Speaker: Roberto Tempo
Abstract: Uncertainty has always been a critical issue in control systems. In recent years, we have observed a growing interest in probabilistic and randomized methods for the analysis and design of these systems. Throughout the lecture, we provide a perspective of this research area and discuss several randomized algorithms. In particular, we introduce the notion of sample complexity, demonstrate its key role in feedback analysis, and study related probabilistic bounds. Regarding control design, we analyze a class of low-complexity algorithms, based on sequential probabilistic validation techniques, which enjoy rigorous convergence properties. Specific applications of these methods to model predictive control and anti-windup design will conclude the lecture.
Speaker: Karl Kunisch
Abstract: In recent years significant advances were made in the analysis and in algorithm development for optimal control problems with sparsity constraints. For optimal control of distributed parameter systems sparsity patterns both in space and in time are of significant practical importance. Not only do they induce "cheaper" controls, but sparsity formulations also lend themselves as versatile approaches to the optimal actuator placement and to inverse source problems, for instance. The price to pay for these advantages is lack of smoothness in the optimal control formulations. To accommodate this challenge semi-smooth Newton techniques can be used for efficient numerical realizations. The analysis of these developments rests on convex analysis techniques. These can also be used effectively to develop novel approaches towards optimal control with switching structure structure guaranteeing, for example, that at most m controls are out of n (> m) are active at any instance of time.
Speaker: Antonis Papachristodoulou
Abstract: Many problems in robust and nonlinear control can be formulated using polynomial positivity conditions: the simplest example is the search of polynomial Lyapunov functions for stability analysis of equilibria of dynamical systems with polynomial vector fields. The discovery that semidefinite programming can be used to test polynomial non-negativity, through a sum of squares relaxation, opens up new directions in nonlinear systems analysis and design. In this talk I will first present how ideas from dynamical systems, positive polynomials and convex optimization can be used to analyse the stability, robust stability, performance and robust performance of systems described by nonlinear ODEs. I will also discuss how hybrid/switched systems, time-delay systems and systems described by PDEs can be analyzed before describing how other, more interesting analysis questions can be answered using sum of squares. Although entirely algorithmic, this approach does not scale well to large system instances. In the second part of my talk I will consider the analysis of large-scale networked systems and discuss how the system structure helps generate robust functionality conditions that scale well with the system size. I will then present more recent work on how to analyse “medium-sized” nonlinear systems, using ideas from graph partitioning, SDP decomposition and reduction.
Speaker: Anders Rantzer
Abstract: Classical control theory does not scale well for large systems like traffic networks, power networks and chemical reaction networks. However, many of these applications can be handled efficiently using the concept of positive system, exploiting that the set of positive states is left invariant by the dynamics. Positive systems, and the nonlinear counterpart monotone systems, are common in many branches of science and engineering. In this presentation, we will highlight several fundamental advantages of positive control systems: Verification and synthesis can be done with a complexity that scales linearly with the number of states and interconnections. Distributed controllers can be designed by convex optimization. Lyapunov functions and storage functions for nonlinear monotone systems can be built from scalar functions of the states, with dramatic simplifications as a result. In spite of a rich set of existing results, several fundamental questions in control of positive systems remain open. For example, negative feedback can easily destroy positivity of the closed loop system. On the other hand, intuition tells us that something is wrong with a traffic control system where fewer cars leads to more congestion. Hence, we need to better understand the limitations and potential of closed loop positive systems.
Speaker: Francesco Borelli
Abstract: Forecasts will play an increasingly important role in the next generation of autonomous and semi-autonomous systems. Applications include transportation, energy, manufacturing and healthcare systems. Predictions of systems dynamics, human behavior and environment conditions can improve safety and performance of the resulting system. However, constraint satisfaction, performance guarantees and real-time computation are challenged by the growing complexity of the engineered system, the human/machine interaction and the uncertainty of the environment where the system operates. In this talk I will first provide an overview of the theory and tools that we have developed over the past ten years for the systematic design of predictive controllers for uncertain linear and nonlinear systems. Then, I will focus on our recent results on real-time computation by using analog optimization. Throughout the talk I will show experiments with self-driving cars to motivate our research and show the benefits of the proposed techniques.
Speaker: Jacquelien Scherpen
Abstract: This talk presents an overview of two perspectives that we take to smart energy systems, both in the power and the gas grid, and the integration thereof. The first is taking a distributed optimal control point of view, applicable to a network of households with production devices, but also with demand side control, and with power-to-gas facilities. The expected future market structure is also considered. The second perspective considers the physics of the power grid, and the full order models that we can build. A port-Hamiltonian perspective is briefly considered, and some questions about the coupling of the two perspectives are raised.
Speaker: Hugues Garnier
Abstract: This talk discusses the importance and relevance of direct continuous-time system identification and how this relates to the solution for model identification problems in practical applications. It first gives a tutorial introduction to the main aspects of the most successful existing approaches for directly identifying continuous-time models of dynamical systems from sampled input-output data, including a review of associated software that has been developed to implement this methodology. Compared with traditional discrete-time model identification methods, the direct continuous-time approaches have some notable advantages that make them more useful in many practical applications. For instance, continuous-time models are more intuitive to control scientists and engineers in their every-day practice and the related estimation methods are particularly well suited to handle rapidly or irregularly sampled data situations. The second part of the talk discusses and illustrates these advantages via simulated and real data examples.
Speaker: Carolyn L. Beck
Abstract: Modelling and control of drug dosing regimens are particularly well-suited for applications of control. These problems frequently incorporate the use of mathematical models, lending themselves to a large range of model-based control methods. In fact, there has been ongoing research aimed at the development of closed-loop drug dosing and delivery in a number of specific medical domains for over five decades. In this talk, we discuss the development of modeling and control methods aimed at closed-loop delivery of pharmaceutical agents. We focus most of this discussion on the problem of controlling sedation levels during surgery.
