abstracts

September 25

Lennart Ljung (Linköping University)
Will Machine Learning Change the System Identification Paradigm?

State-of-the-Art System Identification works with well defined model structures and Maximum-likelihood type parameter estimation algorithms. This paradigm is well founded and supported by theory, algorithms, software and industrial applications. Machine Learning tackles essentially the same family of problems, and has been very successful in attracting wide interest, with a (seemingly) different box of tools. The question is what impact this will have on the system identification community. This presentation looks at a few aspects of this question, primarily at the roles of regularization, kernel methods, and Gaussian process regression.

Le Yi Wang (Wayne State University)
Complexity and Resource Allocations in Decision-Based Identification

This talk presents a new paradigm in the line of complexity-based system identification. System identification extracts information from a system’s operational data to derive a representative model for the system. Studies of system identification have been concentrated on estimation algorithms and their convergence. Focusing on optimal resource allocation under a given reliability requirement, this work studies identification complexity and its relations to decision making. Adaptive resource allocation algorithms are introduced. The algorithms are shown to converge strongly to the optimal resource allocation by employing the ODE approach in stochastic approximation methodologies. Convergence rates, asymptotic normality, and asymptotic efficiency of the algorithms are established.

Håkan Hjalmarsson (KTH Royal Institute of Technology)
Minimizing the Mean-Square-Error of Identified Finite Impulse Response Models

In this presentation we discuss methods for minimizing the mean-squared error of identified finite impulse response models. In particular we consider regularized models and cast the choice of regularization parameter as a direct optimization problem. Several approaches to this problem are considered, including classical SURE (Stein’s Unbiased Risk Estimation) and weighted least-squares. The results are compared with current state-of-the art kernel methods.

Anders Hansson (Linköping University)
System Identification with Missing Data

In this talk we will discuss system identification when some of the data is missing. Mainly two different approaches will be discussed. The first one is based on maximum likelihood estimation. We will see that the an equivalent criterion is to minimize the Euclidean norm of the prediction error vector scaled by a particular function of the covariance matrix of the observed output data. We also provide insight into when simpler and in general sub-optimal schemes are indeed optimal. An efficient implementation is obtained by recognizing that the problem is a separable least squares problem. The second approach is based on a subspace formulation and uses the nuclear norm heuristic for structured low-rank matrix approximation, with the missing input and output values as the optimization variables. Here the key to an efficient implementation is to employ the alternating direction method of multipliers.

Jeff Shamma (Georgia Institute of Technology)
Exploring Bounded Rationality in Game Theory

Solution concepts in game theory, such as Nash equilibrium, traditionally ignore the processes and associated computational costs of how agents go about deriving strategies. The notion of bounded rationality seeks to address such issues through a variety of alternative formulations. This talk presents two settings motivated by bounded rationality. First, we consider incomplete information dynamic games. A Nash equilibrium in this setting requires each agent to solve a partially observed Markov decision problem that requires knowledge of a possibly extensive environment as well as the strategies of other agents. We introduce an alternative notion, called “empirical evidence equilibria”, in which agents form naive models with available measurements. These models reflect an agent’s limited awareness of its surroundings, and the level of naivety or sophistication can be different for each agent. We show that such equilibria are guaranteed to exist for any profile of agent rationality and compare the concept to mean field equilibria. Second, we investigate learning in evolutionary games, where the focus is on the dynamic behaviors away from equilibrium rather than characterizations of equilibrium. A lingering issue in this framework is what constitutes “natural” versus “concocted” learning rules. Building on prior work on so-called “stable games”, we introduce a class of dynamics motivated by control theoretic passivity theory. We show how passivity theory both captures and extends selected prior work on evolutionary games and offers a candidate for what constitutes natural learning.

