Talks

Speaker: Ravi Banavar (Systems and Control Engineering, IIT Bombay)

Title: Consensus and Synchronization on Lie Groups 

Part A: The Machinery of Lie Groups: This will follow up on the basic concepts of manifolds and groups introduced earlier, and present specific machinery of Lie groups. In particular the talk will focus on group actions, the adjoint map, the Lie algebra, the infinitesimal generator, the adjoint and co-adjoint maps, left and right-invariant vector fields. This will set the backdrop for the subsequent talk.

Part B: For a finite number of agents evolving on a Euclidean space and linked to each other by a connected graph, the Laplacian flow that is based on the inter-agent errors, ensures consensus or synchronization for both first and second-order dynamics. When such agents evolve on a circle (the Kuramoto oscillator), the flow that depends on the sinusoid of the inter-agent error angles generalizes the same. In this work, it is shown that the Laplacian flow and the Kuramoto oscillator are special cases of a more general theory of consensus on Lie groups that admit bi-invariant metrics. Such a theory not only enables generalization of these consensus and synchronization algorithms to Lie groups but also provide insight on to the abstract group theoretic and differential geometric properties that ensures convergence in Euclidean space and the circle. 

Speaker: Mayank Baranwal (TCS Research, India)

Title: A Dynamical View on Optimization Algorithms

Abstract: Optimization algorithms are the driving force behind many machine-learning formulations, and the recent progress in this field has been greatly aided by a better understanding of these algorithms and their implementation for specific machine-learning problems. The study of gradient flow and its connection to dynamical systems has a long history in mathematics, and this talk aims to further explore this relationship from a continuous-time, variational perspective. We hope to show the relevance of a large class of gradient, projected-gradient and proximal algorithms for optimization problems that not only converge, but do so quickly. In particular, we introduce a generalized framework for designing accelerated optimization algorithms based on the recent advances in fixed-time stability theory of continuous-time dynamical systems. This framework allows for the strongest possible convergence guarantees, and easily extends to a subclass of non-convex functions. This talk is part of a larger effort to connect the fields of dynamical systems and optimization, and to advance our understanding of the underlying mathematical principles. 

Speaker: Shubhendu Bhasin (Electrical Engineering, IIT Delhi)

Title: Assistive Control Strategies for Soft Wearable Robots 

Abstract: Soft exosuits/wearable robots, made of clothing/fabric-like material, wrap around a person’s limbs to provide actuation in parallel with the human muscles, thus providing assistance by augmenting human strength or in rehabilitation. The main control challenge is estimating human intention and allocating control between the human and the robot, resulting in a reduced "metabolic" cost and effective assistance. The control system design is further complicated by various sources of uncertainty in the human-robot system, e.g., unknown payload, uncertain system parameters, friction, etc. This talk will focus on challenges in modeling, control design, and simulation for a cable-driven soft wearable robot/exosuit. 

Online Talk

Speaker: Sanjay Bhat (TCS Research, India)

Title: A Gentle Introduction to Nonlinear Controllability

Abstract: This talk will provide a gentle, graded introduction to the concepts and results from the theory of controllability of nonlinear input-affine systems. In particular, we will see concepts such as controllability, accessibility, and involutivity, constructs such as reachable sets, integral manifolds and Lie algebras of vector fields, and results such as Chow's theorem. We will use simple examples to motivate why these concepts, constructs and results are the way they are. 

Speaker: Debasish Chatterjee (Systems and Control Engineering, IIT Bombay)

Title: A Novel Approach to Convex Semi-Infinite Programs

Abstract: Robust optimization problems arise naturally in a vast plethora of applications in machine learning, signal processing, control, robotics, and several other disciplines, wherein uncertainty in the underlying model of the optimization problem is unavoidable and robust solutions are essential. Convex semi-infinite programs (SIPs) constitute one of the most important subclasses of robust optimization problems, and they arise naturally in robust linear, quadratic, semidefinite, and discrete optimization, mathematical programs with probabilistic constraints (chance and integrated chance constraints, CVaR constraints, etc.), and a host of other contexts. Despite their central importance in optimization and having been subjected to scrutiny for decades, convex SIPs have largely remained numerically intractable, due primarily to the infinitely many constraints involved in the optimization problem. New results have recently been obtained that offer a fresh perspective on solving convex SIPs. This talk will expose a new algorithm to solve convex SIPs near-optimally by means of targeted sampling of the constraints. An illustrative application of this algorithm to the construction of Lyapunov functions will also be discussed.

