Ahmad T. Al-Hammouri, Michael S. Branicky, Vincenzo Liberatore Case Western Reserve University Stephen M. Phillips Arizona State University April 25, 2006.

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Ahmad T. Al-Hammouri, Michael S. Branicky, Vincenzo Liberatore Case Western Reserve University Stephen M. Phillips Arizona State University April 25, 2006 Support by: NSF CCR , Department of Commerce TOP , NASA NNC04AA12A, and an OhioICE Training grant` Decentralized and Dynamic Bandwidth Allocation in Networked Control Systems

Ahmad Al-HammouriDecentralized and Dynamic Bandwidth Allocation in Networked Control Systems (WPDRTS’06) 2/15 Paper Overview Control over Networks NCSs, DCSs, SANETs, … Control of Networks Efficient BW allocation Congestion control Fairness We propose a “Cof N” scheme to better serve “Cover N”

Ahmad Al-HammouriDecentralized and Dynamic Bandwidth Allocation in Networked Control Systems (WPDRTS’06) 3/15 Control over Networks

Ahmad Al-HammouriDecentralized and Dynamic Bandwidth Allocation in Networked Control Systems (WPDRTS’06) 4/15 Control over Networks

Ahmad Al-HammouriDecentralized and Dynamic Bandwidth Allocation in Networked Control Systems (WPDRTS’06) 5/15 Control over Networks Remote interaction (monitoring & control) with the physical world Applications: Industrial automation & process control Space exploration, e.g., telerobotics Smart homes Medical sensing & surgical simulations Automatic asset mgmt. (RFID)

Ahmad Al-HammouriDecentralized and Dynamic Bandwidth Allocation in Networked Control Systems (WPDRTS’06) 6/15 Control of Networks (Scope of the paper) A bandwidth allocation scheme Objectives: Stability of control systems Efficiency & fairness Fully distributed, asynchronous, & scalable Dynamic & self reconfigurable Formulating the scheme in CT NCSs regulate h based on congestion fed back from the network

Ahmad Al-HammouriDecentralized and Dynamic Bandwidth Allocation in Networked Control Systems (WPDRTS’06) 7/15 Sampling Rate & Network Congestion h=1/r l1l1 l2l2

Ahmad Al-HammouriDecentralized and Dynamic Bandwidth Allocation in Networked Control Systems (WPDRTS’06) 8/15 Problem Formulation Define a utility fn U(r) that is Monotonically increasing Strictly concave Defined for r ≥ r min Optimization formulation

Ahmad Al-HammouriDecentralized and Dynamic Bandwidth Allocation in Networked Control Systems (WPDRTS’06) 9/15 Distributed Implementation Two independent algorithms End-systems (plants) algorithm Router algorithm (later on) NCS PlantNCS Controller Router pp p

Ahmad Al-HammouriDecentralized and Dynamic Bandwidth Allocation in Networked Control Systems (WPDRTS’06) 10/15 NCS-AQM Control Loop tftf q(t) f(q(t)) q`=Σr(t) - C p(t) tbtb NCS PlantQueue Model Plant P(s) = Queue Controller G(s)

Ahmad Al-HammouriDecentralized and Dynamic Bandwidth Allocation in Networked Control Systems (WPDRTS’06) 11/15 Queue Controller G(s) Proportional (P) Controller G P (s) = k p Proportional-Integral (PI) Controller G PI (s) = k p + k i /s q(s) G(s) P(s) q0q0 + _ eu

Ahmad Al-HammouriDecentralized and Dynamic Bandwidth Allocation in Networked Control Systems (WPDRTS’06) 12/15 Determination of k p and k i Stability region in the k i –k p plane Stabilizes the NCS-AQM closed-loop system for delays less or equal d Analysis of quasi-polynomials, f(s,e s )

Ahmad Al-HammouriDecentralized and Dynamic Bandwidth Allocation in Networked Control Systems (WPDRTS’06) 13/15 Simulations & Results 50 NCS Plants: [Branicky et al. 2002] [Zhang et al. 2001]

Ahmad Al-HammouriDecentralized and Dynamic Bandwidth Allocation in Networked Control Systems (WPDRTS’06) 14/15 Simulations & Results (cont.) PI ¤ P¤P¤

Ahmad Al-HammouriDecentralized and Dynamic Bandwidth Allocation in Networked Control Systems (WPDRTS’06) 15/15 Thank You Questions Comments Probing further: