Junior Workshop
# FeedNetBack Junior Workshop – Annecy, Sept. 16^{th} 2010

# Abstracts

Session 1 | |
---|---|

Distributed estimation and control (and applications) | |

9:00-9:20 | Abstract |

Explicit nonlinear MPC: a set theoretic method for verifying feasibility | |

Davide Raimondo | ETHZ |

9:20-9:40 | Abstract |

Distributed Quasi-Newton Method and its Application to the Optimal Reactive Power Flow Problem | |

Saverio Bolognani | Univ. Padova |

9:40-10:00 | Abstract |

Filtering and estimation for localization of underwater plumes using AUVs | |

Stephan Huck | ETHZ |

10:00-10:20 | Abstract |

Elastic Formation Control Based on Affine Transformations | |

Lara Briñon Arranz | INRIA Grenoble |

10:20-10:40 | Abstract |

Multiple Target Tracking via a distributed network of cameras | |

Andrea Masiero | Univ. Padova |

Session 2 | |

Control over networks | |

11:00-11:20 | Abstract |

Lyapunov-Krasovskii functionals for the study of stability and stabilisation of time-delay systems with application to networked control systems | |

Pablo Millan | Univ. Sevilla |

11:20-11:40 | Abstract |

A Nyquist criterion for synchronization in networks of heterogeneous linear systems | |

Enrico Lovisari | Univ. Padova |

11:40-12:00 | Abstract |

Applications of Coalitional Game Theory to Distributed Control and Estimation | |

Jose M. Maestre Torreblanca | Univ. Sevilla |

12:00-12:20 | Abstract |

On the Dual Effect in State-Based Scheduling of Networked Control Systems | |

Chithrupa Ramesh | KTH |

12:20-12:40 | Abstract |

Continuous-time double integrator consensus algorithms improved by an appropriate sampling | |

Gabriel Rodrigues de Campos | Grenoble |

Session 3 | |

Control and communication | |

14:40-15:00 | Abstract |

Source Coding with Common Reconstruction and Action-dependent Side Information | |

Kittipong Kittichokechai | KTH |

15:00-15:20 | Abstract |

Iterative Encoder Controller Design Based on Approximate Dynamic Programming | |

Amirpasha Shirazinia | KTH |

15:20-15:40 | Abstract |

Rate Sufficient Conditions for Closed-loop Control over Half-duplex AWGN Relay Channels | |

Ali A. Zaidi | KTH |

15:40-16:00 | Abstract |

Analytical model of IEEE 802.15.4 for multi-hop networks | |

Piergiuseppe Di Marco | KTH |

**Saverio Bolognani** (Univ. Padova) *Distributed Quasi-Newton Method and its Application to the Optimal Reactive Power Flow Problem*

We consider a distributed system of N agents, on which we define a quadratic optimization problem subject to a linear equality constraint. We assume that the agents can estimate the gradient of the cost function element-wise by measuring the steady state response of the system. Even if the cost function cannot be decoupled into individual terms, and the linear constraint involves the whole system state, we are able to design a distributed, quasi-Newton optimization algorithm. We prove finite time convergence in its centralized version, and by using the tool of average consensus we design its distributed implementation in the case in which a communication graph is given. As a testbed for the proposed method, we consider the problem of optimal distributed reactive power compensation in smart microgrids.

**Lara Briñon Arranz** (INRIA Grenoble) *Elastic Formation Control Based on Affine Transformations*

This talk deals with the control of a fleet of non-linear systems representing AUVs. The purpose is here to design control laws to stabilize the fleet to time-varying formations which are not only circular. We propose a novel framework which is able to express in a simple manner the control law for a larger class of formations. This has been produced by applying a sequence of affine transformations such as translations, rotations and scalings. We consider also the problem of uniform distribution of all the agents along the formation. This is achieved taking into account the communication constraints using a cooperative control which includes the Laplacian matrix of the ommunication graph. The system was implemented in computer simulation, accessible through Web.