Online Talk

Speaker: François Gay-Balmaz (Laboratoire de Météorologie Dynamique, Ecole Normale Supérieure)

Title: Variational Thermodynamics and Applications 

Abstract:  I will present a variational formulation for non-equilibrium thermodynamics which extends the critical action principle of mechanics by including irreversible processes such as friction, heat and matter exchange, and chemical reactions. The nature of this variational formulation is reminiscent from the Lagrange-d’Alembert principle for nonholonomic mechanical systems and electric circuits and gives rise to a formulation in terms of Dirac structures which recovers the symplectic formulation of mechanics in absence of irreversible processes. Applications to interconnection, thermodynamically consistent modelling, and structure preserving discretization will be given for finite and infinite-dimensional systems, such as heat conducting viscous fluids and porous media. 

Speaker: Rohit Gupta (Aerospace Engineering, IIT Bombay)

Title: Constrained Spacecraft Attitude Control on SO(3) Using Fast Nonlinear Model Predictive Control

Abstract: A fast solver for solving the optimization problem arising in the nonlinear model predictive control of spacecraft attitude and the simulation results of its application to constrained spacecraft attitude control, will be presented. The solver exploits the numerical solution of the necessary conditions for optimality in a discrete-time optimal control problem defined over a prediction horizon, where the discrete-time dynamics are based on the Lie group variational integrator model. The inequality constraints (thrust constraint, inclusion/exclusion zone constraints, etc.) are handled using a penalty function approach. 

Speaker: Mandar Inamdar (Civil Engineering, IIT Bombay)

Title: Mechanics and Thermodynamics of Epithelial Tissues 

Abstract: I will discuss mechanics and thermodynamics of epithelial tissues that form a mechanical monolayer of connected polygonal cells. Specifically, I will discuss how cell growth, active forcing, cellular deformations and topological transitions, and topological defects govern deformation kinematics and stress in epithelial monolayers that lead to tissue sculpting and patterning during morphogenesis.  

Speaker: Navin Khaneja (Systems and Control Engineering, IIT Bombay)

Title: Control of Quantum Systems

Abstract: Quantum control is the use of electric and magnetic fields to control  electrons, atoms,  molecules,  spins, etc.  These problems are characteristically different from classical control problems.  In this talk we will highlight the characteristic features of these problems. 

Online Talk

Speaker: D. H. S. Maithripala (Mechanical Engineering, University of Peradeniya)

Title: Simple Mechanical Systems are Literally Simple

Abstract: Be it an unmanned vehicle, a satellite or a linkage mechanism, the equations that model the motion are as simple as it gets provided that you take the underlying geometric machinery into consideration. In this talk we will try to demonstrate why this is so and show some examples on how useful such an approach can be. The talk will be based on the interactive notes that you can find here. 

Online Talk

Speaker: Richard Montgomery (Mathematics, UC Santa Cruz)

Title: Falling Cats, Robots and sub-Riemannian Geometry 

Abstract: My talk will sketch the arc of my work from the falling cat problem to sub-Riemannian geometry and how that  work has interacted with control theory arising in  robotics,  NMR and quantum control.  

Online Talk

Speaker: Michael Muehlebach (Learning and Dynamical Systems, Max Planck Institute for Intelligent Systems)

Title: Optimization with Momentum: A Perspective from Smooth and Non-Smooth Dynamical Systems 

Abstract: My talk will highlight connections between dynamical systems and optimization and will be divided into two parts: The first part presents an analysis of accelerated first-order optimization algorithms, where the continuous dependence of iterates with respect to their initial conditions will be exploited for characterizing the convergence rate. The result establishes criteria for accelerated convergence of a large class of momentum-based optimization algorithms. The criteria, which are easily verifiable, are necessary and sufficient and therefore precisely characterize optimization algorithms that are accelerated. The analysis applies to non-convex functions, unifies discrete-time and continuous-time models, and rigorously explains why structure-preserving (symplectic) discretization schemes are important in optimization. The second part introduces a class of first-order methods for constrained optimization that are based on an analogy to non-smooth dynamical systems. The key underlying idea is to express constraints in terms of velocities instead of positions, which has the algorithmic consequence that optimizations over feasible sets at each iteration are replaced with optimizations over local, sparse convex approximations. The result is a simplified suite of algorithms and an expanded range of possible applications in machine learning. 

