This paper introduces a novel time-freezing reformulation and numerical methods for optimal control of complementarity Lagrangian systems (CLS) with state jumps. We cover the difficult case when the system evolves on the boundary of the dynamic’s feasible set after the state jump. In nonsmooth mechanics, this corresponds to inelastic impacts. The m...
We study the bit complexity of two related fundamental computational problems in linear algebra and control theory. Our results are: (1) An Õ(n^{ω+3}a+n⁴a²+n^ωlog(1/ε)) time algorithm for finding an ε-approximation to the Jordan Normal form of an integer matrix with a-bit entries, where ω is the exponent of matrix multiplication. (2) An Õ(n⁶d⁶a+n...
status: published
Published in Journal of Synchrotron Radiation
FOCUS ( Fast Monte CarlO approach to Coherence of Undulator Sources ) is a new GPU-based simulation code to compute the transverse coherence of undulator radiation from ultra-relativistic electrons. The core structure of the code, which is written in the language C++ accelerated with CUDA, combines an analytical description of the emitted electric ...
Peak Estimation aims to find the maximum value of a state function achieved by a dynamical system. This problem is non-convex when considering standard Barrier and Density methods for invariant sets, and has been treated heuristically by using auxiliary functions. A convex formulation based on occupation measures is proposed in this paper to solve ...
This paper presents a method for calculating Region of Attraction of a target set (not necessarilyan equilibrium) for controlled polynomial dynamical systems, using a hierarchy of semidefinite pro-gramming problems (SDPs). Our approach builds on previous work and addresses its main issue, thefast-growing memory demands for solving large-scale SDPs....
This paper introduces a novel reformulation and numerical methods for optimal control of complementarity Lagrangian systems with state jumps. The solutions of the reformulated system have jump discontinuities in the first time derivative instead of the trajectory itself, which is easier to handle theoretically and numerically. We cover not only the...
This thesis studies the interaction between quantitative homogenization theory and two stochastic models: the supercritical percolation model and interacting particle systems. Stochastic homogenization focuses on large-scale properties in the random environment, and these two models represent generalization in the degenerate random environment and ...
Eigenproblems and their nonlinear generalizations appear as important problems in a wide variety of fields, ranging from quantum chemistry and vibration analysis to macroeconomics and data science. Hence, the development and analysis of numerical algorithms to solve such problems has a broad multiplicative effect on our ability to answer several cr...
This thesis considers the analysis and design of algorithms for the management and control of uncertain intelligent systems which are observable through (limited) online-accessible data. Examples include online equity trading systems under extreme price fluctuations, robotic systems moving in unknown environments, and transportation systems subject...