Ji-Feng Zhang (Chinese Academy of Sciences)
Adaptive Tracking Games for Coupled Stochastic Linear Multi-Agent Systems

This talk is concerned with distributed adaptive tracking-type games for a class of coupled stochastic linear multi-agent systems with uncertainties of unknown structure parameters, external stochastic disturbances, unmodeled dynamics, and unknown agents’ interactions. The control goal is to make the states of all the agents converge to a desired function of the population state average (PSA). Due to the fact that only local information is available for each agent, the control is distributed. For the time-invariant parameter case, the extended least-squares algorithm, Nash certainty equivalence (NCE) principle and certainty equivalence (CE) principle are used to estimate the unknown parameters and the PSA term, and to design adaptive control, respectively. Under some mild conditions, it is shown that the closed-loop system is almost surely uniformly stable with respect to the population number N; the estimate for the PSA term is strongly consistent; the adaptive control is almost surely an asymptotic Nash equilibrium. When the dynamics of each agent contains time-varying parameters and unmodeled dynamics, projected least mean square (LMS) algorithm, NCE principle and CE principle are adopted to estimate the unknown time-varying parameters, and the unknown PSA term, and to design robust adaptive control, respectively. In addition to stability of the closed-loop system and consistency of the PSA estimate, the control law is shown to be robust Nash equilibrium with respect to the unmodeled dynamics, the variation of the unknown parameters, and the external disturbances.

Chiara Mocenni (Università di Siena)
Game Interactions and Dynamics on Complex Networks

The talk presents an extension of the mathematical formulation of evolutionary game dynamics to networked populations. The model, grounded on the standard replicator equation, is modified in order to account for the dynamics of a finite set of players organized in a network of connections (graph). In the proposed framework, the players are located at the vertices of the graph and are modeled as subpopulations of a multipopulation game. Moreover, the dynamical equations are derived by assuming that couples of members belonging to two different and connected subpopulations are engaged at each time instant in two-players games. The obtained equations describe the strategic interactions of a finite set of individuals connected in a graph, without any assumptions on the game payoff matrices and on the adjacency matrix of the graph. The stability of steady states, the existence of Nash equilibria and the presence of evolutionary stable strategies are discussed. The dynamical behavior of the solutions and the potentialities of the model are also investigated by means of extended simulations. Finally, the obtained equations are used for explaining the mechanisms of bacterial aggregation leading to the formation of biofilms.

Bassam Bamieh (University of California, Santa Barbara)
Structured Stochastic Uncertainty for Large Scale Systems

Large-scale systems with structured stochastic uncertainty are useful models in the setting of random networks, stochastic hydrodynamic stability and random materials. I will summarize results on characterization of mean-square stability in a setting where spatial correlations play an important role, and make connections with the theory of linear systems driven by multiplicative noise.

Munther Dahleh (MIT, Boston)
Minimal Realization of Hidden Markov Models: Implications on Learning

Li Qiu (Hong Kong University of Science and Technology)
When MIMO Control Meets MIMO Communication

When we try to stabilize a multi-input system using state feedback, if the control signals are transmitted through a MIMO transceiver with given sub-channel capacities, under what condition the problem is solvable? In this talk, we will show that the solvability condition can be given in terms of a majorization relation between the eigenstructure of the system and the sub-channel capacities of the transceiver.

Andrea Garulli (Università di Siena)
Asymptotic behaviors of a class of threshold models for social networks

We study the asymptotic behaviors of threshold models used to describe the formation of collective actions in social networks. The model has been introduced to analyze the mechanisms underlying the formation of a collective action taking place during political unrest or social revolutions, but can be generalized to networks in which the agents make a choice between two possible actions, at every time instant. The decision of each agent is made on the basis of the actions chosen by the agent’s neighbors and the value of a dynamically updated threshold. The main novelty of the proposed model is the introduction of a parameter accounting for the level of self-confidence of the agents, which affects the dynamic evolution of the threshold and in turn the way the agents make their decision. Three different network topologies are considered and for each of them the possible limiting behaviors of the network are characterized in terms of the self-confidence parameter and of the initial threshold value

Graziano Chesi (University of Hong Kong)
Topological Entropy in Uncertain Networked Control Systems

Measuring the topological entropy is a key problem in networked control systems. This talk considers systems affected by structured uncertainty, and addresses the computation of the worst-case entropy defined by the largest sum of the real parts (continuous-time) or the largest product of the magnitudes (discrete-time) of the unstable eigenvalues over the admissible uncertainties. It is supposed that the coefficients of the system are polynomial functions of an uncertain vector constrained into a semi-algebraic set. It is shown that a sufficient condition for establishing an upper bound of the worst-case entropy can be given in terms of an LMI feasibility test by exploiting SOS matrix polynomials. Moreover, it is shown that under mild assumptions this condition is also necessary by using polynomials of degree sufficiently large. Lastly, a sufficient and necessary condition is presented for establishing the optimality of the computed upper bounds.

