Posted January 13, 2022
Last modified February 21, 2022
Control and Optimization Seminar Questions or comments?
9:30 am - 10:20 am Zoom (Click "Questions or comments?" to request Zoom link)
Pierdomenico Pepe, University of L'Aquila
Sampled-Data Event-Based Stabilization of Retarded Nonlinear Systems
We present an event-based controller for the stabilization of nonlinear retarded systems. The main features of the controller we provide are that (i) only sampled-data measures of the Euclidean internal variable are needed, thus avoiding continuous-time monitoring of the state in infinite dimensional spaces, ii) the event function is only evaluated at sampling instants, and involves a finite number of most recent measures, and iii) discontinuous feedbacks and non- uniform sampling are allowed. The controller guarantees semi-global practical asymptotic stability to an arbitrarily small final target ball around the origin, by suitably fast sampling.
Posted January 31, 2022
Last modified April 6, 2022
Control and Optimization Seminar Questions or comments?
9:30 am - 10:20 am Zoom (Click "Questions or comments?" to request Zoom link)
Franco Rampazzo, Dipartimento di Matematica Pura ed Applicata, Università degli Studi di Padova
Goh and Legendre-Clebsch Conditions for Non-Smooth Optimal Control Problems
Various generalizations of the original Maximum Principle (Pontryagin et al., 1956) have been produced in different theoretical frameworks in the literature, starting from the pioneering works of F. Clarke in the 1970s up to recent papers. For an end-point constrained optimal control problem with control affine dynamics, I will present ideas (from a work in progress with F. Angrisani) in the direction of adding higher order necessary conditions to the Maximum Principle. In particular, one can generalize the classical Goh condition and the Legendre-Clebsch condition (which include Lie brackets) to the case where the data are nonsmooth. In fact, the recently introduced notion of Quasi Differential Quotient (Palladino and R., 2020) allows one to treat two simultaneous kinds of non-smoothness, namely the one concerning the adjoint inclusion and the one connected with the set-valued Lie brackets (R. and Sussmann 2001), within the same framework.
Posted February 6, 2022
Last modified February 18, 2022
Control and Optimization Seminar Questions or comments?
9:30 am - 10:20 am Zoom (Click “Questions or Comments?” to request a Zoom link)
Xiaobo Tan, Michigan State University
IEEE Fellow, NSF CAREER Awardee
Modeling and Control of Hysteresis Using Minimal Representations
Hysteresis remains a key nonlinearity in magnetic and smart material actuators that challenges their control performance. High-fidelity modeling and effective compensation of hysteresis, yet with low computational complexity, are of immense interest. In this talk I will share some recent advances in this direction via several examples. First, I will present the optimal reduction problem for a Prandtl-Ishlinskii (PI) operator, one of the most popular hysteresis models, where an optimal approximation of the original operator with fewer constituent elements (play operators) is obtained via efficient dynamic programming. Second, I will discuss adaptive estimation of play radii, instead of their weights, as an alternative means for accurate modeling of hysteresis with a PI operator of low complexity. Finally, I will report a dynamic inversion approach to hysteresis compensation that requires minimal, qualitative conditions on the system model. Throughout the talk I will use experimental results from smart materials to illustrate the methods.
Posted January 27, 2022
Last modified February 15, 2022
Control and Optimization Seminar Questions or comments?