**Piergiuseppe Di Marco** (KTH) *Analytical model of IEEE 802.15.4 for multi-hop networks*

IEEE 802.15.4 multi-hop wireless networks are an important communication infrastructure for many applications, including industrial control, home automation, and smart grids. Existing analysis of the IEEE 802.15.4 medium access control (MAC) protocol are often based on assumptions of homogeneous traffic and ideal carrier sensing, which are far from the reality when predicting performance for multi-hop networks. In this paper, a generalized analysis of the unslotted IEEE 802.15.4 MAC is presented. The model considers heterogeneous traffic and hidden terminals due to limited carrier sensing capabilities, and allows us to investigate jointly IEEE 802.15.4 MAC and routing algorithms. The analysis is validated via Monte Carlo simulations, which show that routing over multi-hop networks is significantly influenced by the IEEE. 802.15.4 MAC performance. Routing decisions based on packet loss probability may lead to an unbalanced distribution of the traffic load across paths, thus motivating the need of a joint optimization of routing and MAC.

**Stephan Huck** (ETHZ) *Filtering and estimation for localization of underwater plumes using AUVs*

To locate the source of an underwater concentration field, e.g. a fresh water plume, using a fleet of AUVs it is desirable to estimate a set of parameters defining the plume shape and location based on measurement data collected by the AUVs. We investigate how this estimation can be carried out for simple plume shapes using batch optimization and recursive filtering techniques. To ensure that the estimation converges to the correct values, we investigate the identifiability of the underlying model structure. This brings up the issue of the information content of the obtained measurements which, in turn, relates to where the measurements have been taken, i.e. to finding the most informative formation or trajectory for the AUVs.

**Kittipong Kittichokechai** (KTH) *Source Coding with Common Reconstruction and Action-dependent Side Information*

We consider a source coding problem with common reconstruction and action‐dependent side information. An action is taken by an encoder at some costs, e.g., energy. We characterize the optimal rate region which in fact reduces to the sum‐rate distortion and cost function. The result provides a fundamental limit for networked control applications where the observer/encoder can use the actions to adapt the quality of side information about the state of the plant; meanwhile it can monitor the reconstructed state at the decoder/controller based on the common reconstruction constraint.

**Enrico Lovisari** (Univ. Padova) *A Nyquist criterion for synchronization in networks of heterogeneous linear systems*

We study the synchronization of a set of SISO subsystems interconnected via a time-invariant Laplacian matrix. By synchronization we mean that the outputs of all subsystems must be asymptotically equal to each other and behave in the same manner. We assume that the subsystems can be represented as the sum of a common nonzero transfer function plus a perturbation. A Nyquist-type criterion is established which ensures synchronization provided that the convex hull of the frequency responses of the subsystems does not intersect a certain region de ned by the spectrum of the interconnection matrix. The result is applied to a variety of examples of di erent nature for which synchronization takes place. A counter example for which complete synchronization is impossible is also presented.

**Jose M. Maestre Torreblanca** (Univ. Sevilla) *Applications of Coalitional Game Theory to Distributed Control and Estimation*

In this presentation we propose to study the underlying properties of a sensor and actuator network in which a set of agents switch between different communication strategies in order to minimize communicational costs. The problems of how to decide the communication strategy, share the benefits/costs and detect which are the most critical links in the network are solvedusing tools from game theory. The proposed scheme is demonstrated through different simulation examples.

**Andrea Masiero** (Univ. Padova) *Multiple Tarket Tracking via a distributed network of cameras*

In this talk we consider the problem of target tracking in a large network of cameras. In practical applications the computational complexity of a centralized tracking algorithm quickly increases with the number of targets and of cameras, e.g. in real motion capture systems the centralized tracking algorithm has to be executed offline as long as the system is formed by more than a dozen of cameras. Motivated by the interest in applying tracking algorithm in real-time in real motion capture systems, we consider the problem of improving the computational efficiency of commonly adopted tracking algorithms exploiting the distributed network framework.

**Pablo Millan** (Univ. Sevilla) *Lyapunov-Krasovskii functionals for the study of stability and stabilisation of time-delay systems with application to networked control systems*

Time-varying delays are a major source of instability in dynamical systems. Systems in which some of the states or feedback signals are affected by time-varying delays are called time-delay systems. The study of stability for these systems can be carried out using a Lyapunov-Krasovskii approach. Defining a suitable Lyapunov-Krasovskii functional, stability criteria are obtained by solving some Linear Matrix Inequalities. The input-delay approach allows modeling Networked Control Systems as a class of time-delay systems, in such a way that stability properties can be easily inherited. Moreover, others features can be achieved in the design of linear controllers, as an Hinf disturbance rejection or an H2 optimal control.

