Linear-Convex Optimal Steady-State Control

Lawrence, Liam S. P.; Simpson-Porco, John W.; Mallada, Enrique

doi:10.1109/tac.2020.3044275

Cited by 38 publications

(24 citation statements)

References 46 publications

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“…Thus, one could interpret the specification (7) as arising from a steady-state optimization problem where the goal is to minimize a function of the tracking error. This perspective connects our approach directly with recent ideas in autonomous and feedback-based optimization; see [24]- [27] for recent contributions.…”

Section: B Constrained Error-zeroing Specificationmentioning

confidence: 75%

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Low-Gain Stability of Projected Integral Control for Input-Constrained Discrete-Time Nonlinear Systems

Simpson-Porco

2022

IEEE Control Syst. Lett.

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We consider the problem of zeroing an error output of a nonlinear discrete-time system in the presence of constant exogenous disturbances, subject to hard convex constraints on the input signal. The design specification is formulated as a variational inequality, and we adapt a forwardbackward splitting algorithm to act as an integral controller which ensures that the input constraints are met at each time step. We establish a low-gain stability result for the closedloop system when the plant is exponentially stable, generalizing previously known results for integral control of discrete-time systems. Specifically, it is shown that if the composition of the plant equilibrium input-output map and the integral feedback gain is strongly monotone, then the closed-loop system is exponentially stable for all sufficiently small integral gains. The method is illustrated via a simple numerical example.

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Section: B Constrained Error-zeroing Specificationmentioning

confidence: 75%

“…where the summands are defined in (25). We now bound each term in (24) individually. Applying (23c) to |∆V 1 f | we obtain…”

Section: B Low-gain Stability With Dp-i Controlmentioning

confidence: 99%

Low-Gain Stability of Projected Integral Control for Input-Constrained Discrete-Time Nonlinear Systems

Simpson-Porco

2022

IEEE Control Syst. Lett.

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“…Convergence and stability analysis for regulation of linear time-invariant systems towards the optimal solution of a time-varying convex optimisation problem is studied in [16]. Constraints are included in [17], [18] and [19] extends to non-linear systems and non-convex problems.…”

Section: Introductionmentioning

confidence: 99%

Distributed Feedback Optimisation for Robotic Coordination

Sylvain¹,

Perez²,

Badyn³

et al. 2021

Preprint

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Feedback optimisation is an emerging technique aiming at steering a system to an optimal steady state for a given objective function. We show that it is possible to employ this control strategy in a distributed manner. Moreover, we prove asymptotic convergence to the set of optimal configurations. To this scope, we show that exponential stability is needed only for the portion of the state that affects the objective function. This is showcased by driving a swarm of agents towards a target location while maintaining a target formation. Finally, we provide a sufficient condition on the topological structure of the specified formation to guarantee convergence of the swarm in formation around the target location.

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“…The interconnection of input-constrained nonlinear systems with gradient flow dynamics is studied in [17]. A design framework for unconstrained online optimization of LTI systems is presented in [18] and related work on low-gain integral controllers for nonlinear systems can be found in [19]. Finally, the stability of saddle-flow-based FO for a class of nonlinear systems to a constrained convex optimization problem is investigated in [20].…”

Section: Introductionmentioning

confidence: 99%

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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Linear-Convex Optimal Steady-State Control

Cited by 38 publications

References 46 publications

Low-Gain Stability of Projected Integral Control for Input-Constrained Discrete-Time Nonlinear Systems

Low-Gain Stability of Projected Integral Control for Input-Constrained Discrete-Time Nonlinear Systems

Distributed Feedback Optimisation for Robotic Coordination

Sampled-Data Online Feedback Equilibrium Seeking: Stability and Tracking

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