9:30 am - 10:20 am Zoom (Click "Questions or comments?" to request Zoom link)
Andrea Serrani, Ohio State University
Adaptive Feedforward Compensation of Harmonic Disturbances for Convergent Nonlinear Systems
Rejecting periodic disturbances occurring in dynamical systems is a fundamental problem in control theory, with numerous technological applications such as control of vibrating structures, active noise control, and control of rotating mechanisms. From a theoretical standpoint, any design philosophy aimed at solving this problem reposes upon a specific variant of the internal model principle, which states that regulation can be achieved only if the controller embeds a copy of the exogenous system generating the periodic disturbance. In the classic internal model control (IMC), the plant is augmented with a replica of the exosystem, and the design is completed by a unit which provides stability of the closed loop. In a somewhat alternative design methodology, referred to as adaptive feedforward compensation (AFC), a stabilizing controller for the plant is computed first and then an observer of the exosystem is designed to provide asymptotic cancelation of the disturbance at the plant input. In particular, the parameters of the feedforward control are computed adaptively by means of pseudo-gradient optimization, using the regulated error as a regressor. Contrary to IMC, which has been the focus of extensive investigation, application of AFC methods to nonlinear systems has remained so far elusive. This talk aims at presenting results that set the stage for a theory of AFC for nonlinear systems by providing a nonlinear equivalent of the condition for the solvability of the problem in the linear setting, and by re-interpreting classical linear schemes in a fully nonlinear setting. To this end, the problem is approached by combining methods from output regulation theory with techniques for semi-global stabilization.
Posted January 26, 2022
Control and Optimization Seminar Questions or comments?
9:30 am - 10:20 am Zoom (Click "Questions or comments?" to request Zoom link)
Sophie Tarboureich, Laboratoire d'Analyse et d'Architecture des Systèmes (LAAS), France
Algorithms for Event-Triggered Control
Event-triggered control consists of devising event-triggering mechanisms leading to only seldom control updates. In the context of event-triggered control, two objectives that can be pursued are (1) emulation, whereby the controller is a priori predesigned and only the event-triggering rules have to be designed and (2) co-design, where the joint design of the control law and the event-triggering conditions has to be performed. Control systems are connected to generic digital communication networks for implementation, transmission, coding, or decoding. Therefore, event-triggered control strategies have been developed to cope with communication, energy consumption, and computation constraints. The talk is within this scope. Considering linear systems, the design of event-triggering mechanisms using local information is described through linear matrix inequality (or LMI) conditions. From these conditions, the asymptotic stability of the closed loop system, together with the avoidance of Zeno behavior, are ensured. Convex optimization problems are studied to determine the parameters of the event-triggering rule with the goal of reducing the number of control updates.
Posted February 2, 2022
Control and Optimization Seminar Questions or comments?
9:30 am - 10:20 am Zoom (Click “Questions or Comments?” to request a Zoom link)
Monica Motta, Università di Padova, Italy
Stabilizability in Optimal Control
We address the stabilizability of nonlinear control systems, in an optimal control theoretic framework. First, we extend the nowadays classical concepts of sampling and Euler solutions that were developed by F. Clarke, Y. Ledyaev, E. Sontag, A. Subbotin, and R.J. Stern (1997, 2000) for control systems associated to discontinuous feedbacks, by also considering corresponding costs, given by integrals of a nonnegative Lagrangian. In particular, we introduce the notions of sample and Euler stabilizability to a closed target set with regulated cost, which require the existence of a stabilizing feedback that keeps the cost of all sampling and Euler solutions starting from the same point below the same level. Then, under mild regularity hypotheses on the dynamics and on the Lagrangian, we prove that the existence of a special control Lyapunov function, to which we refer to as a minimum restraint function (or MRF), implies not only stabilizability, but also that all sample and Euler stabilizing trajectories have regulated costs. The proof is constructive, being based on the synthesis of appropriate feedbacks derived from the MRF. As in the case of classical control Lyapunov functions, this construction requires that the MRF is locally semiconcave. However, by generalizing an earlier result by L. Rifford (2000) we establish that it is possible to trade regularity assumptions on the data with milder regularity assumptions on the MRF. In particular, we show that if the dynamics and the Lagrangian are locally Lipschitz up to the boundary of the target, then the existence of a mere locally Lipschitz MRF provides sample and Euler stabilizability with regulated cost. This talk is based on a joint work with Anna Chiara Lai (from University Roma La Sapienza, Rome, Italy), which is part of an ongoing, wider investigation of global asymptotic controllability and stabilizability from an optimal control perspective.
Posted August 8, 2022
Control and Optimization Seminar Questions or comments?
