There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

Planning algorithms are impacting technical disciplines and industries around the world, including robotics, computer-aided design, manufacturing, computer graphics, aerospace applications, drug design, and protein folding. This coherent and comprehensive book unifies material from several sources, including robotics, control theory, artificial intelligence, and algorithms. The treatment is centered on robot motion planning but integrates material on planning in discrete spaces. A major part of the book is devoted to planning under uncertainty, including decision theory, Markov decision processes, and information spaces, which are the “configuration spaces” of all sensor-based planning problems. The last part of the book delves into planning under differential constraints that arise when automating the motions of virtually any mechanical system. Developed from courses taught by the author, the book is intended for students, engineers, and researchers in robotics, artificial intelligence, and control theory as well as computer graphics, algorithms, and computational biology.

Planning Algorithms: Introductory Material

关于Semigroups of Linear Operators and Applications to Partial Differential Equations的两个注解

We explore in this chapter questions of existence and uniqueness for solutions to stochastic differential equations and offer a study of their properties. This endeavor is really a study of diffusion processes. Loosely speaking, the term diffusion is attributed to a Markov process which has continuous sample paths and can be characterized in terms of its infinitesimal generator.

Stochastic Differential Equations

Series Preface * Preface to the Third Edition * 1 Linear Systems * 2 Nonlinear Systems: Local Theory * 3 Nonlinear Systems: Global Theory * 4 Nonlinear Systems: Bifurcation Theory * References * Index

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Differential Equations and Dynamical Systems

https://hal.inria.fr/inria-00636102/document

Economic receding horizon control without terminal constraints

Receding horizon control is a well established approach for control of systems with constraints and nonlinearities. Optimization over an infinite time-horizon, which is often computationally intractable, is therein replaced by a sequence of finite horizon problems. This paper provides a method to quantify the performance degradation that comes with this approximation. Results are provided for problems both with and without terminal costs and constraints and for both exactly and practically asymptotically stabilizable systems.

/pdf/on-the-infinite-horizon-performance-of-receding-horizon-2yk0ra8cz3.pdf

On the Infinite Horizon Performance of Receding Horizon Controllers

The recent rapid uptake of residential solar photovoltaic installations provides many challenges for electricity distribution networks designed for one-way power flow from the generator to residential customers via transmission and distribution networks. For grid-connected installations, large amounts of generation during low load periods or intermittent generation can lead to a difficulty in balancing supply and demand, maintaining voltage and frequency stability, and may even result in outages due to overvoltage conditions tripping protection circuits. In this paper, we present four control methodologies to mitigate these difficulties using small-scale distributed battery storage. These four approaches represent three different control architectures: 1) centralized; 2) decentralized; and 3) distributed control. These approaches are validated and compared using data on load and generation profiles from customers in an Australian electricity distribution network.

/pdf/distributed-and-decentralized-control-of-residential-energy-q87l3z5qu0.pdf

Distributed and Decentralized Control of Residential Energy Systems Incorporating Battery Storage

We present a technique for computing stability and performance bounds for unconstrained nonlinear model predictive control (MPC) schemes. The technique relies on controllability properties of the system under consideration, and the computation can be formulated as an optimization problem whose complexity is independent of the state space dimension. Based on the insight obtained from the numerical solution of this problem, we derive design guidelines for nonlinear MPC schemes which guarantee stability of the closed loop for small optimization horizons. These guidelines are illustrated by a finite and an infinite dimensional example.

/pdf/analysis-and-design-of-unconstrained-nonlinear-mpc-schemes-178ta3y414.pdf

Lars Grüne

Papers

Economic receding horizon control without terminal constraints

On the Infinite Horizon Performance of Receding Horizon Controllers

Distributed and Decentralized Control of Residential Energy Systems Incorporating Battery Storage

Analysis and Design of Unconstrained Nonlinear MPC Schemes for Finite and Infinite Dimensional Systems

Lyapunov-based continuous-time nonlinear controller redesign for sampled-data implementation