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Achieving optimal steady-state performance in real-time 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 Time-Invariant (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 steady-state. We analyze the equilibrium characteristics of the closed-loop system and provide conditions for optimality and stability. Our analysis shows that the proposed solution guarantees optimal steady-state 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 input-output properties of our optimization component into sufficient conditions, based on linear matrix inequalities (LMIs), for global exponential asymptotic stability of the closed-loop system. We illustrate several resulting controller designs using a numerical example.
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Nonlinear Data-Driven Control via State-Dependent Representations
Recently, there has been renewed interest in data-driven control, that is, the design of controllers directly from observed data. In the case of linear time-invariant (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 state-dependent representations. This idea allows for synthesizing data-driven controllers by solving at each time step an on-line 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 on-line optimization problem guarantees that the proposed controller renders the origin a globally asymptotically stable equilibrium point of the closed-loop system. These results are illustrated with some simple examples. The paper concludes by briefly discussing the prospects for adding performance criteria.
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- PAR ID:
- 10349422
- Date Published:
- Journal Name:
- 60th IEEE Conf. Decision and Control
- Page Range / eLocation ID:
- 5765 to 5770
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Conference Paper:
- https://doi.org/10.1109/CDC45484.2021.9682919
