Finite and Infinite Horizon Fixed-order Lqg Compensation Using the Delta Operator
نویسنده
چکیده
The strengthened discrete-time optimal projection equations (SDOPE) are presented in a form based on the delta operator. This form unifies discrete-time and continuous-time results. Based on this unification, recently established results and algorithms for finite and infinite-horizon fixed-order LQG compensation of discrete-time systems are carried over to the continuous-time case. The results concern the equivalence of the strengthened optimal projection equations to first-order necessary optimality conditions together with the condition that the compensator is minimal. Furthermore in the finitehorizon continuous-time case the problem of stating the optimal projection equations explicitly in the LQG problem parameters is explained and resolved. The algorithms exploit the resemblance between the strengthened optimal projection equations and the Riccati equations of full-order LQG control. They allow for efficient numerical computation of fixed-order LQG compensators through repeated forward and backward iteration (integration) of the SDOPE. They are illustrated with four numerical examples.
منابع مشابه
Finite and Infinite Horizon Fixed-order Lqg Compensation Using the Delta Operator
The strengthened discrete-time optimal projection equations (SDOPE) are presented in a form based on the delta operator. This form unifies discrete-time and continuous-time results. Based on this unification, recently established results and algorithms for finite and infinite-horizon fixed-order LQG compensation of discrete-time systems are carried over to the continuous-time case. The results ...
متن کاملCompensatability and optimal compensation of systems with white parameters in the delta domain
Using the delta operator, the strengthened discrete-time optimal projection equations for optimal reduced-order compensation of systems with white stochastic parameters are formulated in the delta domain. The delta domain unifies discrete time and continuous time. Moreover, when formulated in this domain, the efficiency and numerical conditioning of algorithms improves when the sampling rate is...
متن کاملOptimal Fixed-Order Compensation of Distributed Parameter Systems
r. Gary Rosen * * Department of Mathematics University of Southern California Los Angeles, CA 90089 In controlling distributed parameter systems it is often desirable to obtain low-order, finitedimensional controllers in order to minimize real-time computational requirements. Standard approaches to this problem employ model/controller reduction techniques in conjunction with LQG theory. In this...
متن کاملOn some fixed points properties and convergence theorems for a Banach operator in hyperbolic spaces
In this paper, we prove some fixed points properties and demiclosedness principle for a Banach operator in uniformly convex hyperbolic spaces. We further propose an iterative scheme for approximating a fixed point of a Banach operator and establish some strong and $Delta$-convergence theorems for such operator in the frame work of uniformly convex hyperbolic spaces. The results obtained in this...
متن کاملDiscrete-Time, Linear Periodic Time-Varying System Norm Estimation Using Finite Time Horizon Transfer Operators
The norm is one of the fundamental concepts of linear algebra and functional analysis. The notion of the norm is often employed in engineering, e.g. in control engineering, where main application is calculating the norm of the transfer function. Unfortunately existing methods are applicable for systems that can be described using Laplace transform, i.e. linear time-invariant (LTI) systems. An o...
متن کامل