Achieving optimal steadystate performance in realtime is an increasingly necessary requirement of many critical infrastructure systems. In pursuit of this goal, this paper builds a systematic design framework of feedback controllers for Linear TimeInvariant (LTI) systems that continuously track the optimal solution of some predefined optimization problem. We logically divide the proposed solution into three components. The first component estimates the system state from the output measurements. The second component uses the estimated state and computes a drift direction based on an optimization algorithm. The third component calculates an input to the LTI system that aims to drive the system toward the optimal steadystate. We analyze the equilibrium characteristics of the closedloop system and provide conditions for optimality and stability. Our analysis shows that the proposed solution guarantees optimal steadystate performance, even in the presence of constant disturbances. Furthermore, by leveraging recent results on the analysis of optimization algorithms using Integral Quadratic Constraints (IQCs), the proposed framework can translate inputoutput properties of our optimization component into sufficient conditions, based on linear matrix inequalities (LMIs), for global exponential asymptotic stability of the closedloop system. We illustrate several resulting controller designs using a numerical example.
This content will become publicly available on December 14, 2022
Nonlinear DataDriven Control via StateDependent Representations
Recently, there has been renewed interest in datadriven control, that is, the design of controllers directly from observed data. In the case of linear timeinvariant (LTI) systems, several approaches have been proposed that lead to tractable optimization problems. On the other hand, the case of nonlinear dynamics is considerably less developed, with existing approaches limited to at most rational dynamics and requiring the solution to a computationally expensive Sum of Squares (SoS) optimization. Since SoS problems typically scale combinatorially with the size of the problem, these approaches are limited to relatively low order systems. In this paper, we propose an alternative, based on the use of statedependent representations. This idea allows for synthesizing datadriven controllers by solving at each time step an online optimization problem whose complexity is comparable to the LTI case. Further, the proposed approach is not limited to rational dynamics. The main result of the paper shows that the feasibility of this online optimization problem guarantees that the proposed controller renders the origin a globally asymptotically stable equilibrium point of the closedloop system. These results are illustrated with some simple examples. The paper concludes by briefly discussing the prospects for adding performance criteria.
 Publication Date:
 NSFPAR ID:
 10349422
 Journal Name:
 60th IEEE Conf. Decision and Control
 Page Range or eLocationID:
 5765 to 5770
 Sponsoring Org:
 National Science Foundation
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