Optimal Radio-Mode Switching for wireless Networked Control Systems N. Cardoso, F. Garin, C. Canudas-de-Wit Presented by: Carlos Canudas de Wit CNRS-GIPSA-Lab, NeCS Team, Grenoble, FRANCE October 17-19 th , 2012 Material from: Energy-aware wireless networked control using radio-mode management, N. Cardoso, Ph.D. Dissertation, University of Grenoble, Oct. 2012. Energy-aware wireless networked control using radio-mode management, N. Cardoso de Castro, C. Canudas-de-Wit, and F. Garin. ACC 2012, Montr´ eal, Canada Smart Energy-Aware Sensors for Event-Based Control, N. Cardoso De Castro; D. E. Quevedo; F. Garin; C. Canudas-de-Wit. IEEE CDC’12 CNRS, GIPSA-lab, NeCS-Team Energy-aware control and communication co-design in wireless NCSs 1/20
Introduction Problem formulation Infinite horizon case Finite horizon case Conclusion Motivation Sensors will be packaged together with communication protocols, 1 RF electronics, and energy management systems. Constraints: low cost, ease of replacement, low energy consumption, 2 and efficient communication links. Implications: intelligent sensors with low consumption (sleep and 3 wake-up modes), for life-time maximization Example: Traffic system with distributed density sensors. Traffic flow sensor CNRS, GIPSA-lab, NeCS-Team Energy-aware control and communication co-design in wireless NCSs 2/20
Introduction Problem formulation Infinite horizon case Finite horizon case Conclusion The smart sensor wireless node Radio is often the main energy-consumer Executing 3 million instructions is equivalent to transmitting 1000 bits at a distance of 100 meters in terms of expended energy CNRS, GIPSA-lab, NeCS-Team Energy-aware control and communication co-design in wireless NCSs 3/20
Introduction Problem formulation Infinite horizon case Finite horizon case Conclusion Physical layer Power Control Transmission power is related to communication reliability Power control aims to save energy , limit interferences, face channel varying conditions Figure: A source can adapt its transmission power level to change the success probability of the transmission. CNRS, GIPSA-lab, NeCS-Team Energy-aware control and communication co-design in wireless NCSs 4/20
Introduction Problem formulation Infinite horizon case Finite horizon case Conclusion Data Link (MAC) layer Radio-mode management Radio-mode = state of activity of the radio chip ( e.g. Tx , Rx , Idle , Sleep ) where some components are turned off Control community only considers ON and OFF θ i –Energy stay cost per unit of time (at node i ), θ i , j –Energy transition costs between i and j . Choosing a mode is a trade-off between energy consumption and node awareness . Figure: Illustration of a 3 radio-modes switching automata CNRS, GIPSA-lab, NeCS-Team Energy-aware control and communication co-design in wireless NCSs 5/20
Introduction Problem formulation Infinite horizon case Finite horizon case Conclusion Data Link (MAC) layer (cont.) Figure: Illustration of a 5 radio-modes switching automata Low-consuming radio-mode not used in control Higher power modes have higher probability of transmission success Problem considered here : co-design of mode management and control laws to save further energy CNRS, GIPSA-lab, NeCS-Team Energy-aware control and communication co-design in wireless NCSs 6/20
Introduction Problem formulation Infinite horizon case Finite horizon case Conclusion Model and setup 2 nodes scenario Battery-powered smart sensor node (with computation capabilities) Energy saving at the sensor side Time-triggered sensing (negligible cost) and Event-Triggered transmission Problem: How to design the radio mode, and the control input u k CNRS, GIPSA-lab, NeCS-Team Energy-aware control and communication co-design in wireless NCSs 7/20
Introduction Problem formulation Infinite horizon case Finite horizon case Conclusion Model and setup x k +1 = Ax k + Bu k + w k x k ∈ R n x , u k ∈ R n u CNRS, GIPSA-lab, NeCS-Team Energy-aware control and communication co-design in wireless NCSs 7/20
Introduction Problem formulation Infinite horizon case Finite horizon case Conclusion Model and setup x k +1 = Ax k + Bu k + w k m k ∈ M � M 1 ∪ M 2 M 1 � { 1 , 2 , · · · , N 1 } M 2 � { N 1 + 1 , N 1 + 2 , · · · , N } θ i , j − Transition cost , ∀ ( i , j ) ∈ M θ i − Stay cost , ∀ ( i ) ∈ M CNRS, GIPSA-lab, NeCS-Team Energy-aware control and communication co-design in wireless NCSs 7/20
