## Research seminars

Each year, MiSCIT and GIPSA-lab invite keynote speakers to give a short class on their research topic. The lectures (typically 15h) are given in the Control Systems Department of GIPSA-lab. They focus on the latest results in a specific topic of control and systems theory, and may include some labs to illustrate specific aspects. The attendance is composed as Master and Ph.D. students, as well as engineers, researchers and professors. A basic knowledge in dynamical systems, linear algebra and control theory is expected.

### Diagnosis (2020)

By*Dr Audine SUBIAS*, Associate Professor of Toulouse University.

**Content:**

- Introduction: definition, principles, classification of approaches problem statement, ...
- Logic Diagnosis
- The Diagnoser approach
- Diagnossability Analysis: diagnoser based, twin-plant & verifier based
- Diagnosis based on Supervision Patterns
- Diagnosis based on Chronicle Recognition
- Diagnosis based on Basis Reachability Graph

### Data-driven control system design (2019)

By*Dr Simone Formentin*, Assistant Professor at 'Politecnico di Milano' (Dipartimento di Elettronica, Informazione e Bioingegneria).

**Abstract:**
For many years, the role of system identification within control projects has been that of computing from data a dynamical model of the plant under control, which is as accurate as possible. A suitable model-based controller is then designed standing on the assumption that the identified model coincides with the real system. In case of a large uncertainty, robust control can be employed to take into consideration not only the nominal model, but also a description of the uncertainty set. Unfortunately, robust controllers may lead to very conservative performance.

This course addresses the interplay between identification and control and shows that, to overcome the major limitations of model-based control, the model and the controller must be designed together. In this way, the identified model does not necessarily fit the data at best, but the related controller maximizes the closed-loop performance. As an effective alternative, the direct mapping of data onto controller parameters is also discussed.

### Polynomial optimization and optimal control (2018)

By*Dr Didier HENRION*, CNRS "Directeur de Recherche" (senior researcher) at LAAS, Toulouse, France and Professor at the Department of Automatic Control of the Faculty of Electrical Engineering of the Czech Technical University in Prague.

**Abstract:**
First, we survey a mathematical technology introduced in 2000 by Jean Bernard Lasserre to solve globally non-convex optimization problems on multivariate polynomials with the help of a hierarchy of convex semidefinite programming problems (linear matrix inequalities or LMI = linear programming problems in the cone of positive semidefinite matrices). Instrumental to the development of this technique is the duality between the cone of positive polynomials (real algebraic geometry) and the cone of moments (functional analysis). These basic objects are introduced and studied in detail, with a special focus on conic optimization duality, and some illustrative examples are described.

Then in a second part, we study polynomial optimal control, which consists of minimizing a polynomial Lagrangian over a polynomial vector field subject to semi-algebraic control and state constraints, typically a nonconvex problem for which there is no solution in classical Lebesgue spaces. To overcome this, polynomial optimal control problems are first formulated as linear programming (LP) problems in the cone of occupation measures (standard objects in Markov decision processes and ergodic theory of dynamical systems), and infinite-dimensional convex duality is used to establish the link with subsolutions of the Hamilton-Jacobi-Bellman (HJB) partial differential equation satisfied by the value function. Then, the Lasserre hierarchy is applied to solve numerically these infinite-dimensional LP problems.

In the third part, we address the problem of computing the region of attraction (ROA) of a target set (e.g., a neighborhood of an equilibrium point) of a polynomial control system. We show that the ROA can be computed by solving an infinite-dimensional LP over occupation measures. In turn, this problem can be solved approximately with the Lasserre hierarchy. Our approach is genuinely primal in the sense that convexity of the problem of computing the ROA is an outcome of optimizing directly over system trajectories. The dual infinite-dimensional LP on nonnegative continuous functions (approximated by polynomial sum-of-squares) allows us to generate a hierarchy of semialgebraic outer approximations of the ROA at the price of solving a sequence of LMI problems with asymptotically vanishing conservatism.

In the final part, we develop further our LP approach for the optimal control of nonlinear switched systems where the control is the switching sequence. This is done by introducing modal occupation measures, which allow to relax the problem as a primal LP. Its dual LP of HJB inequalities is also characterized. The LPs are then solved numerically with the Lasserre hierarchy. Because of the special structure of switched systems, we obtain a much more efficient method than could be achieved by applying the standard Lasserre hierarchy for general optimal control problems.