**Davide Raimondo** (ETHZ) *Explicit nonlinear MPC: a set theoretic method for verifying feasibility*

In this talk an algorithm for nonlinear explicit model predictive control, with guaranteed stability and constraint satisfaction is presented. A low complexity receding horizon control law is obtained by approximating the optimal control law using multiscale basis function approximation. Feasibility and stability of the approximate control law are ensured through the computation of a capture basin (region of attraction) for the closed loop system. In a previous work, interval methods were used to construct the capture basin (feasible region), yet this approach suffered due to slow computation times and high grid complexity. In this paper, we suggest an alternative to interval analysis based on zonotopes. The suggested method significantly reduces the complexity of the combined function approximation and verification procedure through the use of DC programming, Taylor expansion and recursive splitting.

**Chithrupa Ramesh** (KTH) *On the Dual Effect in State-Based Scheduling of Networked Control Systems*

In this paper, we show that there is a dual effect with state-based scheduling. In general, this makes the optimal scheduler and controller hard to find. However, by removing past controls from the scheduling criterion, we find that certainty equivalence holds. This condition is related to the classical result of Bar-Shalom and Tse, and it leads to the design of a sub-optimal scheduler with a certainty equivalent controller. Furthermore, we show that a mapping of the statebased scheduler into one which fulfills this condition, and consequently has an optimal certainty equivalent controller, does not result in an equivalent class of design in the sense of Witsenhausen. Finally, computing the estimate remains hard, but can be simplified by introducing a symmetry constraint on the scheduler.

**Gabriel Rodrigues de Campos** (INRIA Grenoble) *Continuous-time double integrator consensus algorithms improved by an appropriate sampling*

This presentation deals with the double integrator consensus problem. The objective is the design of a new consensus algorithm for continuous-time multi-agent systems. The dynamic of agents is assumed to be of double integrator type. The proposed algorithm considers that there are no sensors to measure the velocity of the agents. Thus the classical double integrator consensus algorithm leads to an oscillatory behavior if the communication graph is undirected and to instability if the graph is directed. The novel algorithm proposes to sampled, in an appropriate manner, part of the multi-agent systems state such that the algorithm converges. An expression of the consensus equilibrium is provided. Some examples are provided to show the efficiency of the new algorithm.

**Amirpasha Shirazinia** (KTH) *Iterative Encoder-Controller Design Based on Approximate Dynamic Programming *

We study the iterative optimization of the encoder‐controller pair for closed‐loop control of a multi‐dimensional plant over a noisy discrete memoryless channel. With the objective to minimize the expected linear quadratic cost over a finite horizon, we propose a joint design of the sensor measurement quantization, channel error protection, and optimal controller actuation. It was shown in our previous work that despite this optimization problem is known to be hard in general, an iterative design procedure can be derived to obtain a local optimal solution. However, in the vector case, optimizing the encoder for a fixed controller is in general not practically feasible due to the curse of dimensionality. In this paper, we propose a novel approach that uses the approximate dynamic programming (ADP) to implement a computationally feasible encoder updating policy with promising performance. Especially, we introduce encoder updating rules adopting the rollout approach. Numerical experiments are carried out to demonstrate the performance obtained by employing the proposed iterative design procedure and to compare it with other relevant schemes.

**Ali A. Zaidi** (KTH)*Rate Sufficient Conditions for Closed-loop Control over Half-duplex AWGN Relay Channels*

The problem of remotely controlling an unstable noiseless linear time invariant system over noisy half‐duplex relay channels with average power constraints is considered. For information transmission, we propose a coding scheme based on the Schalkwijk‐Kailath scheme. Therefore, we derive conditions on rate which are sufficient for mean square stability of the linearly controlled LTI system over non‐orthogonal, orthogonal, and two‐hop AWGN relay channels.