CPS Events
CPSRC Seminar Series: Uniform Asymptotic Stability of Switched Systems via Reduced Control Systems
Abstract:
The stability of switched systems is a challenging problem of current interest. In this talk we will present some new results for the uniform global asymptotic stability of switched nonlinear systems with time/state-dependent switching constraints. These results are based on the existence of weak Lyapunov functions, i.e. positive definite functions for which the time derivative along the subsystems are only semidefinite negative. As a difference with most of the known criteria based on weak Lyapunov functions, our results do not assume any dwell-time condition, and consequently can be applied to switched systems with arbitrary fast switchings. The approach for obtaining the stability results consists of embedding the switched system into a control system whose outputs are related with the time derivatives of the Lyapunov functions, and then studying the behavior of the solutions of that control systems when its outputs are constrained to be identically zero.
Bio:
José Luis Mancilla Aguilar received the Licenciado en Matemática degree (1994) and his Doctor’s degree in Mathematics (2001) from the Universidad Nacional de Buenos Aires (UBA), Argentina. From 1993 to 1995, he received a Research Fellowship from the Argentine Atomic Energy Commission (CNEA) in the area of nonlinear control. Since 1995, he has been with the Department of Mathematics of the Facultad de Ingeniería (UBA), where he is currently a part-time Associate Professor. Since 2005, Dr. Mancilla-Aguilar has held a Professor position at the Department of Mathematics of the Instituto Tecnológico de Buenos Aires (ITBA) and currently is the head of the Centro de Sistemas y Control (CeSyC). His research interests include hybrid systems and nonlinear control.
Watch the seminar on our YouTube channel: https://youtu.be/QQSHfjnLMbk
CPSRC Seminar Series: Observer Design for Nonlinear Systems
Abstract:
Unlike for linear systems, no systematic method exists for the design of observers for nonlinear systems. In fact, observer design may be more or less straightforward depending on the coordinates we choose to express the system dynamics. In particular, some specific structures, called normal forms, have been identified for allowing a direct and easier observer construction. It follows that one can look for a reversible change of coordinates transforming the expression of the system dynamics into one of those normal forms, design an observer in those coordinates, and finally deduce an estimate of the system state in the initial coordinates via inversion of the transformation. This talk gives contributions to each of those three steps.
First, we show the interest of a new triangular normal form with continuous (non-Lipschitz) nonlinearities. Indeed, some systems may not be transformable into the standard Lipschitz triangular form, but rather into an "only continuous" triangular form. In this case, the famous high gain observer no longer is sufficient, and we propose to use homogeneous observers instead.
We also show how the "Luenberger" design, consisting in transforming the system dynamics into a Hurwitz linear form based on the resolution of PDE, can be extended to time-varying/controlled systems.
As for the inversion of the transformation, this step is far from trivial in practice, in particular when the domain and image spaces have different dimensions. When no explicit expression for a global inverse is available, numerical inversion usually relies on the resolution of a minimization problem with a heavy computational cost. That is why we have developed a method to avoid the explicit inversion of the transformation by bringing the observer dynamics (expressed in the canonical form coordinates) back into the initial system coordinates. This is done by dynamic extension, i.e. by adding some new coordinates to the system and transforming an injective immersion into a surjective diffeomorphism.
Bio:
Pauline Bernard graduated from MINES ParisTech in 2014 with a Master degree in Applied Mathematics and Automatic Control. In 2017, she obtained her Ph.D. in Mathematics and Automatic Control at PSL Reserch University, prepared at the Systems and Control Center, MINES ParisTech. She is now a post-doc at the Computer Engineering Department, University California Santa Cruz. Her research interests focus on the observation problem and observer design for nonlinear systems and recently hybrids systems.
Watch the seminar on our YouTube channel: https://youtu.be/JXh4t_jbiSc
CPSRC Seminar Series: Stability and Stabilization of Networked Systems
Abstract:
The so-called Lyapunov-based methods are proposed in order to study some problems related to distributed coordination of multi-agent systems. More precisely, the presentation is divided into three parts. The first part studies consensus problem for a network of single-integrator systems under a bidirectional time-varying graph topology. The second part considers a group of nonlinear agents modeled as nonholonomic mobile robots, distributed control laws are provided in order to solve the leader-follower and the leaderless consensus problems under different assumptions on the communication graph topology and on the leader's trajectories. Finally, using a singular perturbation approach, the last part is advocated to the synchronization of a heterogeneous network of nonlinear oscillators under a sufficiently large coupling gain.