Murti V. Salapaka (University of Minnesota)
Reconstruction of Interconnectedness in Networks of Dynamical Systems Based on Passive Observations

Determining interrelatedness structure of various entities from multiple time series data is of significant interest to many areas. Knowledge of such a structure can aid in identifying cause and effect relationships, clustering of similar entities, identification of representative elements and model reduction. In this talk, a methodology for identifying the interrelatedness structure of dynamically related time series data based on passive observations structure will be presented. The framework will allow for the presence of loops in the connectivity structure of the network. The quality of the reconstruction will be quantified. Results on the how the sparsity of multivariate Wiener filter, the Granger filter and the causal Wiener filter depend on the network structure will be presented. Connections to graphical models with notions of independence posed by d-separation will be highlighted.

Domenico Prattichizzo (Università di Siena)
Connecting Humans and Robots through Wearable Haptics

The complexity of the world around us is creating a demand for interfaces that will simplify and enhance the way we interact with the environment. In this talk we will present the scientific and technological foundations for wearable haptics, a novel concept that will change the way humans will cooperate with robots. This research stems from the need for wearability which is a key element for natural interaction.

 

September 26

Anders Rantzer (Lund University)
Robust Control Revisited: A Quest for Scalability

The concept of Integral Quadratic Constraint (IQC) has long been known as a versatile tool for robustness analysis of dynamical systems. Numerous common model imperfections can be efficiently described this way, for example parametric uncertainty, disturbances with bounded frequency content and nonlinear effects such as friction and hysteresis. Based on this idea, rigorous bounds on performance deviations can be computed using semi-definite programming. Computer tools for robustness analysis using IQCs were developed already in the 1990s. However, computational complexity has remained an obstacle for more wide-spread use in applications.

In this presentation, we will discuss a method to improve the computational scalability of IQC analysis, using sparse decomposition of positive definite matrices. This makes it possible to verify stability and performance of large-scale systems with certificates that can be verified individually for each component. Applications in power systems will be discussed.

S.P. Bhattacharyya (Texas A&M University)
A New Measurement Based, Model Free Approach To Design

We develop a new approach to designing additional elements to be added to an existing   system whose model is unknown. We show that a few measurements strategically processed can enable this redesign. Applications to circuits, as well as mechanical, hydraulic and control systems are described as well as future research directions.

Jie Chen (City University of Hong Kong)
Quantized Control under Multiplicative Noise: Fundamental Conditions of Stabilizability

Quantized channels with random multiplicative noises have found wide utilities in modeling networked control systems subject to, e.g., packet drops, random delays, and fading. In this talk I shall present some of our recent results on stabilization and optimal control of networked feedback systems with communication links modeled as such quantized channels with quantization errors and transmission imperfections described by random multiplicative noises. A particular emphasis will be the development of fundamental conditions of mean square stabilizability which insure that an open-loop unstable system can be stabilized via quantized feedback in the mean square sense. For single-input single-output systems, a general, explicit stabilizability condition is obtained, which provides a fundamental limit on the channel noise variance imposed by the system’s unstable poles, nonminimum phase zeros and time delay. For multi-input multi-output systems, we provide a complete, computationally efficient solution for minimum phase systems possibly containing time delays, construed as the solution to a generalized eigenvalue problem readily solvable by means of linear matrix inequality optimization. Limiting cases and nonminimum phase plants are analyzed in further depth for conceptual insights, with an emphasis on how the directions of unstable poles and nonminimum phase zeros may affect mean square stabilizability in MIMO systems.

Alberto Tesi (Università di Firenze)
Robust Control Design for Adaptive Disturbance Attenuation

Mario Milanese (Modelway Srl)
SMT: Set Membership Theory for Identification, Prediction, Filtering & Control of Nonlinear Systems

The talk will present a theory of inference-making from noisy data measured on nonlinear systems, showing that identification, prediction, filtering and control are specific instances of the theory. The theory is developed within a Set Membership (SM) framework, an alternative view to the classical Parametric Statistical (PS) framework, widely used in investigating the above specific problems.