9:30 am - 10:20 am Zoom (Click “Questions or Comments?” to request a Zoom link)
Lorena Bociu, North Carolina State University
PECASE Awardee
Analysis and Control in Poroelastic Systems with Applications to Biomedicine
Fluid flows through deformable porous media are relevant for many applications in biology, medicine and bio-engineering, including tissue perfusion, fluid flow inside cartilages and bones, and design of bioartificial organs. Mathematically, they are described by quasi-static nonlinear poroelastic systems, which are implicit, degenerate, coupled systems of partial differential equations (PDE) of mixed parabolic-elliptic type. We answer questions related to tissue biomechanics via well-posedness theory, sensitivity analysis, and optimal control for the poroelastic PDE coupled systems mentioned above. One application of particular interest is perfusion inside the eye and its connection to the development of neurodegenerative diseases.
Posted September 4, 2022
Control and Optimization Seminar Questions or comments?
9:30 am - 10:20 am Zoom (Click “Questions or Comments?” to request a Zoom link)
Michael Margaliot, Tel Aviv University
Revisiting Totally Positive Differential Systems: A Tutorial and New Results
A matrix is called totally nonnegative (TN) if all of its minors are nonnegative, and totally positive (TP) if all its minors are positive. Multiplying a vector by a TN matrix does not increase the number of sign variations in the vector. In a largely forgotten paper, Schwarz (1970) considered matrices whose exponentials are TN or TP. He also analyzed the evolution of the number of sign changes in the vector solutions of the corresponding linear system. In a seemingly different line of research, Smillie (1984), Smith (1991), and others analyzed the stability of nonlinear tridiagonal cooperative systems by using the number of sign variations in the derivative vector as an integer-valued Lyapunov function. We provide a tutorial on these topics and show that they are intimately related. This allows us to derive generalizations of the results by Smillie (1984) and Smith (1991) while simplifying the proofs. This also opens the door to many new and interesting research directions. This is joint work with Eduardo D. Sontag from Northeastern University.
Posted September 14, 2022
Last modified September 15, 2022
Control and Optimization Seminar Questions or comments?
9:30 am - 10:20 am Zoom (Click “Questions or Comments?” to request a Zoom link)
Maria Teresa Chiri, Queen's University
Soil Searching by an Artificial Root
We model an artificial root which grows in the soil for underground prospecting. Its evolution is described by a controlled system of two integro-partial differential equations: one for the growth of the body and the other for the elongation of the tip. At any given time, the angular velocity of the root is obtained by solving a minimization problem with state constraints. We prove the existence of solutions to the evolution problem, up to the first time where a "breakdown configuration" is reached. Some numerical simulations are performed, to test the effectiveness of our feedback control algorithm. This is a joint work with Fabio Ancona (University of Padova) and Alberto Bressan (Penn State University).
Posted August 22, 2022
Last modified September 28, 2022
Control and Optimization Seminar Questions or comments?
9:30 am - 10:20 am Zoom (Click “Questions or Comments?” to request a Zoom link)
Christophe Prieur, Université Grenoble Alpes
Stabilization of Nonlinear PDE by Means of Nonlinear Boundary Controls
In this presentation, the focus will be on the design of boundary controls for distributed parameter systems such as those described by linear and nonlinear partial differential equations. Saturated controllers will be discussed in this talk such as those modeling feedback laws in the presence of amplitude constraints. We will review techniques for the stability analysis and the derivation of design conditions for various PDEs such as parabolic and hyperbolic ones. An application to nuclear fusion will conclude this lecture.
Posted August 16, 2022
Last modified September 24, 2022
Control and Optimization Seminar Questions or comments?
9:30 am - 10:20 am Zoom (Click “Questions or Comments?” to request a Zoom link)
Matthew Peet, Arizona State University
An Algebraic Framework for Representation, Analysis, Control and Simulation of Delayed and PDEs
We explain the recently proposed partial integral equation representation and show how it enables us to solve many problems in analysis, control, and simulation of delayed and partial differential equations. We start by defining the *-algebra of partial integral (PI) operators. Next, we show that through a similarity transformation, the solution of a broad class of delayed and partial differential equations may be equivalently represented using a partial integral equation (PIE) - an equation parameterized by PI operators. We then show that many analysis and control problems for systems represented as a PIE may be solved through convex optimization of PI operators. Finally, we discuss software which automates the process of conversion to PIE, analysis, optimal controller synthesis, implementation, and simulation.
