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18059
15/06/2018

Hybrid Regional Stabilization of Linear Systems with Actuator Saturation and Multi-Rate Samplers

F.FERRANTE, R.G.SANFELICE, S.TARBOURIECH

MAC, Arizona, GIPSA-Lab

Manifestation avec acte : European Control Conference ( ECC ) 2018 du 12 juin au 15 juin 2018, Limassol (Chypre), Juin 2018 , N° 18059

Lien : https://hal.archives-ouvertes.fr/hal-01721712

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18083
01/06/2018

Information constraints in multiple agent problems with i.i.d. states

S.LASAULCE, S.TARBOURIECH

L2S, MAC

Ouvrage (contribution) : Control Subject to Computational and Communication Constraints, Springer, N°ISBN 978-3-319-78449-6, Juin 2018, 13p. , N° 18083

Lien : https://hal.archives-ouvertes.fr/hal-01745567

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Abstract

In this chapter we describe several recent results on the problem of coordination among agents when they have partial information about a state which affects their utility, payoff, or reward function. The state is not controlled and rather evolves according to an independent and identically distributed (i.i.d.) random process. This random process might represent various phenomena. In control, it may represent a perturbation or model uncertainty. In the context of smart grids, it may represent a forecasting noise [1]. In wireless communications, it may represent the state of the global communication channel. The approach used is to exploit Shannon theory to characterize the achievable long-term utility region. Two scenarios are described. In the first scenario, the number of agents is arbitrary and the agents have causal knowledge about the state. In the second scenario, there are only two agents and the agents have some knowledge about the future of the state, making its knowledge non-causal.

143080
18088
20/04/2018

Moments and convex optimization for analysis and control of nonlinear partial differential equations

M.KORDA, D.HENRION, J.B.LASSERRE

University of Califo, MAC

Rapport LAAS N°18088, Avril 2018, 33p.

Lien : https://hal.archives-ouvertes.fr/hal-01771699

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Abstract

This work presents a convex-optimization-based framework for analysis and control of nonlinear partial differential equations. The approach uses a particular weak embedding of the nonlinear PDE, resulting in a linear equation in the space of Borel measures. This equation is then used as a constraint of an infinite-dimensional linear programming problem (LP). This LP is then approximated by a hierarchy of convex, finite-dimensional, semidefinite programming problems (SDPs). In the case of analysis of uncontrolled PDEs, the solutions to these SDPs provide bounds on a specified, possibly nonlinear, functional of the solutions to the PDE; in the case of PDE control, the solutions to these SDPs provide bounds on the optimal value of a given optimal control problem as well as suboptimal feedback controllers. The entire approach is based purely on convex optimization and does not rely on spatio-temporal gridding, even though the PDE addressed can be fully nonlinear. The approach is applicable to a very broad class nonlinear PDEs with polynomial data. Computational complexity is analyzed and several complexity reduction procedures are described. Numerical examples demonstrate the approach.

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18081
03/04/2018

Relaxed periodic switching controllers of high-frequency DC-DC converters using the δ-operator formulation

A.CUTILLAS, C.ALBEA SANCHEZ, A.SEURET, F.GORDILLO

Seville, MAC

Rapport LAAS N°18081, Avril 2018, 6p.

Lien : https://hal.archives-ouvertes.fr/hal-01746435

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Abstract

This paper deals with the design of new periodic switching control laws for high frequency DC-DC converters. The contributions are twofolds. On a first hand, the DC-DC converter model are rewritten as a periodic switched affine systems thanks to a δ-operator formulation, which represent an efficient framework for the numerical discretization at high frequencies. On a second hand, three different control laws are provided, the first one being the usual Lyapunov-based control law and the two others being relaxed versions of this first solution. The benefits of these two new control laws over the usual Lyapunov-based one are demonstrated on an simple example. More particularly, it is showed that the selection of sampling period and of the control law strongly influence the size of the region of attraction.

143075
18082
03/04/2018

Representation of distributionally robust chance-constraints

J.B.LASSERRE, T.WEISSER

MAC

Rapport LAAS N°18082, Avril 2018, 31p.

Lien : https://hal.laas.fr/hal-01755147

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Abstract

Given X⊂Rn, ε∈(0,1), a parametrized family of probability distributions (μa)a∈A on Ω⊂Rp, we consider the feasible set X∗ε⊂X associated with the {\em distributionally robust} chance-constraint X∗ε={x∈X:Probμ[f(x,ω)>0]>1−ε,∀μ∈Ma}, where Ma is the set of all possibles mixtures of distributions μa, a∈A. For instance and typically, the family Ma is the set of all mixtures of Gaussian distributions on R with mean and standard deviation a=(a,σ) in some compact set A⊂R2. We provide a sequence of inner approximations Xdε={x∈X:wd(x)<ε}, d∈N, where wd is a polynomial of degree d whose vector of coefficients is an optimal solution of a semidefinite program. The size of the latter increases with the degree d. We also obtain the strong and highly desirable asymptotic guarantee that λ(X∗ε∖Xdε)→0 as d increases, where λ is the Lebesgue measure on X. Same results are also obtained for the more intricated case of distributionally robust ``joint" chance-constraints.

