Data-driven Inverse Optimization with Imperfect Information

In data-driven inverse optimization an observer aims to learn the preferences of an agent who solves a parametric optimization problem depending on an exogenous signal. Thus, the observer seeks the agent's objective function that best explains a historical sequence of signals and corresponding optimal actions. We focus here on situations where the observer has imperfect information, that is, where the agent's true objective function is not contained in the search space of candidate objectives, where the agent suffers from bounded rationality or implementation errors, or where the observed signal-response pairs are corrupted by measurement noise. We formalize this inverse optimization problem as a distributionally robust program minimizing the worst-case risk that the {\em predicted} decision ({\em i.e.}, the decision implied by a particular candidate objective) differs from the agent's {\em actual} response to a random signal. We show that our framework offers rigorous out-of-sample guarantees for different loss functions used to measure prediction errors and that the emerging inverse optimization problems can be exactly reformulated as (or safely approximated by) tractable convex programs when a new suboptimality loss function is used. We show through extensive numerical tests that the proposed distributionally robust approach to inverse optimization attains often better out-of-sample performance than the state-of-the-art approaches

Directly Coupled Observers for Quantum Harmonic Oscillators with Discounted Mean Square Cost Functionals and Penalized Back-action

This paper is concerned with quantum harmonic oscillators consisting of a quantum plant and a directly coupled coherent quantum observer. We employ discounted quadratic performance criteria in the form of exponentially weighted time averages of second-order moments of the system variables. A coherent quantum filtering (CQF) problem is formulated as the minimization of the discounted mean square of an estimation error, with which the dynamic variables of the observer approximate those of the plant. The cost functional also involves a quadratic penalty on the plant-observer coupling matrix in order to mitigate the back-action of the observer on the covariance dynamics of the plant. For the discounted mean square optimal CQF problem with penalized back-action, we establish first-order necessary conditions of optimality in the form of algebraic matrix equations. By using the Hamiltonian structure of the Heisenberg dynamics and related Lie-algebraic techniques, we represent this set of equations in a more explicit form in the case of equally dimensioned plant and observer.Comment: 11 pages, a brief version to be submitted to the IEEE 2016 Conference on Norbert Wiener in the 21st Century, 13-15 July, Melbourne, Australi

Motion Planning for Optimal Information Gathering in Opportunistic Navigation Systems

Motion planning for optimal information gathering in an opportunistic navigation (OpNav) environment is considered. An OpNav environment can be thought of as a radio frequency signal landscape within which a receiver locates itself in space and time by extracting information from ambient signals of opportunity (SOPs). The receiver is assumed to draw only pseudorange-type observations from the SOPs, and such observations are fused through an estimator to produce an estimate of the receiver’s own states. Since not all SOP states in the OpNav environment may be known a priori, the receiver must estimate the unknown SOP states of interest simultaneously with its own states. In this work, the following problem is studied. A receiver with no a priori knowledge about its own states is dropped in an unknown, yet observable, OpNav environment. Assuming that the receiver can prescribe its own trajectory, what motion planning strategy should the receiver adopt in order to build a high-fidelity map of the OpNav signal landscape, while simultaneously localizing itself within this map in space and time? To answer this question, first, the minimum conditions under which the OpNav environment is fully observable are established, and the need for receiver maneuvering to achieve full observability is highlighted. Then, motivated by the fact that not all trajectories a receiver may take in the environment are equally beneficial from an information gathering point of view, a strategy for planning the motion of the receiver is proposed. The strategy is formulated in a coupled estimation and optimal control framework of a gradually identified system, where optimality is defined through various information-theoretic measures. Simulation results are presented to illustrate the improvements gained from adopting the proposed strategy over random and pre-defined receiver trajectories.Aerospace Engineering and Engineering Mechanic

Research on output feedback control

A summary is presented of the main results obtained during the course of research on output feedback control. The term output feedback is used to denote a controller design approach which does not rely on an observer to estimate the states of the system. Thus, the order of the controller is fixed, and can even be zero order, which amounts to constant gain ouput feedback. The emphasis has been on optimal output feedback. That is, a fixed order controller is designed based on minimizing a suitably chosen quadratic performance index. A number of problem areas that arise in this context have been addressed. These include developing suitable methods for selecting an index of performance, both time domain and frequency domain methods for achieving robustness of the closed loop system, developing canonical forms to achieve a minimal parameterization for the controller, two time scale design formulations for ill-conditioned systems, and the development of convergent numerical algorithms for solving the output feedback problem