Posted September 12, 2022
Last modified October 17, 2022
Control and Optimization Seminar Questions or comments?
9:30 am - 10:20 am Zoom (Click “Questions or Comments?” to request a Zoom link)
Craig Woolsey, Virginia Tech
Port-Hamiltonian Modeling and Energy-Based Control of Ocean and Atmospheric Vehicles
The dynamics of a wide variety of vehicles can be represented using noncanonical Hamiltonian system models with dissipation and exogenous inputs. The Hamiltonian structure captures energy exchange among subsystem elements, the noncanonical form accommodates rotating reference frames, and the exogenous inputs allow for control commands and for disturbances that are not readily incorporated into the Hamiltonian form. Because these models typically describe a system's behavior within a large region of state space, and because the system structure provides a natural starting point for Lyapunov-based control design, noncanonical Hamiltonian models are especially well-suited to developing large-envelope nonlinear control laws. The presentation will include several examples from the speaker's experience, such as space vehicles, autonomous underwater vehicles (AUVs), and uncrewed air vehicles (UAVs). A particular emphasis will be recent theoretical results, supported by experimental demonstrations, of passivity-based control laws for fixed-wing aircraft. In considering these examples, a unifying theme will emerge: recognizing and exploiting the nonlinear mechanical system structure of the governing equations to obtain provably effective control strategies.
Posted September 11, 2022
Last modified October 21, 2022
Control and Optimization Seminar Questions or comments?
9:30 am - 10:20 am Zoom (Click “Questions or Comments?” to request a Zoom link)
Na (Lina) Li, Harvard University
Donald P. Eckman, AFOSR YIP, NSF CAREER, and ONR YIP Awardee
Scalable Distributed Control and Learning of Networked Dynamical Systems
Recent radical evolution in distributed sensing, computation, communication, and actuation has fostered the emergence of cyber-physical network systems. Regardless of the specific application, one central goal is to shape the network's collective behavior through the design of admissible local decision-making algorithms. This is nontrivial due to various challenges such as local connectivity, system complexity and uncertainty, limited information structure, and the complex intertwined physics and human interactions. In this talk, I will present our recent progress in formally advancing the systematic design of distributed coordination in network systems via harnessing special properties of the underlying problems and systems. In particular, we will present three examples and discuss three types of properties: i) how to use network structure to ensure the performance of the local controllers; ii) how to use the information and communication structure to develop distributed learning rules; iii) how to use domain-specific properties to further improve the efficiency of the distributed control and learning algorithms.
Posted June 12, 2022
Last modified September 14, 2022
Control and Optimization Seminar Questions or comments?
9:30 am - 10:20 am Zoom (Click “Questions or Comments?” to request a Zoom link)
Naomi Leonard, Princeton University
MacArthur Fellow, and Fellow of ASME, IEEE, IFAC, and SIAM.
Nonlinear Opinion Dynamics on Networks: Agreeing, Disagreeing, and Avoiding Indecision
I will present continuous-time multi-option nonlinear opinion dynamics for a group of agents that observe or communicate opinions over a network. Nonlinearity is introduced by saturating opinion exchanges: this enables a wide range of analytically tractable opinion-forming behaviors, including agreement and disagreement, deadlock breaking, tunable sensitivity to input, oscillations, flexible transition between opinion configurations, and opinion cascades. I will discuss how network-dependent tuning rules can robustly control the system behavior and how state-feedback dynamics for model parameters make the behavior adaptive to changing external conditions. The model provides new means for systematic study and design of dynamics on networks in nature and technology, including the dynamics of decision-making, spreading processes, polarization, games, navigation, and task allocation. I will demonstrate with applications to multi-robot teams. This is joint work with Anastasia Bizyaeva and Alessio Franci and based on the paper https://doi.org/10.1109/TAC.2022.3159527 with reference to other key papers with additional collaborators, including https://doi.org/10.1109/LCSYS.2022.3185981 and https://doi.org/10.1109/LCSYS.2021.3138725.