In the SM framework, a bound only on the gradient of the system regression function is assumed, at difference from PS methods which assume a parametric functional form of the regression function. Moreover, the SM theory assumes only that the noises corrupting the data are bounded, in contrast with PS approaches, which rely on noise assumptions such as stationarity, uncorrelation, type of distribution, etc.

The basic notions of the theory are presented and main results that can be obtained for the specific cases of identification, prediction, filtering and control are reviewed.

The talk will conclude with a discussion of two basic questions:

– what may be gained by using the presented SM theory instead of the widely diffused PS theory?

– is the theory practically viable, allowing to efficiently deal with complex real world applications?

The discussion will be based both on theoretical as well as experimental results.

Sandor Veres (University of Sheffield)
Complexity and Error Control in Polytope Computations

It is only in pure mathematics that a hyperplane cuts through a high dimensional polytope without problems of decisions about vertex-facet adjacency. In computations of polytopes for control systems and robotics there are numerical challenges. The talk will review the relevance of the problem in control for bounding methods and will state some results about how to control complexity while remaining useful in engineering solutions.

Marco Casini (Università di Siena)
Feasible Parameter Set Approximation for Linear Models with Bounded Uncertain Regressors

Nonconvex feasible parameter sets are encountered in set membership identification whenever the regressor vector is affected by bounded uncertainty. This occurs for example when considering standard output error models, or when the available measurements are provided by binary or quantized sensors. In this paper, a unifying framework is proposed to deal with several identification problems involving a nonconvex feasible parameter set and a procedure is proposed for approximating the minimum volume orthotope containing the feasible set. The procedure exploits different relaxations for autoregressive and input parameters, based on the solution of a sequence of linear programming problems. The proposed technique is shown to provide tight bounds in some special cases. Moreover, it is extended to cope with bounds not aligned with the parameter coordinates, in order to obtain polytopic approximations of the feasible set. A number of numerical tests on randomly generated models and data sets demonstrates the accuracy of the computed set approximations.

Kameshwar Poolla (University of California, Berkeley)
The Future Grid: Renewables, Regulation, and Control

Pressing environmental problems, energy supply security issues, and nuclear power safety concerns drive the worldwide interest in renewable energy. Variability in renewable generation is the most important obstacle to deep integration of renewable generation. The current approach is to absorb this variability in operating reserves. This works at today’s modest penetration levels. But it will not scale. At deep penetration levels, the levels of necessary reserves are economically untenable, and defeat the net carbon benefit.

So how can we economically enable deep penetration of renewable generation? The emerging consensus is that much this new generation must be placed at millions of points in the distribution system, and that the attendant variability can be absorbed by the coordinated aggregation of distributed resources such as storage and flexible loads. Tomorrow’s grid will have an intelligent periphery. We will explore the architectural and algorithmic components for managing this intelligent periphery for flexible load management. We consider two classes of flexible loads: electric vehicles and thermostatically controlled loads.In each case, we show that the aggregate flexibility can be modeled as electricity storage. Uncertainty from ambient conditions, availability, and other factors require us to treat the storage model stochastically. This simple, portable model greatly simplifies regulation procurement. Upstream, it isolates the system operator from the load details, and downstream it allows handling AGC commands from the system operator as operational constraints. We close by suggesting several challenging problems in monetizing and incentivizing resource participation.

Gianni Bianchini (Università di Siena)
Model Estimation of Photovoltaic Power Generation Using Partial Information

In this talk, we present a heuristic method for the estimation of a model of a photovoltaic plant, to be used for generation forecasting purposes by a Distribution System Operator (DSO). The problem is addressed in the peculiar scenario where measurements of meteorological variables at the plant site are not available, which is frequent in the case of a DSO dealing with a large number of independently owned and operated plants connected to the low voltage grid. This method efficiently exploits only power generation measurements and theoretical clear-sky irradiance, and is characterized by very low computational effort. The proposed procedure is currently in use at several DSO control centres in Italy.

