Extremum control of linear systems based on output feedback

Michalowsky, Simon; Ebenbauer, Christian

doi:10.1109/cdc.2016.7798711

Cited by 11 publications

(11 citation statements)

References 10 publications

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“…Proposition 4.14 (Stabilizability and Detectability Using RFS-OM): Consider the augmented plant (15) using the RFS-OM (24) as the optimality model (ϕ, h ) for the OSS control problem with optimization problem (29). This augmented plant is stabilizable and detectable for a given δ ∈ δ if and only if (i) (C m (δ), A(δ), B(δ)) is stabilizable and detectable;…”

Section: Stabilizer Designmentioning

confidence: 99%

“…A number of recent publications have formulated problem statements and solutions for variants of the OSS control problem [19]- [26]. Many of the currently-proposed controllers, however, have limited applicability: some solutions only apply to systems of a special form [23]; some require asymptotic stability of the uncontrolled plant [25], [26]; some attempt to optimize only the steady-state input [21] or output [20], [24], [27], [28] alone; some apply only to equality-constrained [26] or unconstrained optimization problems [29]; and in all cases, the effects of parametric modelling uncertainty are omitted from consideration.…”

mentioning

confidence: 99%

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Linear-Convex Optimal Steady-State Control

Lawrence

Simpson-Porco

Mallada

2021

IEEE Trans. Automat. Contr.

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We consider the problem of designing a feedback controller for a multivariable linear time-invariant system which regulates an arbitrary system output to the solution of a constrained convex optimization problem despite parametric modelling uncertainty and unknown constant exogenous disturbances; we term this the linear-convex optimal steady-state control problem. We introduce the notion of an optimality model, and show that the existence of an optimality model is sufficient to reduce the problem to a stabilization problem; several instances of optimality models are given under various assumptions. This yields a constructive design framework for optimal steady-state control that unifies and extends many existing design methods in the literature. We illustrate our contributions via several numerical examples, including an application to optimal frequency control of power networks, where our methodology recovers centralized and distributed controllers reported in the recent literature.

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Section: Stabilizer Designmentioning

confidence: 99%

mentioning

confidence: 99%

Linear-Convex Optimal Steady-State Control

Lawrence

Simpson-Porco

Mallada

2021

IEEE Trans. Automat. Contr.

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“…This opens the doors for considering non-linear vehicle models with quasi-LPV representations. The framework developed in this paper can be applied to extremum-seeking control problems [18] or problems involving realtime-optimization [19]. Although the setup considered in [19] is the similar as in this paper (except for the LPV extension), the focus there is on designing an optimizer and obtaining conditions for optimality and stability with static α−IQCs.…”

Section: Related Workmentioning

confidence: 99%

Robust Performance Analysis of Source-Seeking Dynamics with Integral Quadratic Constraints

Datar¹,

Werner²

2021

Preprint

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We analyze the performance of source-seeking dynamics involving either a single vehicle or multiple flockingvehicles embedded in an underlying strongly convex scalar field with gradient based forcing terms. For multiple vehicles under flocking dynamics embedded in quadratic fields, we show that the dynamics of the center of mass are equivalent to the dynamics of a single agent. We leverage the recently developed framework of α-integral quadratic constraints (IQCs) to obtain convergence rate estimates. We first present a derivation of hard Zames-Falb (ZF) α-IQCs involving general non-causal multipliers based on purely time-domain arguments and show that a parameterization of the ZF multiplier, suggested in the literature for the standard version of the ZF IQCs, can be adapted to the α-IQCs setting to obtain quasi-convex programs for estimating convergence rates. Owing to the time-domain arguments, we can seamlessly extend these results to linear parameter varying (LPV) vehicles possibly opening the doors to non-linear vehicle models with quasi-LPV representations. We illustrate the theoretical results on a linear time invariant (LTI) model of a quadrotor, a non-minimum phase LTI plant and two LPV examples which show a clear benefit of using general non-causal dynamic multipliers to drastically reduce conservatism.

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“…We emphasize that any papers in the literature revolve around the case l = 0 leading to a multiplier without dynamics, which is related to the so-called circle-criterion or a version of the small-gain theorem. For example in [21], controllers are assumed to have an observer structure incorporating an integrator, and the design is split up into sequential observer and state-feedback synthesis steps relying on the smallgain theorem, both of which are typically conservative. The paper [23] fixes a control structure and is confined to stability analysis for l = 0 only.…”

Section: 3mentioning

confidence: 99%

“…Among the many concrete instantiations of extremum control, we concentrate on the case where some linear system is given, the cost function f is only known to belong to the class S m,L , and the gradient of the cost function can be evaluated [21,23,15]. To be concrete, we assume that the system is described as…”

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confidence: 99%

Convex Synthesis of Accelerated Gradient Algorithms

Scherer¹,

Ebenbauer²

2021

Preprint

Self Cite

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We present a convex solution for the design of generalized accelerated gradient algorithms for strongly convex objective functions with Lipschitz continuous gradients. We utilize integral quadratic constraints and the Youla parameterization from robust control theory to formulate a solution of the algorithm design problem as a convex semidefinite program. We establish explicit formulas for the optimal convergence rates and extend the proposed synthesis solution to extremum control problems.

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Extremum control of linear systems based on output feedback

Cited by 11 publications

References 10 publications

Linear-Convex Optimal Steady-State Control

Linear-Convex Optimal Steady-State Control

Robust Performance Analysis of Source-Seeking Dynamics with Integral Quadratic Constraints

Convex Synthesis of Accelerated Gradient Algorithms

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