Posted August 8, 2022
Control and Optimization Seminar Questions or comments?
9:30 am - 10:20 am Zoom (Click “Questions or Comments?” to request a Zoom link)
Nader Motee, Lehigh University
AFOSR YIP and ONR YIP Awardee
Finite-Section Approximation of Carleman Linearization and Its Exponential Convergence
The Carleman linearization is one of the mainstream approaches to lift a finite-dimensional nonlinear dynamical system into an infinite-dimensional linear system with the promise of providing accurate finite-dimensional linear approximations of the original nonlinear system over larger regions around the equilibrium for longer time horizons with respect to the conventional first-order linearization approach. Finite-section approximations of the lifted system has been widely used to study dynamical and control properties of the original nonlinear system. In this context, some of the outstanding problems are to determine under what conditions, as the finite-section order (i.e., truncation length) increases, the trajectory of the resulting approximate linear system from the finite-section scheme converges to that of the original nonlinear system and whether the time interval over which the convergence happens can be quantified explicitly. In this talk, I will present explicit error bounds for the finite-section approximation and prove that the convergence is indeed exponential as a function of finite-section order. For a class of nonlinear systems, it is shown that one can achieve exponential convergence over the entire time horizon up to infinity. Our results are practically plausible, including approximating nonlinear systems for model predictive control and reachability analysis of nonlinear systems for verification, control, and planning purposes, as our proposed error bound estimates can be used to determine proper truncation lengths for a given sampling period.
Posted August 31, 2022
Last modified November 27, 2022
Control and Optimization Seminar Questions or comments?
9:30 am - 10:20 am Zoom (Click “Questions or Comments?” to request a Zoom link)
Wei Ren, University of California Riverside
IEEE Fellow
Distributed Average Tracking and Continuous-time Optimization in Multi-agent Networks
We introduce a distributed average tracking problem and present distributed discontinuous control algorithms to solve the problem. The idea of distributed average tracking is that multiple agents track the average of multiple time-varying reference signals in a distributed manner based only on local information and local communication with adjacent neighbors. We study cases where the time-varying reference signals have bounded derivatives and accelerations. We also use the distributed average tracking idea to solve a continuous-time distributed convex optimization problem. Tools from nonsmooth analysis are used to analyze the stability of the systems. Simulation and experimental results are presented to illustrate the theoretical results.
Posted September 14, 2022
Last modified September 27, 2022
Control and Optimization Seminar Questions or comments?
9:30 am - 10:20 am Zoom (Click “Questions or Comments?” to request a Zoom link)
Maryam Yashtini, Georgetown University
Counting Objects by Diffused Index: Geometry-Free and Training-Free Approach
Counting objects is a fundamental but challenging problem. In this talk, we propose diffusion-based, geometry-free, and learning-free methodologies to count the number of objects in images. The main idea is to represent each object by a unique index value regardless of its intensity or size, and to simply count the number of index values. First, we place different vectors, referred to as seed vectors, uniformly throughout the mask image. The mask image has boundary information of the objects to be counted. Secondly, the seeds are diffused using an edge-weighted harmonic variational optimization model within each object. We propose an efficient algorithm based on an operator splitting approach and alternating direction minimization method, and theoretical analysis of this algorithm is given. An optimal solution of the model is obtained when the distributed seeds are completely diffused such that there is a unique intensity within each object, which we refer to as an index. For computational efficiency, we stop the diffusion process before a full convergence, and propose to cluster these diffused index values. We refer to this approach as Counting Objects by Diffused Index (CODI). We explore scalar and multi-dimensional seed vectors. For scalar seeds, we use Gaussian fitting in a histogram to count, while for vector seeds, we exploit a high-dimensional clustering method for the final step of counting via clustering. The proposed method is flexible even if the boundary of the object is not clear nor fully enclosed. We present counting results in various applications such as biological cells, agriculture, concert crowds, and transportation. Some comparisons with existing methods are presented.
