MPC‐based approximate dual controller by information matrix maximization

Abstract

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

Model-predictive control for non-domestic buildings: a critical review and prospects

“…Nonetheless, re-identification under closed-loop has its technical challenges since the nature of feedback control will treat any input stimulus designed to elicit the system response as a disturbance, which the control system will try to eliminate. The basic approach is to inject a 'dither' signal uncorrelated to the disturbance (Genceli & Nikolaou, 1996;Rathouský & Havlena, 2013;Marafioti, Bitmead, & Hovd, 2014). Typically, this dither signal is used to perturb the system setpoints (Zhu & Butoyi, 2002) although other approaches have been explored (Sotomayor, Odloak, and Moro, 2009).…”

Experimental Evaluation of a MIMO Adaptive Dual MPC

“…A nonconvex excitation constraint was derived and imposed on the first of the open-loop optimal input variables, resulting in a periodic input signal generated by the controller. Another M.P.C.-based method was developed by Rathouský and Havlena (2013) and later extended by Žáčeková, Prívara, and Pčolka (2013). In the most recent version of the algorithm, the first step is to solve a standard M.P.C.…”

“…The controllers in Paper A are based on adding a term to a nominal cost for the purpose of rewarding uncertainty reduction. A related approach, taken by for instance Rathouský and Havlena (2013), is to optimize for nominal control and excitation separately. Their algorithm first solves a nominal M.P.C.…”

Robust dual control MPC with guaranteed constraint satisfaction

“…While the problem formulation in the time domain is highly nonconvex, developing such techniques is desirable, and thus the focus of recent work [6]- [10]. In [3] and [11], convex relaxations of the input design problem in the time domain are presented.…”

“…They either do not include state constraints [6], or they may violate state constraints during the learning transient due to a certainty equivalence assumption, that is, using parameter estimates as if they were the true values [7]. Approaches that are able to enforce constraints may be computationally intensive due to solving min-max problems [8], or conservative due to enforcement of open-loop robustness in a receding horizon framework, uncertainty compensation using a fixed feedback law, or only handling additive uncertainty [8]- [10].…”