Invariant Sets Analysis for Constrained Switching Systems

Αθανασόπουλος, Νικόλαος; Smpoukis, Konstantinos; Jungers, Raphaël M.

doi:10.1109/lcsys.2017.2714840

Cited by 22 publications

(18 citation statements)

References 35 publications

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“…is a special case of the switched system (1) with  i = {0} for each mode i ∈ I. Thus, this paper generalizes the results from the works of Dehghan and Ong 18 and Athanasopoulos et al 19…”

Section: Switched Constrained Systemsupporting

confidence: 73%

“…However, the class of switched systems studied did not include control inputs. Thus, this paper complements and extends those results 18,19 to nonautonomous switched systems.…”

Section: Introductionsupporting

confidence: 76%

“…Remark The autonomous switched system

\begin{matrix} x (t + 1) = & f_{σ (t)} (x (t)) \\ x (t) \in & X_{σ (t)} \end{matrix}

is a special case of the switched system (1) with

{scriptU}_{i} = false{0 false}

for each mode

i \in double-struckI

. Thus, this paper generalizes the results from the works of Dehghan and Ong and Athanasopoulos et al…”

Section: Problem Statementsupporting

confidence: 62%

“…In this paper, the roles of the control‐inputs and disturbances are reversed, ie, the switching signal is the disturbance and the inputs to each mode are controlled, which obviously leads to substantially different results. The works of Dehghan and Ong and Athanasopoulos et al studied robust positive invariant sets for switched systems in which the switching signal is a disturbance, as in this paper. However, the class of switched systems studied did not include control inputs.…”

Section: Introductionmentioning

confidence: 99%

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Necessary and sufficient conditions for constraint satisfaction in switched systems using switch‐robust control invariant sets

Danielson

Bridgeman

Cairano

2019

Intl J Robust & Nonlinear

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Summary This paper studies the control of constrained systems whose dynamics and constraints switch between a finite set of modes over time according to an exogenous input signal. We define a new type of control invariant sets for switched constrained systems, called switch–robust control invariant (switch‐RCI) sets, that are robust to unknown mode switching and exploit available information on minimum dwell‐time and admissible mode transitions. These switch‐RCI sets are used to derive novel necessary and sufficient conditions for the existence of a control‐law that guarantees constraint satisfaction in the presence of unknown mode switching with known minimum dwell‐time. The switch‐RCI sets are also used to design a recursively feasible model predictive controller (MPC) that enforces closed‐loop constraint satisfaction for switched constrained systems. We show that our controller is nonconservative in the sense that it enforces constraints on the largest possible domain, ie, constraints can be recursively satisfied if and only if our controller is feasible. The MPC and switch‐RCI sets are demonstrated on a vehicle lane‐changing case study.

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Section: Switched Constrained Systemsupporting

confidence: 73%

“…However, the class of switched systems studied did not include control inputs. Thus, this paper complements and extends those results 18,19 to nonautonomous switched systems.…”

Section: Introductionsupporting

confidence: 76%

“…Remark The autonomous switched system

\begin{matrix} x (t + 1) = & f_{σ (t)} (x (t)) \\ x (t) \in & X_{σ (t)} \end{matrix}

is a special case of the switched system (1) with

{scriptU}_{i} = false{0 false}

for each mode

i \in double-struckI

. Thus, this paper generalizes the results from the works of Dehghan and Ong and Athanasopoulos et al…”

Section: Problem Statementsupporting

confidence: 62%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Necessary and sufficient conditions for constraint satisfaction in switched systems using switch‐robust control invariant sets

Danielson

Bridgeman

Cairano

2019

Intl J Robust & Nonlinear

View full text Add to dashboard Cite

show abstract

“…For further work, the application of the tools used in Section III, such as the observer graph, to refine the analysis of Section IV remains to be investigated. On a more practical side, the common Lyapunov function representation presented in Section III could allow us to better leverage Path-Complete techniques for reachability and invariance analysis [4].…”

Section: Discussionmentioning

confidence: 99%