Non-Convex Feedback Optimization with Input and Output Constraints

Verena, Häberle,; Hauswirth, Adrian; Ortmann, Lukas; Bolognani, Saverio; Dörfler, Florian

doi:10.1109/lcsys.2020.3002152

Cited by 22 publications

(44 citation statements)

References 45 publications

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“…Furthermore, the feedback structure contributes to robustness against unmeasured disturbances and model mismatch [18], [19], as well as autonomous tracking of trajectories of optimal solutions of time-varying problems [20]- [25]. Some works [20], [22], [23], [26] consider fast-stable plants that are abstracted as algebraic steady-state maps. Others take system dynamics into account and characterize sufficient conditions for the closedloop stability, including in continuous-time [21], [27]- [29] and sampled-data settings [30].…”

Section: A Related Workmentioning

confidence: 99%

“…Others take system dynamics into account and characterize sufficient conditions for the closedloop stability, including in continuous-time [21], [27]- [29] and sampled-data settings [30]. Specifically, among works that handle nonconvex objectives and nonlinear systems, [22], [26] address discrete-time systems represented by algebraic maps, while [28] tackles continuous-time systems. The results on nonconvex feedback optimization for discrete-time nonlinear dynamical systems are still lacking.…”

Section: A Related Workmentioning

confidence: 99%

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Model-Free Nonlinear Feedback Optimization

He¹,

Bolognani²,

He³

et al. 2022

Preprint

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Feedback optimization is a control paradigm that enables physical systems to autonomously reach efficient operating points. Its central idea is to interconnect optimization iterations in closed-loop with the physical plant. Since iterative gradient-based methods are extensively used to achieve optimality, feedback optimization controllers typically require the knowledge of the steady-state sensitivity of the plant, which may not be easily accessible in some applications. In contrast, in this paper we develop a model-free feedback controller for efficient steady-state operation of general dynamical systems. The proposed design consists in updating control inputs via gradient estimates constructed from evaluations of the nonconvex objective at the current input and at the measured output. We study the dynamic interconnection of the proposed iterative controller with a stable nonlinear discrete-time plant. For this setup, we characterize the optimality and the stability of the closed-loop behavior as functions of the problem dimension, the number of iterations, and the rate of convergence of the physical plant. To handle general constraints that affect multiple inputs, we enhance the controller with Frank-Wolfe type updates.

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Section: A Related Workmentioning

confidence: 99%

Section: A Related Workmentioning

confidence: 99%

Model-Free Nonlinear Feedback Optimization

He¹,

Bolognani²,

He³

et al. 2022

Preprint

Self Cite

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“…In our problem setting, w is not measurable (nor constant), so we run the algorithm (11) in parallel with the plant and replace evaluations of the steady-state map h with measurements of y obtained from the system. This online-feedbackequilibrium-seeking strategy renders the optimization routine robust to unmeasured w and to modelling errors 2 .…”

Section: Control Strategymentioning

confidence: 99%

“…where ε ∈ (0, 1] is a relaxation parameter used to regulate the control action generated by (11). We next provide two concrete examples of equilibrium seeking algorithms before proceeding to a closed-loop stability analysis.…”

Section: Control Strategymentioning

confidence: 99%

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Sampled-Data Online Feedback Equilibrium Seeking: Stability and Tracking

Belgioioso

Liao‐McPherson

Badyn

et al. 2021

2021 60th IEEE Conference on Decision and Control (CDC)

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This paper proposes a general framework for constructing feedback controllers that drive complex dynamical systems to "efficient" steady-state (or slowly varying) operating points. Efficiency is encoded using generalized equations which can model a broad spectrum of useful objectives, such as optimality or equilibria (e.g. Nash, Wardrop, etc.) in noncooperative games. The core idea of the proposed approach is to directly implement iterative solution (or equilibrium seeking) algorithms in closed loop with physical systems. Sufficient conditions for closed-loop stability and robustness are derived; these also serve as the first closed-loop stability results for sampleddata feedback-based optimization. Numerical simulations of smart building automation and game-theoretic robotic swarm coordination support the theoretical results.

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Reinforcement learning‐based optimized backstepping control for strict‐feedback nonlinear systems subject to external disturbances

Yan

Cao

et al. 2023

Optim Control Appl Methods

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This article investigates a reinforcement learning‐based optimal backstepping control strategy for strict‐feedback nonlinear systems, which contain output constraints, external disturbances and uncertain unknown dynamics. The simplified reinforcement learning algorithm with the identifier‐critic‐actor architecture is constructed in the control design to build optimal virtual and actual controllers. To compensate for the disturbance, a lemma is adopted to transform external disturbances into an unknown “bounding functions‘’, which satisfy a triangular condition. Moreover, the unknown nonlinear functions, which composed of unknown dynamics and external disturbances, approximated by neural networks. Meanwhile, in order to avoid violating output constraints, a barrier‐type Lyapunov function approach is integrated into the optimal control strategy to satisfy output constraints requirements under the framework of backstepping technique. Furthermore, the presented optimal control strategy guarantees that all signals in the closed‐loop system are semi‐globally uniformly ultimately bounded. Finally, the effectiveness of the proposed optimal control approach is performed by a numerical example.

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Non-Convex Feedback Optimization with Input and Output Constraints

Cited by 22 publications

References 45 publications

Model-Free Nonlinear Feedback Optimization

Model-Free Nonlinear Feedback Optimization

Sampled-Data Online Feedback Equilibrium Seeking: Stability and Tracking

Reinforcement learning‐based optimized backstepping control for strict‐feedback nonlinear systems subject to external disturbances

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