On the equivalence between complementarity systems, projected systems and differential inclusions

Brogliato, Bernard; Daniilidis, Aris; Lemaréchal, Claude; Acary, Vincent

doi:10.1016/j.sysconle.2005.04.015

Cited by 132 publications

(107 citation statements)

References 19 publications

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“…Corollary 1 will be used in the next section to assert the existence and uniqueness of solutions to system Σ g . See [12]- [14] for a detailed development of PDS, and [15] for known relations to other system descriptions.…”

Section: Corollary 1 ( [18 Corollary 1])mentioning

confidence: 99%

“…Observe that PDS is a significant line of independent research that has attracted the attention of economists and mathematicians, among others. The link to PDS thus enables cross utilization of ideas and methods, as demonstrated in [15]. Using results from the PDS literature, existence and uniqueness of solutions to the GPAW compensated system can thus be easily established, as shown in Section IV.…”

Section: Introductionmentioning

confidence: 99%

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Gradient Projection Anti-windup Scheme on Constrained Planar LTI Systems

Teo¹,

How²

2010

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Abstract-The gradient projection anti-windup (GPAW) scheme was recently proposed as an anti-windup method for nonlinear multi-input-multi-output systems/controllers, the solution of which was recognized as a largely open problem in a recent survey paper. This paper analyzes the properties of the GPAW scheme applied to an input constrained first order linear time invariant (LTI) system driven by a first order LTI controller, where the objective is to regulate the system state about the origin. We show that the GPAW compensated system is in fact a projected dynamical system (PDS), and use results in the PDS literature to assert existence and uniqueness of its solutions. The main result is that the GPAW scheme can only maintain/enlarge the exact region of attraction of the uncompensated system.

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Section: Corollary 1 ( [18 Corollary 1])mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Gradient Projection Anti-windup Scheme on Constrained Planar LTI Systems

Teo¹,

How²

2010

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“…To the same end, one might posit P = N C in (1), but doing so offers no advantages: Proposition 1. (Coincidence of trajectories and viability 4 ) In (1) let P (t, ·) = 4 For more on equivalent viable systems see [11].…”

Section: Pursuing Regular Setsmentioning

confidence: 99%

Feasibility in finite time

2009

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It is common to tolerate that a system's performance be unsustainable during an interim period. To live long however, its state must eventually satisfy various constraints. In this regard we design here differential inclusions that generate, in one generic format, two distinct phases of system dynamics. The first ensures feasibility in finite time; the second maintains that property forever after.

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“…Then the closed-loop system, i.e. the system obtained from the system (1) connected with controller (4) or (5) in a feedback loop, has an equilibrium point with x p =x p (w), wherex p (w) denotes the minimizer of the optimization problem (2) for some w ∈ W .…”

Section: Dynamic Kkt Controllersmentioning

confidence: 99%

On constrained steady-state optimal control: Dynamic KKT controllers

Jokic

Lazăr

Bosch

2008

2008 American Control Conference

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Abstract-This paper presents a solution to the problem of controlling a general linear time-invariant dynamical system (plant) to a time-varying economically optimal operating point. The plant is characterized by a set of exogenous inputs as an abstraction of time-varying loads and disturbances. The economically optimal operating point is implicitly defined as a solution to a given constrained convex optimization problem, which is related to steady-state operation of the plant. A subset of the plant's states and the exogenous inputs represent respectively the decision variables and the parameters in the optimization problem. The proposed control structure, which is proven to solve the considered control problem, is explicitly defined and is based on the dynamic extension of the KarushKuhn-Tucker (KKT) optimality conditions for the steady-state related optimization problem.

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On the equivalence between complementarity systems, projected systems and differential inclusions

Cited by 132 publications

References 19 publications

Gradient Projection Anti-windup Scheme on Constrained Planar LTI Systems

Gradient Projection Anti-windup Scheme on Constrained Planar LTI Systems

Feasibility in finite time

On constrained steady-state optimal control: Dynamic KKT controllers

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