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...

This paper presents an explicit solution to a two player distributed LQR problem in which communication between controllers occurs across a communication link with varying delay. We extend known dynamic programming methods to accommodate this varying delay, and show that under suitable assumptions, the optimal control actions are linear in their information, and that the resulting controller ha...

In this paper we examine the question when the LQR Riccati equation for matrices with components in a subalgebra A of L(H), where H is a Hilbert space, will have a unique nonnegative exponentially stabilizing solution with components in A. We give counterexamples to results claimed in the literature and some positive results for 2× 2 matrices. In addition, we pose a conjecture and an algebraic ...

This paper studies the robustness of reinforcement learning algorithms to errors in process. Specifically, we revisit benchmark problem discrete-time linear quadratic regulation (LQR) and study long-standing open question: Under what conditions is policy iteration method robustly stable from a dynamical systems perspective? Using advanced stability results control theory, it shown that for LQR ...

In this paper, we present a discussion of the proper orthogonal decomposition (POD) as applied to simulation and feedback control of the one dimensional heat equation. We provide two examples of input collections to which the POD process is applied. First, we apply POD directly to the nite element basis of linear B-splines. Next we additionally include time snapshots. We show that although the ...

A large class of problems in robotics, e.g., trajectory tracking with obstacle avoidance, compliant motion control, and complex assembly, can be formulated as a least-squares tracking problem on the Euclidean group subject to constraints on the state and/or control. In this note we develop an optimal control framework for this general class of problems, and derive analytic solutions for the loc...

We consider ensembles of particles or systems, all obeying the same dynamics or, equivalently, dynamical systems with uncertain states. In either case, we discuss i) the problem of optimally steering ensembles to a desired probability density, and ii) the problem of maintaining an ensemble at a specified admissible stationary distribution. In the context of linear dynamics and Gaussian distribu...

The linear quadratic regulator (LQR) problem is a cornerstone of automatic control, and it has been widely studied in the data-driven setting. various approaches can be classified as indirect (i.e., based on an identified model) versus direct or robust taking uncertainty into account) certainty-equivalence. Here we show how to bridge these different formulations propose novel, direct, regulariz...

A tape transport system consisting of a take-up reel servo, a supply-reel servo, and a capstan servo is proposed. The mathematical model of the system is derived. Two well know controllers – Linear Quadratic Regulator (LQR) and P/PI controller, are designed to regulate the output of the system. An input gain matrix N is calculated and applied to the LQR to eliminate steady-state offset. Simulat...

This paper provides a strategy to schedule a real time distributed system. Modifications on frequency transmission (task periods) of system’s individual components impact on system quality performance. In this work the authors propose a dynamic linear time invariant model based upon frequency transmission of agents in a distributed system and using LQR control approach to bring the system into ...