### PDE Control Methods (2017)

By*Dr Eduardo CERPA*, Associate Professor in the Department of Mathematics at Universidad Tecnica Federico Santa Maria, Valpara iso (Chili)

**Abstract:**
In this course we study controllability and stabilization methods for infinite-dimensional systems described by partial differential equations (PDEs). Classical PDEs as the transport equation, the heat equation, and the wave equation are considered in detail. Moreover, other models as the Korteweg-de Vries equation and the Kuramoto-Sivashinsky equation are studied from a control viewpoint.

### Fault prognostics of engineering systems (2016) *[class description]*

By *Dr Piero BARALDI*, Associate Professor of Nuclear Engineering at the Department of Energy at the Politecnico di Milano (Italy)

**Abstract:**
For industry, unforeseen failures of engineering systems are extremely costly in terms of repair costs and lost revenues.
To anticipate failures, predictive maintenance approaches are being developed, based on the assessment of the actual degradation condition of the engineering system and on the prediction of its evolution for setting the optimal time for maintenance, with the intent of improving its safety and economic performances.
Fault prognostics is a field of research and application which aims at making use of past, present and future information on the environmental, operational and usage conditions of an engineering system in order to predict and proactively manage its failures.
The goal of this course is to provide participants with the methodological competences and the computational tools necessary to tackle critical problems in the areas of prognostics.
The course presents methods to improve safety, increase efficiency, manage equipment aging and obsolescence and reduce maintenance costs of engineering systems.

### Introduction to network coordination (2015)

By*Dr Paolo Frasca*, Associate Professor at University of Twente, Faculty of Electrical Engineering, Mathematics and Computer Science (The Netherlands)

**Abstract:**
The consensus problem is possibly the simplest example of network coordination, where the nodes of a networks need to agree on a common value by only communication with their neighbors. This course will provide a formal but accessible and self-contained introduction to linear discrete-time dynamics that solve the consensus problem. The course will also cover several extensions and applications, from distributed estimation to dynamics over social networks.

### Linear Matrix Inequalities and Sum-of-Squares Optimization in Systems and Controls Theory: A Practical and Theoretical Overview (2014)

By*Dr Mattew M. Peet*, Associate Professor of Aerospace Engineering, Arizona State University (USA)

**Abstract:**
The topic of this course will be the use of LMI methods for optimal control of linear, nonlinear and infinite-dimensional systems. We will start by posing all major finite-dimensional optimal control problems as LMIs. This includes both output and full-state feedback control for both the H_\infty and H_2 (LQG) system norms. We will also give a brief introduction to the popular SDP solver SeDuMi. Next, we will give a background on the use of LMIs for optimization of polynomial variables such as in the Sum-of-Squares framework - including the use of the Matlab toolbox SOSTOOLS. We will discuss several theoretical tools for the optimization of polynomials such as various versions of the Positivstellensatz. Finally, we will discuss how LMIs and polynomial optimization have been use to resolve long-standing problems in analysis of nonlinear systems and systems with delay, and how these results have been extended to synthesize optimal controllers for systems with delay and certain classes of partial-differential equations.

### Hyperbolic systems, from the statement to the stability (2014)

By*Dr Valerie Dos Santos*, Associate Professor at Laboratoire d'Automatique et du Genie des Procedes (LAGEP), UCB Lyon 1.

**Abstract:**
This course aims at reviewing various types of so-called hyperbolic equations, related numerical issues, mathematical properties of solutions, and some recent applications in control (including simulation and experimental examples).

### Model Reduction (Approximation) of Large-Scale Systems (2013)

By*Dr Charles Poussot-Vassal*, Researcher at Onera - The French Aerospace Lab.

**Abstract:**
In the engineering area (e.g. aerospace, automotive, biology, circuits), dynamical systems are the basic framework used for modelling, controlling and analysing a large variety of systems and phenomena. Due to the increasing use of dedicated computer-based modelling design software, numerical simulation turns to be more and more used to simulate a complex system or phenomenon and shorten both development time and cost. However, the need of an enhanced model accuracy inevitably leads to an increasing number of variables and resources to manage at the price of a high numerical cost. This counterpart is the justification for model reduction (see Figure 1).

The objective of the lecture is to introduce the model reduction (or approximation) problem, within the linear framework only, and, in an increase complexity, some of the well established and modern techniques to solve this class of problem. The lecture is also coupled with two Matlab-based labs, in order to emphasize the numerical difficulties and to provide the participant an insight of the existing tools.