Bio:
Mohamed Adlene Maghenem received his Control-Engineer degree from the Polytechnical School of Algiers, Algeria, in 2013, his M.S. and Ph.D. degrees in control from the University of Paris-Saclay, France, in 2014 and 2017, respectively. He is currently a Postdoctoral Fellow at the Computer Engineering Department at the University of California Santa Cruz. His interests include distributed coordination of multi-agent systems, Synchronization of oscillators, Systems with Persistency of Excitation, Hybrid dynamical systems.
Watch the seminar on our YouTube channel: Https://Youtu.Be/TJpLU4bWcQI
CPSRC Seminar Series: Hybrid Systems Determined by Set-Value Dynamics and Random-in-Time Jumps with Control Applications
Abstract:
We discuss modeling and analysis for a class of stochastic hybrid systems with random-in-time jumps. In particular, we present natural Lyapunov-based sufficient conditions for asymptotic stability in probability and for an alternative property called recurrence.
We consider models that admit not necessarily unique flows or jumps. In this setting, we emphasize that the solutions must depend causally on the random inputs that affect solutions. Otherwise, Lyapunov functions may fail to be sufficient for establishing stability properties. After discussing general models, we show how the analysis results can be used in two different settings. The first application involves certifying the behavior of control systems where the control signal is updated at random times; this situation is in contrast to the situation where control signal updates are triggered by events or are periodic. The second application involves certifying the behavior of algorithms that set tolls in societal systems to induce optimal behavior, in the setting where actors in the society exhibit random behavior.
Bio:
Andrew R. Teel received his A.B. degree in Engineering Sciences from Dartmouth College in Hanover, New Hampshire, in 1987, and his M.S. and Ph.D. degrees in Electrical Engineering from the University of California, Berkeley, in 1989 and 1992, respectively. After receiving his Ph.D., he was a postdoctoral fellow at the Ecole des Mines de Paris in Fontainebleau, France. In 1992 he joined the faculty of the Electrical Engineering Department at the University of Minnesota, where he was an assistant professor until 1997. Subsequently, he joined the faculty of the Electrical and Computer Engineering Department at the University of California, Santa Barbara, where he is currently a Distinguished Professor and director of the Center for Control, Dynamical systems, and Computation. His research interests are in nonlinear and hybrid dynamical systems, with a focus on stability analysis and control design. He has received NSF Research Initiation and CAREER Awards, the 1998 IEEE Leon K. Kirchmayer Prize Paper Award, the 1998 George S. Axelby Outstanding Paper Award, and was the recipient of the first SIAM Control and Systems Theory Prize in 1998. He was the recipient of the 1999 Donald P. Eckman Award and the 2001 O. Hugo Schuck Best Paper Award, both given by the American Automatic Control Council, and also received the 2010 IEEE Control Systems Magazine Outstanding Paper Award. In 2016, he received the Certificate of Excellent Achievements from the IFAC Technical Committee on Nonlinear Control Systems. He is Editor-in-Chief for Automatica, and a Fellow of the IEEE and of IFAC.
From Hummingbirds to Honeybees: Algorithms for Agile Micro Aerial Vehicles with On-Board Perception
Abstract
Agile micro aerial vehicles will have a massive societal impact over the next decades, creating novel opportunities for large-scale precision agriculture, fast delivery of medical supplies, and disaster response, and providing new perspectives on environmental monitoring and artificial pollination. This future requires the design of lightweight and robust perception algorithms, which interpret sensor data into a coherent world representation, in the face of measurement noise and outliers, and enable on-board situational awareness and decision-making. In this talk, I present my work on lightweight and robust robot perception. I start by discussing an algorithm for fast visual-inertial navigation, which estimates the motion of the robot from visual and inertial cues, and demonstrate its use for agile flight of micro aerial vehicles. Then, I focus on robustness and show that fundamental insights from optimization and Riemannian geometry lead to the design of estimation techniques that are provably robust to large noise, providing the first certifiably correct algorithm for localization and mapping. I also discuss the challenges connected to scaling down perception to nano and pico aerial vehicles, where sensing and computation are subject to strict payload and power constraints. I argue that enabling autonomy on miniaturized platforms requires a paradigm shift in perception, sensing, and communication, and discuss how we can draw inspiration from nature in designing the next generation of flying robots.
Bio
Luca Carlone is a research scientist in the Laboratory for Information and Decision Systems at the Massachusetts Institute of Technology. Before joining MIT, he was a postdoctoral fellow at Georgia Tech (2013-2015), and a visiting researcher at the University of California Santa Barbara (2011). He got his Ph.D. from the Polytechnic University of Turin, Italy, in 2012. His research interests include nonlinear estimation, numerical and distributed optimization, computer vision and probabilistic inference applied to sensing, perception, and control of single and multi robot systems. He published more than 60 papers on international journals and conferences, including a best paper award finalist at RSS 2015 and a best paper award winner at WAFR 2016.
