## Control, Estimation, and Modelling of Networked Dynamical Systems

Venue: Crowne Plaza, Coogee, Lady Penryhn room

Date: Saturday 9th of December, 2017

Organisers: Ian Manchester and Guodong Shi

Supported by the Centre for Robotics and Intelligent Systems, University of Sydney

### Schedule*:

- 8:30-9: Coffee and Welcome
**9-10: Session 1: Consensus****John Baras**, University of Maryland

*Trust is the Cure to Distributed Consensus with Adversaries*

abstractExtensive research efforts have been devoted to distributed consensus with adversaries. Many diverse applications drive this increased interest in this area including distributed collaborative sensor networks, sensor fusion and distributed collaborative control. We consider the problem of detecting Byzantine adversaries in a network of agents with the goal of reaching consensus. We propose a novel trust model that establishes both local trust based on local evidences and global trust based on local exchange of local trust values. We describe a trust-aware consensus algorithm that integrates the trust evaluation mechanism into the traditional consensus algorithm and propose various local decision rules based on local evidence. To further enhance the robustness of trust evaluation itself, we also provide a trust propagation scheme in order to take into account evidences of other nodes in the network. The algorithm is flexible and extensible to incorporate more complicated designs of decision rules and trust models. To demonstrate the power of our trust propagation scheme, we provide theoretical security performance in terms of miss detection rate and false alarm rate under regular trust graph and relaxed security performance bound under general trust graph. In addition, we demonstrate through simulation that the trust-aware consensus algorithm can effectively detect Byzantine adversaries and excluding them from consensus iterations even in sparse networks with connectivity less than 2f + 1, where f is the number of adversaries. These results can be applied for fusion of trust evidences as well as for sensor fusion when malicious sensors are present like for example in power grid sensing and monitoring.

- 10-10:30: Morning tea, coffee, snacks
**10:30-12:30: Session 2: Control of Large-Scale Systems****Anders Rantzer**, Lund University

*Towards a Scalable Theory of Control*

abstractClassical control theory does not scale well for large systems like traffic networks, power networks and chemical reaction networks. To change this situation, new approaches need to be developed, not only for analysis and synthesis of controllers, but also for modelling and verification. In this lecture we will present a class of networked control problems for which scalable distributed controllers can be proved to achieve the same performance as the best centralized ones. The control objective is stated in terms of frequency weighted H-infinity norms, which makes it possible to combine disturbance rejection at low frequencies with robustness to high frequency measurement noise and model errors. An optimal controller is given in the form of a multi-variable PI controller, which is distributed in the sense that control action along a given network edge is entirely determined by states at nodes connected by that edge. We will discuss some application examples, as well as connections to other aspects of scalability.**Claudio Altafini**, Linköping University

*Minimum energy driver node selection for complex networks*

abstractThe aim of this presentation is to shed light on the problem of controlling a complex network with minimal control energy. We show first that the control energy depends on the time constant of the modes of the network, and that the closer the eigenvalues are to the imaginary axis of the complex plane, the less energy is required for complete controllability. A general heuristic principle for energetically efficient driver node selection is also proposed: the overall cost of controlling a network is reduced when the controls are concentrated on the nodes with highest ratio of weighted outdegree vs indegree. In the special case of networks having all purely imaginary eigenvalues (e.g. networks of coupled harmonic oscillators), several constructive algorithms for minimum control energy driver node selection are developed. They all rely on the Gramian being diagonally dominant, and all lead to effective (heuristic or exact) algorithms.

- 12:30-2: Lunch
**:**buffet at Blue Salt Restaurant (at venue) + time for a quick swim **2-3: Spotlight talks**(<=10min each) + tea, coffee, snacks:- Jochen Trumpf, Australian National University,
*Controllability and stabilizability of networks of linear systems* - Jie Bao, University of New South Wales,
*Distributed plantwide process control using dissipativity theory* - Hendra Nurdin, University of New South Wales,
*Model reduction in the quantum context* - Adrian WIlls, University of Newcastle,
*Optimization challenges in maskless lithography* - Guodong Shi, University of Sydney/Australian National University,
*Toward in-network quantum computation* - Ian Manchester, University of Sydney,
*Convex sets of contracting nonlinear observers*

- Jochen Trumpf, Australian National University,
**3-5: Session 3: Controllability and Identification****Harry Trentelman**, Groningen University

*Structural Controllability of Systems on Coloured Graphs*

abstractI will discuss strong structural controllability of systems on graphs. With any directed graph and subset of its vertex set (the so-called leader set), we can associate a whole class of leader-follower networks. The state matrix of any of these network has a fixed zero-nonzero pattern as dictated by the arcs in the graph, but the nonzero entries for the rest are free. The input matrix is determined by the choice of leader set. Strong structural controllability of the graph means that all leader follower-networks associated with the graph and leader set are controllable in the classical sense. A necessary and sufficient condition for strong structural controllability is that the leader set is a zero forcing set of the graph.In this talk I will discuss the extension of the above results to coloured graphs. In this case any arc of the network graph has a unique colour associated with it. Arcs having the same colour,means that their weights are identical. This gives rise to a structured class of leader-follower networks: the colours in the graph dictate which entries in the state matrix are identical, but for the rest are nonzero and free. I will discuss how to extend the classical colour change rule to a colour change rule that is relevant for checking controllability of classes of networks associated with such coloured graphs.**Thomas Schön**, Uppsala University

*Constructing probabilistic quasi-Newton algorithms and nonlinear state space models using flexible models*

abstractIt has recently been shown that many of the existing quasi-Newton algorithms can be formulated as learning algorithms, capable of learning local models of the cost functions. Importantly, this understanding allows us to start assembling probabilistic Newton-type algorithms, applicable in situations where we only have access to noisy observations of the cost function and its derivatives. This is where our interest lies. We will show how we can make use of the non-parametric and probabilistic Gaussian process model in solving these stochastic optimisation problems. Specifically, we present a new algorithm that unites these approximations with recent probabilistic line search routines to deliver a probabilistic quasi-Newton approach. We also show that the probabilistic optimisation algorithms deliver promising results on challenging nonlinear system identification problems where the very nature of the problem is such that we can only access the cost function and its derivative via noisy observations, since there are no closed-form expressions available. The Gaussian process model also allows us to construct a nonlinear state-space model with interesting properties and interpretations.

- 5-7pm: Free time
- 7pm: Dinner, Barzura

*- subject to mild adjustment

### Participants

- Claudio Altafini, Linköping University
- John Baras, University of Maryland
- Jie Bao, University of New South Wales
- Tom Chaffey, University of Sydney
- Jiayin Chen, Australian National University
- Felix Kong, University of Sydney
- He Kong, University of Sydney
- Ian Manchester, University of Sydney
- Hendra Nurdin, University of New South Wales
- Anders Rantzer, Lund University
- Max Revay, University of Sydney
- Thomas Schön, Uppsala University
- Guodong Shi, University of Sydney/Australian National University
- Vera Somers, University of Sydney
- Harry Trentelman, Grongingen University
- Jochen Trumpf, Australian National University
- Ray Wang, University of New South Wales
- Adrian Wills, University of Newcastle