper is known to be very difficult and has not been wel...

In this paper some new results concerning linear quadratic regulator (LQR) design for lossless systems are proved. The first result gives a necessary and sufficient condition which allows to obtain directly the optimal gains of an LQR problem for a lossless system, without solving the CARE equation, when a particular quadratic index is considered. The given results can also be viewed as an inve...

This paper presents a method to solve the constrained infinite-time linear quadratic regulator (LQR) problem. We use an operator splitting technique, namely the alternating minimization algorithm (AMA), to split the problem into an unconstrained LQR problem and a projection step, which are solved repeatedly, with the solution of one influencing the other. The first step amounts to the solution ...

In this paper we investigate the finite horizon linear quadratic regulation (LQR) problem for a linear continuous time system with time-varying delay in control input and a quadratic criterion. We assume that the time-varying delay is of a known upper bound, then the LQR problem is transformed into the optimal control problem for systems with multiple input channels, each of which has single co...

We present Extended LQR, a novel approach for locally-optimal control for robots with non-linear dynamics and non-quadratic cost functions. Our formulation is conceptually different from existing approaches, and is based on the novel concept of LQR-smoothing, which is an LQR-analogue of Kalman smoothing. Our approach iteratively performs both a backward Extended LQR pass, which computes approxi...

We review the example of linear quadratic regulator (LQR) problem given in paper[2] by A. Chapelon and C.-Z. Xu. We discuss three different algebraic Riccati equations that are associated to such LQR problems.

In this paper we present a set of projection-based designs for constructing simplified linear quadratic regulator (LQR) controllers for large-scale network systems. When such systems have tens of thousands of states, the design of conventional LQR controllers becomes numerically challenging, and their implementation requires a large number of communication links. Our proposed algorithms bypass ...

Dealing with a LQR controller surface subject to power and torque constraints, is an issue of nonlinear problem that is difficult to implement. This paper employs a fuzzy controller surface to replace the LQR surface subject to power and torque constraints by using class stacking, least square and Sugenotype fuzzy inference mode. Through this type of transformation, called “Optimal fuzzy contro...