The workshop will provide a comprehensive view of the subject of nonlinear control of physical systems. As geometry and calculus of variations are of fundamental importance for physics and nonlinear control, the workshop will promote the use of these techniques in both theoretical engineering and applications. It will focus on the structure of configuration/state spaces, symmetry and reduction in dynamics and control, exactly-solvable nonlinear control problems, control and stabilization of underactuated systems with constraints, and numerical techniques for nonlinear control, including structure-preserving geometric integrators. Examples will be drawn from recent work, chosen to illustrate the broad range of applicability these methods have in engineering. Professor Anthony M. Bloch is a leading researcher and widely recognized contributor to the field of nonlinear dynamics and control. His 60th birthday is celebrated with this workshop devoted to the exploration of nonlinear control methods as applied to physical systems, both classical and quantum, the areas in which Professor Bloch made fundamental contributions. He is a fellow of the IEEE, AMS, and SIAM, Editor in Chief of SIAM Journal on Control and Optimization, and current or former member of editorial boards of many excellent journals.
The intended audience would include graduate students and post-doctoral researchers, and industry participants with a focus on analysis and design of nonlinear control systems in a wide variety of physical settings. Only pre-requisites assumed would be knowledge of differential equations, matrix algebra, basic mechanics, and interest in the interplay of physics and control. Senior researchers and designers of numerical software for modeling and control may also find this workshop useful.
Welcome and Opening Remarks
Topological Aspects of Optimal Fusion of Multispectral Sensor Data
John Baillieul keynote pdf powerpoint
The talk will describe techniques for simultaneously exploring image segments concentrated in different parts of the optical spectrum (IR, visible spectrum, UV, etc.). The problem to be addressed is that of representing multispectral sensory information in a way is optimally aligned with human perceptual abilities.
Control of Quantum Systems
Roger Brockett powerpoint
Spin systems, and their optimization through effective design of interrogatory RF pulses play a significant role in modern studies of quantum systems. The geometry and optimal control of nonholonomic systems provide essential foundations in this area.
Bipedal Locomotion on Small Feet
Jessy Grizzle pdf
Differential geometry in combination with numerical optimization is proving to be a powerful tool for designing gaits for bipedal robots that do not rely on flat-footed walking. We discuss recent progress with our bipedal robot MARLO.
Global Nonlinear Control for Multi-Body Dynamics
Harris McClamroch pdf
The talk will address the key role of geometry in global models, both analytical and numerical, of control of multi-body systems. The results will be illustrated with examples of nonlinear control problems that arise in robotics and spacecraft control.
Hamiltonian Structures and Variational Principles
Tudor Ratiu pdf
Recent work on higher order variational principles has proved to be useful in application areas such as image processing, and in understanding the physics of materials (fluids, liquid crystals, ferromagnets etc.) with internal degrees of freedom. This talk will discuss the underlying mathematical principles and connections to control theory.
Parallelometers: Mechanical Devices that Measure Curvature
Alberto Rojo powerpoint
I will discuss mechanical devices that measure parallel transport and curvatures, in particular, the “parallelometer” and the “torsiometer”, different from devices previously presented in the literature. The torsiometer measures the torsion of a curve, in the same way as does the rotation of the polarization axis for light traveling on a coiled optical fiber. The parellelometer provides an analogy to the gravity probe B measurement. Finally I will discuss the non-holonomy of a rolling sphere and its connection to spin ½ and the Landau–Zener formula.
Topologically Protected Edge States in Continuous Honeycomb Structures
Edge states are a type of energy-localization along a line-defect, the interface between different media. Topologically protected edge states are a class of edge states which are stable to strong local distortions of the edge. They are therefore potential vehicles for robust energy-transfer in the presence of imperfections. In this talk I will explain their occurrence in two-dimensional honeycomb structures, such as graphene.
Energy Shaping and Variational Integrators
Dmitry Zenkov pdf
Long-term simulation algorithms and computation with physical models should preserve essential structures in the models, such as conservation laws, dissipation inequalities, etc. Feedback control laws, and in particular, digital feedback stabilizers, that are compatible with underlying Lagrangian and Hamiltonian structures, will be considered.
Dynamics of Collective Decision Making
Naomi Leonard pdf
I will discuss a realization theory for bio-inspired collective decision-making using the singularity theory approach to bifurcations. The theory is used to study mechanisms that explain the remarkable decision-making of animal groups and to leverage these mechanisms in distributed feedback control design for autonomous decision-making networks.
Discussions and Felicitations
The 2015 American Control Conference Homepage
Workshop Registration Fee: $225 (Regular, before April 15), $275 (Regular, after April 15), $115 (Student, before April 15), $140 (Student, after April 15)