Introduction Problem formulation Infinite horizon case Finite horizon case Conclusion Model and setup x k +1 = Ax k + Bu k + w k P { β k = 0 | m k = m } = ǫ ( m ) m k ∈ M � M 1 ∪ M 2 M 1 � { 1 , 2 , · · · , N 1 } M 2 � { N 1 + 1 , N 1 + 2 , · · · , N } θ i , j − Transition cost , ∀ ( i , j ) ∈ M θ i − Stay cost , ∀ ( i ) ∈ M CNRS, GIPSA-lab, NeCS-Team Energy-aware control and communication co-design in wireless NCSs 7/20
Introduction Problem formulation Infinite horizon case Finite horizon case Conclusion Model and setup x k +1 = Ax k + Bu k + w k P { β k = 0 | m k = m } = ǫ ( m ) m k ∈ M � M 1 ∪ M 2 u k = µ ( x k , u k − 1 , m k ) ˆ M 1 � { 1 , 2 , · · · , N 1 } M 2 � { N 1 + 1 , N 1 + 2 , · · · , N } θ i , j − Transition cost , ∀ ( i , j ) ∈ M θ i − Stay cost , ∀ ( i ) ∈ M CNRS, GIPSA-lab, NeCS-Team Energy-aware control and communication co-design in wireless NCSs 7/20
Introduction Problem formulation Infinite horizon case Finite horizon case Conclusion Model and setup x k +1 = Ax k + Bu k + w k P { β k = 0 | m k = m } = ǫ ( m ) m k ∈ M � M 1 ∪ M 2 ˆ u k = µ ( x k , u k − 1 , m k ) M 1 � { 1 , 2 , · · · , N 1 } v k = η ( x k , u k − 1 , m k ) M 2 � { N 1 + 1 , N 1 + 2 , · · · , N } θ i , j − Transition cost , ∀ ( i , j ) ∈ M θ i − Stay cost , ∀ ( i ) ∈ M CNRS, GIPSA-lab, NeCS-Team Energy-aware control and communication co-design in wireless NCSs 7/20
Introduction Problem formulation Infinite horizon case Finite horizon case Conclusion Model and setup x k +1 = Ax k + Bu k + w k P { β k = 0 | m k = m } = ǫ ( m ) m k ∈ M � M 1 ∪ M 2 u k = µ ( x k , u k − 1 , m k ) ˆ M 1 � { 1 , 2 , · · · , N 1 } v k = η ( x k , u k − 1 , m k ) M 2 � { N 1 + 1 , N 1 + 2 , · · · , N } � β k ˆ u k + (1 − β k ) u k − 1 , if Tx, u k = θ i , j − Transition cost , ∀ ( i , j ) ∈ M u k − 1 , otherwise. θ i − Stay cost , ∀ ( i ) ∈ M CNRS, GIPSA-lab, NeCS-Team Energy-aware control and communication co-design in wireless NCSs 7/20
Introduction Problem formulation Infinite horizon case Finite horizon case Conclusion Switched model ∀ k : choice between N radio-modes ⇒ N subsystems Switching is triggered by the switching decision v k Given µ and η : z k +1 = f v k ( z k , ˆ u k , β k , ω k ) m k +1 = v k = η ( z k , m k ) ˆ u k = µ ( z k , m k ), f v k ( z k , ˆ u k , β k , ω k ) = Φ v k ( β k ) z k + Γ v k ( β k )ˆ u k + ω k ˜ u k = u k − 1 (control memory) � x k � z k = (augmented state) ˜ u k ( z k , m k ) ∈ X = R n x + n u × M (switched system state) CNRS, GIPSA-lab, NeCS-Team Energy-aware control and communication co-design in wireless NCSs 8/20
Introduction Problem formulation Infinite horizon case Finite horizon case Conclusion Switched model ∀ k : choice between N radio-modes ⇒ N subsystems Switching is triggered by the switching decision v k If v ∈ M 1 (Tx case): Given µ and η : � A � 0 Φ CL = if β k =1 0 0 z k +1 = f v k ( z k , ˆ u k , β k , ω k ) Φ v k ( β k )= � A � m k +1 = v k = η ( z k , m k ) B Φ OL = if β k =0. 0 I u k = µ ( z k , m k ), ˆ � B � Γ CL = if β k = 1 f v k ( z k , ˆ u k , β k , ω k ) I Γ v k ( β k ) = = Φ v k ( β k ) z k + Γ v k ( β k )ˆ u k + ω k � 0 � Γ OL = if β k = 0. 0 ˜ u k = u k − 1 (control memory) � x k � z k = (augmented state) ˜ u k ( z k , m k ) ∈ X = R n x + n u × M (switched system state) CNRS, GIPSA-lab, NeCS-Team Energy-aware control and communication co-design in wireless NCSs 8/20
Introduction Problem formulation Infinite horizon case Finite horizon case Conclusion Switched model ∀ k : choice between N radio-modes ⇒ N subsystems Switching is triggered by the switching decision v k If v ∈ M 1 (Tx case): Given µ and η : � A � 0 Φ CL = if β k =1 0 0 z k +1 = f v k ( z k , ˆ u k , β k , ω k ) Φ v k ( β k )= � A � m k +1 = v k = η ( z k , m k ) B Φ OL = if β k =0. 0 I ˆ u k = µ ( z k , m k ), � B � Γ CL = if β k = 1 f v k ( z k , ˆ u k , β k , ω k ) I Γ v k ( β k ) = = Φ v k ( β k ) z k + Γ v k ( β k )ˆ u k + ω k � 0 � Γ OL = if β k = 0. 0 If v ∈ M 2 (no Tx case): u k = u k − 1 (control memory) ˜ Φ v k ( β k ) = Φ OL ∀ β k � x k � Γ v k ( β k ) = Γ OL ∀ β k z k = (augmented state) ˜ u k ( z k , m k ) ∈ X = R n x + n u × M (switched system state) CNRS, GIPSA-lab, NeCS-Team Energy-aware control and communication co-design in wireless NCSs 8/20
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