Adaptive sampling for linear state estimation

When a sensor has continuous measurements but sends occasional messages over a data network to a supervisor which estimates the state, the available packet rate fixes the achievable quality of state estimation. When such rate limits turn stringent, the sensor’s messaging policy should be designed anew. What are the good causal messaging policies ? What should message packets contain ? What is the lowest possible distortion in a causal estimate at the supervisor ? Is Delta sampling better than periodic sampling ? We answer these questions for a Markov state process under an idealized model of the network and the assumption of perfect state measurements at the sensor. If the state is a scalar, or a vector of low dimension, then we can ignore sample quantization. If in addition, we can ignore jitter in the transmission delays over the network, then our search for efficient messaging policies simplifies. Firstly, each message packet should contain the value of the state at that time. Thus a bound on the number of data packets becomes a bound on the number of state samples. Secondly, the remaining choice in messaging is entirely about the times when samples are taken. For a scalar, linear diffusion process, we study the problem of choosing the causal sampling times that will give the lowest aggregate squared error distortion. We stick to finite-horizons and impose a hard upper bound N on the number of allowed samples. We cast the design as a problem of choosing an optimal sequence of stopping times. We reduce this to a nested sequence of problems, each asking for a single optimal stopping time. Under an unproven but natural assumption about the least-square estimate at the supervisor, each of these single stopping problems are of standard form. The optimal stopping times are random times when the estimation error exceeds designed envelopes. For the case where the state is a Brownian motion, we give analytically: the shape of the optimal sampling envelopes, the shape of the envelopes under optimal Delta sampling, and their performances. Surprisingly, we find that Delta sampling performs badly. Hence, when the rate constraint is a hard limit on the number of samples over a finite horizon, we should should not use Delta sampling

Robust Adaptive Control of Linear Parameter-Varying Systems with Unmatched Uncertainties

This paper presents a robust adaptive control solution for linear parameter-varying (LPV) systems with unknown input gain and unmatched nonlinear (state- and time-dependent) uncertainties based on the $\mathcal{L}_1$ adaptive control architecture and peak-to-peak gain (PPG) analysis/minimization from robust control. Specifically, we introduce new tools for stability and performance analysis leveraging the PPG bound of an LPV system that is computable using linear matrix inequality (LMI) techniques. A piecewise-constant estimation law is introduced to estimate the lumped uncertainty with quantifiable error bounds, which can be systematically improved by reducing the estimation sampling time. We also present a new approach to attenuate the unmatched uncertainty based on the PPG minimization that is applicable to a broad class of systems with linear nominal dynamics. In addition, we derive transient and steady-state performance bounds in terms of the input and output signals of the actual closed-loop system as compared to the same signals of a virtual reference system that represents the possibly best achievable performance. Under mild assumptions, we prove that the transient performance bounds can be uniformly reduced by decreasing the estimation sampling time, which is subject only to hardware limitations. The theoretical development is validated by extensive simulations on the short-period dynamics of an F-16 aircraft

Adaptive sampling for UAV sensor network in oil spill management

In this paper we propose a method for adaptive sampling using Unmanned Aerial Vehicles (UAVs) in oil spill management. The goal is to measure and estimate oil spill concentrations at the sea surface, while at the same time identify the leak rates of sources at known positions. First we construct a cost which approximates the benefit of sampling locations at specific times. This cost is based on measures of observability and of persistency of excitation for the oil spill model. A receding horizon Mixed-Integer Linear Programming (MILP) problem is solved in order to find UAV trajectories which are optimal with respect to the cost. For UAV trajectory tracking we use a Lyapunov based controller. The oil spill concentration measurements taken by the UAVs by following these tracks are used in an adaptive observer, which provides state (concentration) and parameter (leak rate) estimates. Under the assumption that the sampling strategy described above lead to uniform complete observability and persistency of excitation, we prove Uniform Global Asymptotic Stability (UGAS) of the state estimation, parameter identification and UAV trajectory tracking errors. Finally, we provide a simulation of the proposed strategy, and compare it with two other strategies.acceptedVersio

A Nonparametric Adaptive Nonlinear Statistical Filter

We use statistical learning methods to construct an adaptive state estimator for nonlinear stochastic systems. Optimal state estimation, in the form of a Kalman filter, requires knowledge of the system's process and measurement uncertainty. We propose that these uncertainties can be estimated from (conditioned on) past observed data, and without making any assumptions of the system's prior distribution. The system's prior distribution at each time step is constructed from an ensemble of least-squares estimates on sub-sampled sets of the data via jackknife sampling. As new data is acquired, the state estimates, process uncertainty, and measurement uncertainty are updated accordingly, as described in this manuscript.Comment: Accepted at the 2014 IEEE Conference on Decision and Contro