Control of nonlinear switched systems based on validated simulation

Coënt, Adrien Le; Sandretto, Julien Alexandre Dit; Chapoutot, Alexandre; Fribourg, Laurent

doi:10.1109/snr.2016.7479377

Cited by 7 publications

(16 citation statements)

References 27 publications

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“…Example Consider a building comprised of two rooms subject to heat transfer between the rooms, the external environment, and the human beings described by the following equations (see the works of Le Coent et al and Meyer et al for a more general and detailed setting)

{\overset{normalΘ}{true}}_{i} = \sum_{j \in J} {italicς}_{i j} false({normalΘ}_{j} - {normalΘ}_{i} false) + {italicς}_{i e x t} false({normalΘ}_{e x t} - {normalΘ}_{i} false) + κ_{i} ω_{i} ((), {\overset{normalΘ}{true}}_{i}^{4} - {normalΘ}_{i}^{4}) + u_{i}, i \in false{1, 2 false},

where J ={1,2}, Θ i , i ∈{1,2} is the temperature in the i th room, Θ ext is the outside temperature, u i the control input, ς i j , j ∈ J the heat transfer coefficient between room i and its environment (other rooms, the outside), and ω i is a perturbation indicating the presence of humans ( ω i =1 if someone is present in room i and ω i =0 otherwise) in room i ; κ i ,

{\overset{normalΘ}{true}}_{i}

, and ν i are known coefficients given by Meyer et al and recalled in Table (see Appendix B.1). The control goal is to keep the state (each room temperature) around the point

{normalΘ}^{o b j} = {([], \begin{matrix} center center \\ array Θ_{1}^{o b j} & array Θ_{2}^{o b j} \end{matrix})}^{⊤} = {([], \begin{matrix} center center \\ array 25 & array 25 \end{matrix})}^{⊤}

.…”

Section: Resultsmentioning

confidence: 99%

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Input‐to‐state stability of switched nonlinear systems with delay in the active mode detection

Motchon

Etienne

Lecœuche

2019

Intl J Robust & Nonlinear

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Summary A switched nonlinear system subject to disturbances is considered in this paper. The switching signal admits an average dwell time and a state feedback control depending on the system operating modes, detected with a maximum time delay, is applied to the system. In this framework, the input‐to‐state stability problem of the closed‐loop system is addressed. Based on some established existence conditions of mode‐dependent Lyapunov‐like functions, the values of the maximum time delay and the average dwell time that allow to achieve the input‐to‐state stability of the closed‐loop system are determined. In order to obtain more tractable results, the existence conditions of the mode‐dependent Lyapunov‐like functions are given in terms of sum‐of‐squares programming in the case of polynomial nonlinearities. In the linear case, they are expressed in terms of linear matrix inequalities and a procedure for the synthesis of the mode‐dependent controller is provided in this situation. The established theoretical results are illustrated through a control problem of a building ventilation system and a switched control problem of a vehicle suspension system.

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{\overset{normalΘ}{true}}_{i} = \sum_{j \in J} {italicς}_{i j} false({normalΘ}_{j} - {normalΘ}_{i} false) + {italicς}_{i e x t} false({normalΘ}_{e x t} - {normalΘ}_{i} false) + κ_{i} ω_{i} ((), {\overset{normalΘ}{true}}_{i}^{4} - {normalΘ}_{i}^{4}) + u_{i}, i \in false{1, 2 false},

{\overset{normalΘ}{true}}_{i}

, and ν i are known coefficients given by Meyer et al and recalled in Table (see Appendix B.1). The control goal is to keep the state (each room temperature) around the point

{normalΘ}^{o b j} = {([], \begin{matrix} center center \\ array Θ_{1}^{o b j} & array Θ_{2}^{o b j} \end{matrix})}^{⊤} = {([], \begin{matrix} center center \\ array 25 & array 25 \end{matrix})}^{⊤}

.…”

Section: Resultsmentioning

confidence: 99%

“…Example 1. Consider a building comprised of two rooms subject to heat transfer between the rooms, the external environment, and the human beings described by the following equations (see the works of Le Coent et al 30 and Meyer et al 31 for a more general and detailed setting)…”

Section: Tractable Iss Conditions In the Polynomial Casementioning

confidence: 99%

Input‐to‐state stability of switched nonlinear systems with delay in the active mode detection

Motchon

Etienne

Lecœuche

2019

Intl J Robust & Nonlinear

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“…As said in [10], in the methods of symbolic analysis and control of hybrid systems, the way of representing sets of state values and computing reachable sets for systems defined by ordinary differential equations (ODEs) is fundamental (see, e.g., [2,14]). An interesting approach appeared recently, based on the propagation of reachable sets using guaranteed Runge-Kutta methods with adaptive step size control (see [6,17]).…”

Section: Introductionmentioning

confidence: 99%

“…An interesting approach appeared recently, based on the propagation of reachable sets using guaranteed Runge-Kutta methods with adaptive step size control (see [6,17]). In [10] such guaranteed integration methods are used in the framework of sampled switched systems.…”

Section: Introductionmentioning

confidence: 99%

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Control Synthesis of Nonlinear Sampled Switched Systems using Euler's Method

Coënt

Vuyst

Chamoin

et al. 2017

Electron. Proc. Theor. Comput. Sci.

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In this paper, we propose a symbolic control synthesis method for nonlinear sampled switched systems whose vector fields are one-sided Lipschitz. The main idea is to use an approximate model obtained from the forward Euler method to build a guaranteed control. The benefit of this method is that the error introduced by symbolic modeling is bounded by choosing suitable time and space discretizations. The method is implemented in the interpreted language Octave. Several examples of the literature are performed and the results are compared with results obtained with a previous method based on the Runge-Kutta integration method.

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Distributed Synthesis of State-Dependent Switching Control

Coënt

Fribourg

Markey

et al. 2016

Lecture Notes in Computer Science

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Abstract. We present a correct-by-design method of state-dependent control synthesis for linear discrete-time switching systems. Given an objective region R of the state space, the method builds a capture set S and a control which steers any element of S into R. The method works by iterated backward reachability from R. More precisely, S is given as a parametric extension of R, and the maximum value of the parameter is solved by linear programming. The method can also be used to synthesize a stability control which maintains indefinitely within R all the states starting at R. We explain how the synthesis method can be performed in a distributed manner. The method has been implemented and successfully applied to the synthesis of a distributed control of a concrete floor heating system with 11 rooms and 2 11 = 2048 switching modes.

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Control of nonlinear switched systems based on validated simulation

Cited by 7 publications

References 27 publications

Input‐to‐state stability of switched nonlinear systems with delay in the active mode detection

Input‐to‐state stability of switched nonlinear systems with delay in the active mode detection

Control Synthesis of Nonlinear Sampled Switched Systems using Euler's Method

Distributed Synthesis of State-Dependent Switching Control

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