Online Talk

Speaker: Juan-Pablo Ortega (School of Physical and Mathematical Sciences, Nanyang Technological University)

Title: Generalized Synchronizations with Reservoir Systems

Abstract: In this talk, we show that that the celebrated Embedding Theorem of Takens is a particular case of a much more general statement according to which, randomly generated linear state-space representations of generic observations of an invertible dynamical system carry in their wake an embedding of the phase space dynamics into the chosen Euclidean state space. This embedding coincides with a natural generalized synchronization that arises in this setup and that yields a topological conjugacy between the state-space dynamics driven by the generic observations of the dynamical system and the dynamical system itself. This result provides additional tools for the representation, learning, and analysis of chaotic attractors and sheds additional light on the reservoir computing phenomenon that appears in the context of recurrent neural networks. This work is a collaboration with Lyudmila Grigoryeva (St. Gallen) and Allen Hart (Bath).

Speaker: Ramkrishna Pasumarthy (Electrical Engineering, IIT Madras)

Title: Topology and Input Design for Network Controllability

Abstract: Controllability of complex networks poses challenges when we apply tools from classical control theory due to the large size of networks. These challenges manifest themselves in form insufficient knowledge of edge weights and impracticable energy requirements for control purposes. In this talk we present algorithms to solve the problem of optimal topology design to maximize the average controllability and optimal input design for structural controllability of temporal networks. 

Speaker: Abhilash Patel (Electrical Engineering, IIT Kanpur)

Title: Dynamics and Control in Biology: Robustness and Constraint

Abstract: Biological system employs key control design principles to achieve dynamical behaviour such as bistability, oscillations, and adaptation. In this talk, we will discuss some feedback designs used by natural biological systems and the challenges that arise in implementing such feedback in synthetic biological systems. We will specifically discuss two design aspects, robustness and resource constraint, and the role of control engineering to address these.

Speaker: Amuthan Ramabathiran (Aerospace Engineering, IIT Bombay)

Title: A First Look at Manifolds, Vector Fields and Flows

Abstract: This introductory talk is meant to provide a gentle introduction to the modern mathematical theory of manifolds. The need for an intrinsic geometric description of a class of subsets of Euclidean spaces--parametrized curves and surfaces, level sets of functions, and implicitly defined surfaces--will be used to motivate the definition of a differentiable manifold. The foundational idea of locally mapping a manifold to an open subset of a Euclidean space, and the systematic outsourcing of all computations thereof will be emphasized. The notion of tangents to parametrized curves will then be introduced using two distinct approaches: as equivalence class of curves, and as an algebraic derivation. This will then be used to introduce the notions of tangent and cotangent spaces, and the corresponding global notions of tangent and cotangent bundles. Special conditions under which tangent and cotangent spaces may be identified, namely in the presence of additional structures like a metric or a symplectic form, will be briefly touched upon. Vector fields will subsequently be introduced as sections of the tangent bundle. The talk will conclude with a discussion of the flow associated with vector fields, and an introduction to the Lie derivative. The talk will feature a variety of examples and highlight various connections to appropriate notions in classical mechanics.

Speaker: Shaunak Sen (Electrical Engineering, IIT Delhi)

Title: Robustness to Temperature in Biomolecular Circuits 

Abstract: Temperature is a key perturbation to biomolecular circuits due to its effect on underlying system parameters. The standard mechanism to design robustness is to have parameter matching, but the role of other mechanisms is generally unclear. We have provided initial evidence for the temperature robustness effect due to parameter regimes such as strong negative feedback. Ongoing work is towards strengthening this evidence using computational models and experimental measurements as well as through a theoretical investigation. These results should help in the design of synthetic biomolecular circuits for potential applications in agriculture and medicine.