Analysis of approximations of dual control

Abstract

The dual-control problem for time-varying or non-linear stochastic systems is inherently analytically and computationally untractable due to the demand of alternating minimizations and mean value computations. Hence, it has to be approached using approximations leading to suboptimal dual control. The core of the successful approximative controller is its ability to be able to consider future changes in the development of the parameters.This paper presents an analysis of the dual-control concept, and a comparison between a number of suboptimal controllers. The analytical comparisons are based on a reformulation of the dual-control problem. This reformulation makes it possible to interpret and understand the nature of di!erent approximations to dual control, in particular the Adaptive Predictive Controller (APC) and the Active Suboptimal Dual Controller (ASOD). Furthermore it makes the origin of the computational problems encountered more clear, and suggests new alternatives for approximation. The analysis is carried through on relatively simple examples and is illustrated with simulations. The performance of the controllers when applied to more complicated time-varying systems is illustrated with simulations as well.

Robotic motion planning in dynamic, cluttered, uncertain environments

“…In fact, Fel'dbaum first introduced the dual effect of control actions: actions affect the information gathered about the system, as well as progress the system towards the goal. This field is known as dual control, and the reader is referred to the survey by Filatov and Unbehauen [21] and the paper by Londoff et al [39]. Historically, the dual control research community has been interested in controlling a system with unknown parameters and states, so that the controls must be chosen to optimally gather information about the model parameters, and drive the system towards the goal.…”

“…The reader is referred to the survey by Filatov and Unbehauen [21] and the paper by Londoff et al [39].…”

Approximate Dynamic Programming Strategy for Dual Adaptive Control

“…Due to the difficulties in computing the exact solution to the DP formulation, several approximate solutions have been proposed (Wittenmark, 2002). One of them is to find an approximate solution for two-step ahead cost-to-go function (Lindoff et al, 1999). It is, however, still very complex and is restricted to simple problems.…”

“…It has been thought that the DP solution for the problem is intractable, and only a few very simple examples have been solved this way after reducing the problem size through some analytical insights into the specific problem (Åström and Helmersson, 1986). Due to the computational complexity, most researchers approached the problem by introducing cautious and active probing features to simpler suboptimal controllers in a somewhat ad hoc manner (Lindoff et al, 1999;Chikkula and Lee, 2000).…”

A Feasible Control Strategy for LQG Control Problem with Parameter and Structure Uncertainties

“…Shalom [3]. An analysis of various approximations in LQG control problem was given by Lindoff, Holst and Wittenmark [4]. Filatov and Unbehauen developed a bi-criteria approach to cope with the two conflicting goals in LQG control problem: optimization and estimation [5].…”