Palestras da Escola de Altos Estudos

System Identification

Lennart Ljung


Automatic Control

 Linköpings universitet





System identification is the art and science of building mathematical models of dynamical systems based on observed inputs and outputs. In this presentation, the basic concepts and tools for this process will be described. The talk will focus on the basic three entities:  the model structure, the data set and  principles for fitting models to data.

Both linear and nonlinear models will be discussed. Of particular importance is how to gain confidence in the estimated model: Model validation.

The talk will also deal with the practical side of system identification: What are the software tools to efficiently construct models from data, and how does one make sure that the experimental data contains relevant information?

Discrete Event Systems

ChristosG. Cassandras


Division of Systems Engineering,

Department of Electrical and Computer Engineering, and

Center for Information and Systems Engineering (CISE)

Boston University





We will contrast time-driven to event-driven systems so as to motivate new modeling frameworks and associated techniques developed for the analysis, control, and optimization of Discrete Event Systems (DES). Formal models for DES will be presented with emphasis on automata, timed automata, and stochastic timed automata, which are best suited to tackle resource contention problems commonly encountered in computer, communication, and sensor networks, in manufacturing, in transportation, and in new problems related to energy management. Discrete event simulation will be presented as a direct implementation of stochastic timed automata. The uses and limitations of simulation-based methods will be discussed.


The absence of analytical, closed-form expressions quantifying the performance of most DES of interest has motivated the development of techniques that take maximal advantage of the properties of DES state dynamics. This includes the ability to carry out efficient sensitivity estimation for performance metrics with respect to critical design and control parameters. Resulting techniques lead to “rapid learning” of the behavior of such systems under different parameter settings without having to actually simulate or implement all such settings. We will present the theoretical foundations of Infinitesimal Perturbation Analysis (IPA) and Concurrent Estimation (CE) and their use for control and optimization purposes.


Despite many advances, DES remain highly complex to analyze and recent efforts have focused on developing abstraction models and methods that extract the salient features of a DES through hybrid dynamic system models. Recent developments will be presented on an “IPA calculus” for stochastic hybrid systems and its robustness properties that allow us to now study highly complex DES through proper modeling abstractions and new analysis tools. Applications to various control and optimization problems for DES will be included.

Nonlinear Systems

Hassan K. Khalil

University Distinguished Professor

Department of Electrical and Computer Engineering

Michigan State University


This tutorial talk will give an introduction to nonlinear systems and control. It will describe essentially nonlinear phenomena and Lyapunov’s method for studying stability. It will present techniques for nonlinear control design, including feedback linearization, backstepping, passivity-based control, and sliding mode Control. Finally it will present techniques for nonlinear observer design, including observers with linear error dynamics and high-gain observers, and will illustrate the use of such observers in output feedback control.

It is assumed that attendees have undergraduate knowledge of control systems and differential equations. Knowledge of state models of linear systems is helpful.

Power System Automation: Challenges and Opportunities

Om P. Malik, Ph.D., LFIEEE


University of Calgary






Modern electric power systems have developed into very large and complex systems. The fundamental principle in the effective operation of interconnected power systems requires that electric power generation and load remain balanced at all time.


When a disturbance occurs, protection and control actions are required to minimize the impact of the disturbance and restore the system to a normal state. Control and protection actions can be taken at various levels of the power system hierarchy depending on the type and severity of the disturbance.

At the upper levels, the control center operators must deal with large scale power system problems in a very complex situation. Many times they rely on heuristic solutions and policies. Systems with automated solutions designed to detect predetermined system conditions having a high probability of causing stress on the power system and provide system-wide control and protection solutions are being developed.


Local protection and control devices at the generation and sub-station levels arrest the propagation of emergencies through automatic actions by addressing local system or equipment specific problems.


A broad understanding of the power system specific problems, and protection, control and automation measures being employed and under development to improve power system integrity and reliability at both the system and local levels, will be provided in this presentation.

Intelligent Systems: Analysis and Design-A Perspective of Computational Intelligence


Witold Pedrycz


Department of Electrical & Computer Engineering

University of Alberta, Edmonton Canada


Systems Research Institute, Polish Academy of Sciences

Warsaw, Poland






The talk offers a comprehensive introduction to intelligent systems along with their analysis, design methodologies and practice. We start with a concept of intelligent systems and review existing definitions (descriptions) of such architectures. Then we look at the key features of intelligent systems as well as discuss several representative examples of practical relevance.  We cast the analysis and design of intelligent systems in the framework of Computational Intelligence (CI) and demonstrate that CI offers a comprehensive environment supporting both system analysis and design. A special attention is paid to various ways of knowledge representation along with an evaluation of the features of the corresponding knowledge representation schemes to facilitate or enhance learning abilities in intelligent systems. A number of selected commonly encountered learning mechanisms are elaborated on and assessed vis-à-vis a nature of the problem at hand. Intelligent classifiers regarded as an important category of intelligent systems are investigated. A class of collaborative intelligent systems is discussed as well.


  The talk is self-contained and all required prerequisites will be covered

Fluid & Hybrid Petri Nets

Manuel Silva


Universidad de Zaragoza





The talk will start providing a presentation of the fluidization of discrete event dynamic systems (DEDS), as a relaxation (or over-approximation) technique for dealing with the classical state explosion problem. This is particularly interesting when dealing with DEDS provided with large populations such in some manufacturing, traffic, logistics or population systems.

Even if named as continuous or fluid, the obtained relaxed models are frequently hybrid in a technical sense. Thus, techniques used for logical verification, performance evaluation or control studies in discrete, hybrid and continuous models can be adapted in some sense. Moreover, the possibilities for transferring concepts and techniques from one modelling paradigm to others are very significant, so there is much space for synergy. As a central modelling paradigm for concurrent and synchronized DEDS, Petri nets (PNs) will be considered.

Being a relaxation of DEDS, the analysis and synthesis problems on fluid models are frequently much more tractable at the computational level. Nevertheless, timed fluid PNs (under so called infinite server semantics) are able to simulate Turing Machines (!), so great “expressive power” and “undecidabilities” appear in the horizon. Being an approximation, problems like the loss of some discrete properties by means of fluidization will be considered. Otherwise stated, not all Petri Nets allows a “reasonable approximation” by fluidization (like not all ordinary differential equations, even provided with constant coefficients, allows a reasonable linearization, for example). Equally important, “non-monotonic behaviours” in untimed and timed models will be stressed, what raises the importance of control strategies. After discussing observability and controllability issues, we will conclude with some remarks and possible directions for future research.

Among the aspects that distinguish the adopted approach are: the focus on the relationships between discrete and continuous PN models, both for untimed, i.e., fully non-deterministic abstractions, and timed versions; the use of structure theory of (discrete) PNs, algebraic and graph based concepts and results; and the bridge to Automatic Control Theory.