Posted December 12, 2022
Control and Optimization Seminar Questions or comments?
10:30 am - 11:20 am Zoom (Click “Questions or Comments?” to request a Zoom link)
Giulia Giordano, University of Trento, Italy
SIAG on Control and Systems Theory Prize Awardee
What We Can Learn from the System Structure in Biology and Epidemiology
Biological, ecological and epidemiological systems can be seen as dynamical networks, namely dynamical systems that are naturally endowed with an underlying network structure, because they are composed of subsystems that interact according to an interconnection. Despite their large scale and complexity, natural systems often exhibit extraordinary robustness that preserves fundamental properties and qualitative behaviors even in the presence of huge parameter variations and environmental fluctuations. First, we focus on biochemical reaction networks and look for the source of the amazing robustness that often characterizes them, by identifying properties and emerging behaviors that exclusively depend on the system structure (i.e., the graph structure along with qualitative information), regardless of parameter values. We introduce the BDC-decomposition to capture the system structure and enable the parameter-free assessment of important properties, including the stability of equilibria and the sign of steady-state input-output influences, thus allowing structural model falsification and structural comparison of alternative mechanisms proposed to explain the same phenomenon. Then, inspired by the COVID-19 pandemic and the observation that compartmental models for epidemics can be seen as a special class of chemical reaction networks, we consider epidemiological systems describing the spread of infectious diseases within a population, along with control approaches to curb the contagion. We illustrate strategies to cope with the deep uncertainty affecting parameter values and optimally control the epidemic.
Posted January 27, 2023
Last modified January 29, 2023
Control and Optimization Seminar Questions or comments?
10:30 am - 11:20 am Zoom (Click “Questions or Comments?” to request a Zoom link)
Raphael Jungers, Université Catholique de Louvain
Data-Driven Control of Hybrid Systems and Chance-Constrained Optimization
Control systems are increasingly complex, often to the point that obtaining a model for them is out of reach. In some situations, (parts of) the systems are proprietary, so that the very equations that rule their behavior cannot be known. On the other hand, the ever-growing progress in hardware technologies often enables one to retrieve massive data, e.g., from embedded sensors. Due to these evolutions, control theory can alternatively be viewed as a model-free and data-driven paradigm. For linear time-invariant systems, classical results from identification theory provide a rather straightforward approach. However, these approaches become least inefficient if one relaxes the assumptions they rely upon, e.g., linearity, Gaussian noise, etc. This is especially the case in safety-critical applications, where one needs guarantees on the performance of the obtained solution. Despite these difficulties, one may sometimes recover firm guarantees on the behavior of the system. This may require changing one's point of view on the nature of the guarantees we seek. I will provide examples of such results for different control tasks and different complex systems, and will raise the question of theoretical fundamental barriers for these problems.
Posted December 12, 2022
Last modified February 8, 2023
Control and Optimization Seminar Questions or comments?
10:30 am - 11:20 am Zoom (Click “Questions or Comments?” to request a Zoom link)
Patrick L. Combettes, North Carolina State University
IEEE Fellow
Perspective Functions
I will discuss mathematical and computational issues pertaining to perspective functions, a powerful concept that makes it possible to extend a convex function to a jointly convex one in terms of an additional scale variable. Recent results on perspective functions with nonlinear scales will also be discussed. Applications to inverse problems and statistics will also be presented.
Posted February 3, 2023
Last modified February 6, 2023
Control and Optimization Seminar Questions or comments?