143078
16253
23/03/2018

Well-posedness and output regulation for implicit time-varying evolution variational inequalities

A.TANWANI, B.BROGLIOATO, C.PRIEUR

MAC, INRIA Rhône-Alpes, GIPSA-Lab

Revue Scientifique : SIAM Journal on Control and Optimization, Vol.56, N°2, pp.751-781, Mars 2018 , N° 16253

Lien : https://hal.archives-ouvertes.fr/hal-01360325

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Abstract

A class of evolution variational inequalities (EVIs), which comprises ordinary differential equations (ODEs) coupled with variational inequalities (VIs) associated with time-varying set-valued mappings, is proposed in this paper. We first study the conditions for existence and uniqueness of solutions. The central idea behind the proof is to rewrite the system dynamics as a differential inclusion which can be decomposed into a single-valued Lipschitz map, and a time-dependent maximal monotone operator. Regularity assumptions on the set-valued mapping determine the regularity of the resulting solutions. Complementarity systems with time-dependence are studied as a particular case. We then use this result to study the problem of designing state feedback control laws for output regulation in systems described by EVIs. The derivation of control laws for output regulation is based on the use of internal model principle, and two cases are treated: First, a static feedback control law is derived when full state feedback is available; In the second case, only the error to be regulated is assumed to be available for measurement and a dynamic compensator is designed. As applications, we demonstrate how control input resulting from the solution of a variational inequality results in regulating the output of the system while maintaining polyhedral state constraints. Another application is seen in designing control inputs for regulation in power converters.

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18072
22/03/2018

Uncertain Saturated Discrete-Time Sliding Mode Control for A Wind Turbine Using A Two-Mass Model

C.ZAAFOURI, B.TORCHANI, A.SELLAMI, G.GARCIA

ENIT, ESSTT, MAC

Revue Scientifique : Asian Journal of Control, Vol.20, N°7, Mars 2018, doi 10.1002/asjc.1594 , N° 18072

Lien : https://hal.laas.fr/hal-01735088

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Abstract

The aim of this paper is to propose a new design variable speed wind turbine control by discrete-time sliding mode approach. The control objective is to obtain a maximum extraction of wind energy, while reducing mechanical loads and rotor speed tracking combined with an electromagnetic torque. For this application, we designed a discrete time sliding mode control using the equivalent discrete time reaching law. Furthermore, a systematic and improved design procedure for uncertainties discrete-time sliding mode control (SMC) with saturation problem is provided in this paper. The saturation constraint is reported on inputs vector. LMI technique and polytopic models are used in the design of the switching surface. To achieve some performance requirements and good robustness, in the sliding mode, the pole clustering method is investigated. Based on the unit vector control approach, a robust control is developed, then, to direct and maintain the system states onto the sliding manifold in finite time. Finally, a systematic design procedure for DSMC required to achieve a given performance level is provided and its effectiveness is varied by applying it to variable speed wind turbine systems.

142933
18071
15/03/2018

Embedding a SDP-based control algorithm for the orbital rendezvous hovering phases

F.CAMPS, P.R.ARANTES GILZ, M.M.JOLDES, C.LOUEMBET

IDEA, MAC

Rapport LAAS N°18071, Mars 2018, 10p.

Lien : https://hal.laas.fr/hal-01729956

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In this paper we present the procedures for embedding a semidefinite programming-based control algorithm for the impulsive rendezvous hovering phases problem on a board containing a synthesized LEON3 microprocessor. The performance of this algorithm is benchmarked by means of simulations against traditional linear programming-based constraint discretization approaches.

142892
18061
14/03/2018

Exponential Lyapunov Stability Analysis of a Drilling Mechanism

M.BARREAU, A.SEURET, F.GOUAISBAUT

MAC

Rapport LAAS N°18061, Mars 2018, 6p.

Lien : https://hal.laas.fr/hal-01725416

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Abstract

This article deals with the stability analysis of a drilling system which is modelled as a coupled ordinary differential equation / string equation. The string is damped at the two boundaries but leading to a stable open-loop system. The aim is to derive a linear matrix inequality ensuring the exponential stability with a guaranteed decay-rate of this interconnected system. A strictly proper dynamic controller based on boundary measurements is proposed to accelerate the system dynamics and its effects are investigated through the stability theorem and simulations. It results in an efficient finite dimension controller which subsequently improves the system performances.

142827
18067
14/03/2018

Hybrid control algorithm for a DC-AC converter

C.ALBEA SANCHEZ, O.LOPEZ SANTOS, D.A.ZAMBRANO-PRADA, F.GORDILLO, G.GARCIA

MAC, Unibague, Seville

Rapport LAAS N°18067, Mars 2018, 13p.

Lien : https://hal.archives-ouvertes.fr/hal-01730522

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Abstract

This paper presents a control law based on Hybrid Dynamical Systems (HDS) theory for a dc-ac converter. This theory is very suited for analysis of power electronic converters, since they combine continuous (voltages and currents) and discrete (on-off state of switches) signals avoiding, in this way, the use of averaged models. Here, practical stability results are induced for this tracking problem, ensuring a minimum dwell-time associated with an LQR performance level during the transient response and an admissible chattering around the operating point. The effectiveness of the resultant control law is validated by means of simulations and experiments.

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