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

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Convex Analysisの二,三の進展について

This paper presents control and coordination algorithms for groups of vehicles. The focus is on autonomous vehicle networks performing distributed sensing tasks where each vehicle plays the role of a mobile tunable sensor. The paper proposes gradient descent algorithms for a class of utility functions which encode optimal coverage and sensing policies. The resulting closed-loop behavior is adaptive, distributed, asynchronous, and verifiably correct.

Coverage control for mobile sensing networks

In this chapter, you will see how the simplex method simplifies when it is applied to a class of optimization problems that are known as “network flow models.” You will also see that if a network flow model has “integer-valued data,” the simplex method finds an optimal solution that is integer-valued.

Flows in Networks

The Theory of Incentives I: The Principal-Agent Model

The Fourth Industrial Revolution incorporates the digital revolution into the physical world, creating a new direction in a number of fields, including artificial intelligence, quantum computing, nanotechnology, biotechnology, robotics, 3D printing, autonomous vehicles, and the Internet of Things. The artificial intelligence field has encountered a turning point mainly due to advancements in machine learning, which allows machines to learn, improve, and perform a specific task through data without being explicitly programmed. Machine learning can be utilized with machining processes to improve product quality levels and productivity rates, to monitor the health of systems, and to optimize design and process parameters. This is known as smart machining, referring to a new machining paradigm in which machine tools are fully connected through a cyber-physical system. This paper reviews and summarizes machining processes using machine learning algorithms and suggests a perspective on the machining industry.

Smart Machining Process Using Machine Learning: A Review and Perspective on Machining Industry

We consider the problem of constructing control policies that are robust against distribution errors in the model parameters of Markov decision processes. The Wasserstein metric is used to model the ambiguity set of admissible distributions. We prove the existence and optimality of Markov policies and develop convex optimization-based tools to compute and analyze the policies. Our methods, which are based on the Kantorovich convex relaxation and duality principle, have the following advantages. First, the proposed dual formulation of an associated Bellman equation resolves the infinite dimensionality issue that is inherent in its original formulation when the nominal distribution has a finite support. Second, our duality analysis identifies the structure of a worst-case distribution and provides a simple decentralized method for its construction. Third, a sensitivity analysis tool is developed to quantify the effect of ambiguity set parameters on the performance of distributionally robust policies. The effectiveness of our proposed tools is demonstrated through a human-centered air conditioning problem.

A Convex Optimization Approach to Distributionally Robust Markov Decision Processes With Wasserstein Distance

We propose a risk-aware motion planning and decision-making method that systematically adjusts the safety and conservativeness in an environment with randomly moving obstacles. The key component of this method is the conditional value-at-risk (CVaR) used to measure the safety risk that a robot faces. Unlike chance constraints, CVaR constraints are coherent, convex, and distinguish between tail events. We propose a two-stage method for safe motion planning and control: A reference trajectory is generated by using RRT* in the first stage, and then a receding horizon controller is employed to limit the safety risk by using CVaR constraints in the second stage. However, the second stage problem is nontrivial to solve, as it is a triple-level stochastic program. We develop a computationally tractable approach through 1) a reformulation of the CVaR constraints; 2) a sample average approximation; and 3) a linearly constrained mixed integer convex program formulation. The performance and utility of this risk-aware method are demonstrated via simulation using a 12-dimensional model of quadrotors.

Risk-Aware Motion Planning and Control Using CVaR-Constrained Optimization

In recent years, there has been a growing demand for micro holes. However, electrochemical machining has rarely been employed in drilling these holes because of problems with electrolyte diffusion. In this research, a semi-cylindrical tool was used as a tool electrode to increase the flow space of the electrolyte, and electrolyte diffusion was improved via the application of ultrasonic vibrations. Micro holes with a specified diameter of 76 μm were drilled on a 304 stainless steel plate of 300μm thickness. The proposed technique reduced both the machining time and the machining gap.

Insoon Yang

Papers

Smart Machining Process Using Machine Learning: A Review and Perspective on Machining Industry

A Convex Optimization Approach to Distributionally Robust Markov Decision Processes With Wasserstein Distance

Risk-Aware Motion Planning and Control Using CVaR-Constrained Optimization

Micro ECM with Ultrasonic Vibrations Using a Semi-cylindrical Tool

A dynamic game approach to distributionally robust safety specifications for stochastic systems