10:30 am - 11:20 am Zoom (Click “Questions or Comments?” to request a Zoom link)
Enrique Zuazua, Friedrich-Alexander-Universität Erlangen-Nürnberg
2022 SIAM W.T. and Idalia Reid Prize Winner
Control and Machine Learning
In this lecture, we present some recent results on the interplay between control and machine learning, and more precisely, supervised learning and universal approximation. We adopt the perspective of the simultaneous or ensemble control of systems of residual neural networks (or ResNets). Roughly, each item to be classified corresponds to a different initial datum for the Cauchy problem of the ResNets, leading to an ensemble of solutions to be driven to the corresponding targets, associated to the labels, by means of the same control. We present a genuinely nonlinear and constructive method, allowing us to show that such an ambitious goal can be achieved, estimating the complexity of the control strategies. This property is rarely fulfilled by the classical dynamical systems in mechanics and the very nonlinear nature of the activation function governing the ResNet dynamics plays a determinant role. It allows deformation of half of the phase space while the other half remains invariant, a property that classical models in mechanics do not fulfill. The turnpike property is also analyzed in this context, showing that a suitable choice of the cost functional used to train the ResNet leads to more stable and robust dynamics. This lecture is inspired in joint work, among others, with Borjan Geshkovski (MIT), Carlos Esteve (Cambridge), Domènec Ruiz-Balet (IC, London) and Dario Pighin (Sherpa.ai).
Posted January 17, 2023
Last modified February 27, 2023
Control and Optimization Seminar Questions or comments?
10:30 am - 11:20 am Zoom (Click “Questions or Comments?” to request a Zoom link)
Spring Berman, Arizona State University
DARPA Young Faculty and ONR Young Investigator Awardee
Scalable Control of Robotic Swarms with Limited Information
Robotic swarms are currently being developed for many applications, including environmental sensing, exploration and mapping, infrastructure inspection, disaster response, agriculture, and logistics. However, significant technical challenges remain before they can be robustly deployed in uncertain, dynamic environments. We are addressing the problem of controlling swarms of robots that lack prior data about the environment and reliable inter-robot communication. As in biological swarms, the highly resource-constrained robots would be restricted to information obtained through local sensing and signaling. We are developing scalable control strategies that enable swarms to operate largely autonomously, with user input consisting only of high-level directives that map to a small set of robot parameters. In this talk, I describe control strategies that we have designed for collective tasks that include coverage, mapping, and cooperative manipulation. We develop and analyze models of the swarm at different levels of abstraction based on differential equations, Markov chains, and graphs, and we design robot controllers using feedback control theory and optimization techniques. We validate our control strategies in simulation and on experimental test beds with small mobile robots.
Posted November 30, 2022
Last modified February 28, 2023
Control and Optimization Seminar Questions or comments?
10:30 am - 11:20 am Zoom (Click “Questions or Comments?” to request a Zoom link)
Jacquelien Scherpen, University of Groningen
IEEE Fellow, Automatica Best Paper Prize Awardee
Model Reduction for Nonlinear Control Systems Based on Differential Balancing and Data
We present the standard balancing theory for nonlinear systems, which is based on an analysis around equilibrium points. Its extension to the contraction framework offers computational advantages, and is presented as well. We provide definitions for controllability and observability functions and their differential versions which can be used for simultaneous diagonalization procedures, providing a measure for importance of the states, as can be shown by the relation to the Hankel operator. In addition, we propose a data-based model reduction method based on differential balancing for nonlinear systems whose input vector fields are constants by utilizing its variational system. The difference between controllability and reachability for the variational system is exploited for computational reasons. For a fixed state trajectory, it is possible to compute the values of the differential Gramians by using impulse and initial state responses of the variational system. Therefore, differential balanced truncation is doable along state trajectories without solving nonlinear partial differential equations.
Posted February 14, 2023
Control and Optimization Seminar Questions or comments?
10:30 am - 11:20 am Zoom (Click “Questions or Comments?” to request a Zoom link)
Frank Allgower, University of Stuttgart
IFAC Fellow
Data-driven Model Predictive Control: Concepts, Algorithms and Properties
While recent years have shown rapid progress of learning-based and data-driven methods to effectively utilize data for control tasks, providing rigorous theoretical guarantees for such methods is challenging and an active field of research. This talk will be about a recently developed framework for model predictive control (MPC) of unknown systems based only on input-output data which admits exactly such guarantees. The proposed approach relies on the Fundamental Lemma of Willems et al. which parametrizes trajectories of unknown linear systems using data. First, we cover MPC schemes for linear systems with a focus on theoretical guarantees for the closed loop, which can be derived even if the data are noisy. Building on these results, we then move towards the general, nonlinear case. Specifically, we present a data-driven MPC approach which updates the data used for prediction online at every time step and, thereby, stabilizes unknown nonlinear systems using only input-output data. In addition to introducing the framework and the theoretical results, we also report on successful applications of the proposed framework in simulation and real-world experiments.