Simone Paoletti (Università di Siena)
New Issues in Electric Load Forecasting for Smart Grids

Electric load forecasting is a well-established topic and a rich variety of approaches has been proposed in the literature. However, the advent of smart grids opens new issues in load forecasting related to new factors affecting the electricity demand in the smart grid environment. Among these, Active Demand (or Demand Response) represents a scenario in which households and small commercial consumers “participate” in the grid management through appropriate modifications of their consumption profiles during certain time periods in return of a monetary reward. The participation is mediated by a new player, called aggregator, who designs the consumption profile modifications to make up standardized products to be sold on the energy market. The presence of this new “input” generated by aggregators modifies the consumers’ behavior, asking for load forecasting algorithms which explicitly take into account the Active Demand effect. This talk illustrates an approach to load forecasting in the presence of Active Demand based on grey-box models, where the seasonal component of the load is extracted through a suitable pre-processing and the Active Demand is considered as an exogenous input to a linear transfer function model. The approach is thought for a distribution system operator which performs technical validation of Active Demand products, and therefore possesses full information about Active Demand in the network. A comparison of the performance of the proposed approach with techniques not using the information on Active Demand and with approaches based on nonlinear black-box models is performed using real measurements, representing the aggregated load of about 60 consumers from an Italian LV network.

Antonello Giannitrapani (Università di Siena)
Bidding Strategies for Electric Power Producers from Renewable Sources in the Presence of Weather Forecasts

In this talk, we consider the problem of offering energy generated from renewable sources in an electricity market featuring “soft” penalties, i.e. penalties that are applied only if the delivered power deviates from the nominal bid more than a given relative tolerance. The optimal bidding strategy, based on the knowledge of the prior power generation statistics, is derived analytically. Then, we present a possible way to integrate weather forecasts in the bidding strategy. The proposed approach consists in classifying the days into one of several predetermined classes, for each of which an optimal generation profile is precomputed. Weather forecasts are then used to predict the class the next day will belong to so that the appropriate profile can be selected. Finally, we focus on photovoltaic (PV) power plants and show how the bidding strategy can be suitably modified in order to take into account the effects of seasonal variations and the non stationary nature of PV power generation. The performance of the optimal bidding strategy in the presence of weather forecasts is demonstrated on real data from Italian wind and PV power plants.

Mustafa Khammash (ETH, Zurich)
Feedback Control of Living Cells

Norbert Wiener’s 1948 Cybernetics presented a vision unifying the study of control and communication in the animal and the machine. Predating the discovery of the structure of DNA and the ensuing molecular biology revolution, applications in the life sciences at the time were limited. Today, the confluence of modern genetic manipulation techniques, powerful measurement technologies, and advanced analysis methods is enabling a new area of research in which systems and control notions are used for regulating cellular processes at the gene level. This presentation describes novel analytical and experimental work that demonstrates how de novo control systems can be interfaced with living cells and used to control their dynamic behavior. The feedback systems can either be realized on a computer (in-silico control) using optogenetics or through genetically encoded parts (in-vivo control). The two approaches will be compared and contrasted, and applications in biotechnology and therapeutics will be described.

Jorge Zubelli (INPA)
Identification and boundary parameterization of reaction-diffusion ecological models

This presentation concerns modelling aspects of aquatic systems, in particular the study of the Serra da Mesa lake. We discuss issues of parameter identification and we also address the problem of parameterizing the boundary data for reaction-diffusion partial differential equations
that models the dynamics of the lake. The boundaries are modeled as fast oscillating periodic structures and are endowed with Neumann or Dirichlet boundary conditions. Using techniques from homogenization theory and multiple-scale analysis we derive the effective equation and boundary conditions that are satisfied by the homogenized solution. The work discussed here involves a long term collaboration project between IMPA and the University of Siena with the participation of Chiara Mocenni, Antonio Vicino and Emiliano Sparacino.

Antonio Vicino (Università di Siena)
A Branching Process Model for Adaptive Immune Response

Quantifying T-cell proliferation provides useful information for understanding essential features of the immune response to vaccine or infection stimulus. Mathematical models, which play an important role for this analysis, have been used almost exclusively for studying in vitro experiments.
In this contribution, we adopt a multi-type branching process to model T-cell proliferation in in vivo experiments. Since the real system consists of a complex network of connected nodes where cells circulate and proliferate, both trafficking and proliferation phenomena need be modeled.
A quasi maximum likelihood approach is adopted to estimate model parameters, using T-cell relative frequencies instead of cell counts. Parameter estimates which represent the probabilities of division, death, migration and splitting of the different cell generations, provide meaningful information on T-cell population kinetics.