The linear quadratic regulator problem for a class of controlled systems modeled by singularly perturbed Ito differential equations

This paper discusses an infinite-horizon linear quadratic (LQ) optimal control problem involving state- and control-dependent noise in singularly perturbed stochastic systems. First, an asymptotic structure along with a stabilizing solution for the stochastic algebraic Riccati equation (ARE) are newly established. It is shown that the dominant part of this solution can be obtained by solving a parameter-independent system of coupled Riccati-type equations. Moreover, sufficient conditions for the existence of the stabilizing solution to the problem are given. A new sequential numerical algorithm for solving the reduced-order AREs is also described. Based on the asymptotic behavior of the ARE, a class of O(√ε) approximate controller that stabilizes the system is obtained. Unlike the existing results in singularly perturbed deterministic systems, it is noteworthy that the resulting controller achieves an O(ε) approximation to the optimal cost of the original LQ optimal control problem. As a result, the proposed control methodology can be applied to practical applications even if the value of the small parameter ε is not precisely known. © 2012 Society for Industrial and Applied Mathematics.Vasile Dragan, Hiroaki Mukaidani and Peng Sh

Improving the Asymmetric TSP by Considering Graph Structure

Recent works on cost based relaxations have improved Constraint Programming (CP) models for the Traveling Salesman Problem (TSP). We provide a short survey over solving asymmetric TSP with CP. Then, we suggest new implied propagators based on general graph properties. We experimentally show that such implied propagators bring robustness to pathological instances and highlight the fact that graph structure can significantly improve search heuristics behavior. Finally, we show that our approach outperforms current state of the art results.Comment: Technical repor

Functional reasoning in diagnostic problem solving

This work is one facet of an integrated approach to diagnostic problem solving for aircraft and space systems currently under development. The authors are applying a method of modeling and reasoning about deep knowledge based on a functional viewpoint. The approach recognizes a level of device understanding which is intermediate between a compiled level of typical Expert Systems, and a deep level at which large-scale device behavior is derived from known properties of device structure and component behavior. At this intermediate functional level, a device is modeled in three steps. First, a component decomposition of the device is defined. Second, the functionality of each device/subdevice is abstractly identified. Third, the state sequences which implement each function are specified. Given a functional representation and a set of initial conditions, the functional reasoner acts as a consequence finder. The output of the consequence finder can be utilized in diagnostic problem solving. The paper also discussed ways in which this functional approach may find application in the aerospace field

Naive Problem Solving and Naive Mathematics

AI problem solvers have almost always been given a complete and correct axiomatization of their problem domain and of the operators available to change it. Here I discuss a paradigm for problem solving in which the problem solver initially is given only a list of available operators, with no indication as to the structure of the world or the behavior of the operators. Thus, to begin it is "blind" and can only stagger about in the world tripping over things until it begins to understand what is going on. Eventually it will learn enough to solve problems in the world as well as if it the world had been explained to it initially. I call this paradigm naive problem solving. The difficulty of adequately formalizing all but the most constrained domains makes naive problem solving desirable. I have implemented a naive problem solver that learns to stack blocks and to use an elevator. It learns by finding instances of "naive mathematical cliches" which are common mental models that are likely to be useful in any domain.MIT Artificial Intelligence Laborator

Consider Collateral Consequences: The Inherent Hypocrisy of Veterans Treatment Courts’ Failure to Dismiss Criminal Charges

American veterans are often plagued by psychological and physical injuries, among other hardships, which, when unaddressed, can lead to substance abuse, criminal behavior, and suicide. As public awareness of the difficulties that American veterans face was growing, the problem-solving court movement was also gaining momentum. Largely inspired by therapeutic jurisprudence, an interdisciplinary framework that sees the law as a way to reach therapeutic outcomes, problem-solving courts seek to identify the root causes of criminal behavior and address those causes in ways that promote rehabilitation and reduce recidivism. Veterans Treatment Courts (“VTCs”) emerged when veterans advocacy intersected with the problem-solving court movement. This Note explores the origins, growth, and general structure of VTCs. Focusing on the legal implications for veterans who graduate from VTCs, this Note argues that leaving veterans with a criminal conviction directly contradicts the reasons the programs were created and exposes veterans to collateral consequences, only adding additional barriers to reintegration into American civil society

On the accuracy of solving confluent Prony systems

In this paper we consider several nonlinear systems of algebraic equations which can be called "Prony-type". These systems arise in various reconstruction problems in several branches of theoretical and applied mathematics, such as frequency estimation and nonlinear Fourier inversion. Consequently, the question of stability of solution with respect to errors in the right-hand side becomes critical for the success of any particular application. We investigate the question of "maximal possible accuracy" of solving Prony-type systems, putting stress on the "local" behavior which approximates situations with low absolute measurement error. The accuracy estimates are formulated in very simple geometric terms, shedding some light on the structure of the problem. Numerical tests suggest that "global" solution techniques such as Prony's algorithm and ESPRIT method are suboptimal when compared to this theoretical "best local" behavior