Posted February 13, 2023
Last modified March 7, 2023
Control and Optimization Seminar Questions or comments?
10:30 am - 11:20 am Zoom (Click “Questions or Comments?” to request a Zoom link)
Ningshi Yao, George Mason University
Resolving Contentions Through Real-Time Control and Scheduling for Cyber Physical Human Systems
Shared resources, such as cloud computing and communication networks, are widely used in large-scale real-time systems to increase modularity and flexibility. When multiple systems need to access a shared resource at the same time and the demands exceed the total supply, a contention occurs. A scheduling strategy is needed to determine which systems can access the resource first to resolve contentions. However, such a scheduling mechanism inevitably introduces time-varying delays and may degrade the system performance or even sabotage the stability of control systems. Considering the coupling between scheduling and control, this talk presents a novel sample-based method to co-design scheduling strategies and control laws for coupled control systems with shared resources, which aims to minimize the overall performance degradation caused by contentions. The co-design problem is formulated as a mixed integer optimization problem with a very large search space, rendering difficulty in computing the optimal solution. To solve this challenge, we describe a contention resolving model predictive control (CRMPC) method to dynamically design optimal scheduling and control in real-time. With fundamental assumptions in scheduling theory, the solution computed by CRMPC can be proved to be globally optimal. CRMPC is a theoretical framework that is general and can be applied to many applications in cyber-physical-human systems. The effectiveness of CRMPC has been verified in real-world applications, such as networked control systems, traffic intersection management systems, and human multi-robot collaboration systems. The performance of CRMPC was compared with well-known scheduling methods and demonstrated significant improvements.
Posted January 18, 2023
Last modified March 2, 2023
Control and Optimization Seminar Questions or comments?
10:30 am - 11:20 am Zoom (Click “Questions or Comments?” to request a Zoom link)
Maruthi Akella, University of Texas
Fellow of AIAA, IEEE, and AAS
Sub-Modularity Measures for Learning and Robust Perception in Aerospace Autonomy
Onboard learning and robust perception can be generally viewed to characterize autonomy as overarching system-level properties. The complex interplay between autonomy and onboard decision support systems introduces new vulnerabilities that are extremely hard to predict with most existing guidance and control tools. In this seminar, we review some recent advances in learning-oriented and information-aware path- planning, and sub-modularity metrics for non-myopic sensor scheduling for “plug-and- play” systems. The concept of “learning-oriented” path-planning is realized through certain new classes of exploration inducing distance metrics. These technical foundations will be highlighted through aerospace applications with active learning inside dynamic and uncertain environments.
Posted December 12, 2022
Last modified March 6, 2023
Control and Optimization Seminar Questions or comments?
10:30 am - 11:20 am Zoom (Click “Questions or Comments?” to request a Zoom link)
Maria Elena Valcher, University of Padova
Fellow of IEEE and of IFAC
TBA
Posted January 17, 2023
Control and Optimization Seminar Questions or comments?
10:30 am - 11:20 am Zoom (Click “Questions or Comments?” to request a Zoom link)
Weiwei Hu, University of Georgia
TBA
Posted January 26, 2023
Control and Optimization Seminar Questions or comments?
10:30 am - 11:20 am Zoom (Click “Questions or Comments?” to request a Zoom link)
Wim Michiels, KU Leuven
TBA
Posted February 13, 2023
Last modified February 14, 2023
Control and Optimization Seminar Questions or comments?
10:30 am - 11:20 am Zoom (Click “Questions or Comments?” to request a Zoom link)
Matthew Hale, University of Florida
AFOSR Young Investigator, ONR Young Investigator, and NSF CAREER Program Awardee
TBA