MPC-based approximate dual controller by information matrix maximization

doi:10.1002/acs.2370

2012-12-04

PRE

Jan Rathouský *

Vladimı́r Havlena

DOI：10.1002/acs.2370

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摘要

En 中文

This paper proposes a method to approximate a dual controller by a computationally feasible algorithm. Dual control that optimally solves the problem of simultaneous control and identification of a system with uncertain parameters is known to be both analytically and computationally unsolvable. This paper proposes a multiple-step active control algorithm that gives a suboptimal but tractable solution to the original dual control problem. The algorithm is based on model predictive control (MPC) and approximates persistent system excitation in terms of the increase of the lowest eigenvalue of the parameter estimate information matrix. The problem is formulated as a two-phase optimization problem, where first an MPC solution is found and then the lowest eigenvalue of the information matrix is maximized in the next step within a given permitted input perturbation. Unlike similar methods, the proposed algorithm predicts the information matrix for more than one step of control, which makes it possible to uniformly excite the parameter space. The use of MPC in the first design phase instead of a cautious controller is justified by showing unfavorable properties of cautious control. The advantage of the multiple-step prediction over single-step prediction is shown by examples and simulations. The proposed algorithm is analyzed in terms of convergence and complexity, and stability issues are addressed. The formal proofs are included in the Appendix. Copyright (c) 2012 John Wiley & Sons, Ltd.

Keyword:

model predictive control

dual control

persistent excitation

cautious control