Lingji Chen

Adaptive Control Design for Nonaffine Models Arising in Flight Control

Adaptive tracking control algorithms are developed for a class of models encountered in flight control that are nonaffine in the control input. The essence of the approach is to differentiate the function that is nonlinear in the control input and obtain an increased-order system that is linear in the derivative of the control signal and can be used as a new control variable. A systematic procedure is developed and related theoretical and practical issues are discussed. The proposed procedure, referred to as the controller for nonaffine plants, is developed for several cases of nonaffine models with unknown parameters. It is shown that the key aspect in the adaptive control design is the definition of the estimate of the derivative of systems state, which results in a convenient error model from which the adaptive laws can be written in a straightforward manner. The proposed approach is tested using a three-degree-of-freedom simulation of a typical fighter aircraft and is shown to result in a substantially improved system response.

How to Tell a Bad Filter Through Monte Carlo Simulations

In this note, we propose one particular method to address the issue of how to numerically evaluate nonlinear filtering algorithms and/or their software implementations, through Monte Carlo simulations. We introduce a quantitative performance indicator whose computation can be automated and does not depend on any specific definition of point estimate. The method is based on conditional probability integral transform and maximum deviation of an empirical cumulative distribution function from a uniform distribution. The usefulness of such an indicator is illustrated through an example.

Multivariable adaptive controller design for a class of non-affine models arising in flight control

In this paper we extend our previous results on adaptive tracking control design for single-input non-affine dynamic models to the multivariable case. The proposed procedure was first developed for the case of known parameters, and then extended to the adaptive control design in the case of uncertain parameters. It is shown that the key design aspect is the definition of the estimate of the derivative of systems state, which results in a convenient error model from which the adaptive laws can be written by inspection. The proposed approach is tested using a 3DOF simulation of a typical fighter aircraft, and is shown to result in substantially improved response of the system.

PFLib: an object-oriented MATLAB toolbox for particle filtering

Under a United States Army Small Business Technology Transfer (STTR) project, we have developed a MATLAB toolbox called PFLib to facilitate the exploration, learning and use of Particle Filters by a general user. This paper describes its object oriented design and programming interface. The software is available under a GNU GPL license.

Optimal measurement selection for Any-time Kalman Filtering with processing constraints

In an embedded system with limited processing resources, as the number of tasks grows, they interfere with each other through preemption and blocking while waiting for shared resources such as CPU time and memory. The main task of an Any-time Kalman Filter (AKF) is real-time state estimation from measurements using available processing resources. Due to limited computational resources, the AKF may have to select only a subset of all the available measurements or use out-of-sequence measurements for processing. This paper addresses the problem of measurement selection needed to implement AKF on systems that can be modeled as double-integrators, such as mobile robots, aircraft, satellites etc. It is shown that a greedy sequential selection algorithm provides the optimal selection of measurements for such systems given the processing constraints.

Unscented kalman filter for multiple spacecraft formation flying

Abstract In this paper, Unscented Kalman Filter (UKF) is presented both in its canonical form and in a form that is suitable for spacecraft attitude estimation using quaternions. An atti- tude quaternion has a unit norm, resulting in a singular co- variance matrix. Techniques have been developed in the past to deal with this problem, in the context of Extended Kalman Filter (EKF), and the current paper presents the counterpart in the context of UKF. Simulation studies con- firm that at low noise level, EKF and UKF behave in essen- tially the same way, while at high noise level, UKF is more accurate and robust. For multiple-spacecraft formation fly- ing, robustness with respect to noise level and choice of co- ordinate frame is highly desirable, hence it is argued that UKF is better suited for the task than EKF, especially in view of the fact that the additional computational cost asso- ciated with UKF is not significant. 1 Introduction Relative state estimation is an integral part of any forma- tion flying mission. One way of solving the nonlinear es- timation problem is by using the Extended Kalman Filter

On communication in decentralized pole-placement formation control and parallel estimation

We consider a class of decentralized formation flying control algorithms that stem from assigning the closed loop poles for the Multi-Input-Multi-Output formation system, and examine the role communication plays. First we revisit Smith and Hadaegh [2007], where as many parallel estimators as there are spacecraft are used. We show an intuitive way of demonstrating the existing results, and by a re-interpretation of the quantities communicated, extend the results to the case where observability of the full formation state at each spacecraft is not available. Next we show that the pole-placement formation control can be carried out with only one estimator and no communication, for the double-integrator system used to model deep space formation flying. We treat the task of having one estimator on each spacecraft as separate from the task of control, and show how it can be accomplished with communication.

Reformulating Kalman Filter Based Optimal Dynamic Coverage Control

Abstract Our objective in this paper is to examine the problem formulation of one particular published result, make logical extensions, and consider the question of whether we should obtain solutions under such a formulation, or pursue alternative formulations. The problem considered in “A Kalman Filter-Based Control Strategy for Dynamic Coverage Control” by I. I. Hussein is for a network of mobile sensors with limited range to traverse and estimate a spatially-decoupled scalar field. In that paper the optimal trajectories are generated by an online procedure that minimizes the trace of the instantaneous covariance of the estimation error obtained from Kalman Filtering, using a finite set of admissible control inputs. We extend the formulation by observing that the procedure can be performed offline, that the cost function can be defined over a finite horizon, and that the set of control inputs can be a continuum. We illustrate, with simple examples, the kind of solutions that can be obtained using dynamic programming, and ask the question “Is this the type of trajectories that we want?” Alternative formulations are suggested and are left for future work.

Comparing Antenna Conical Scan Algorithms for Spacecraft Position Estimation

I NTHISNote,wewill examine nonlinear estimation techniques to solve nonlinear problems that have been traditionally solved by linear methods. In the area of nonlinear estimation, a class of sampling algorithms known asMarkov chainMonte Carlo (MCMC) was extensively used to obtain a solution that is often a general, nonGaussian, nonunimodal probability distribution. Therefore, there is a natural question to ask regarding problems that have been solved in practice by linear/Gaussian approximations: Canwe do better with nonlinear methods such asMCMC? If so, how much better? This Note examines the problem of estimating spacecraft position using scanning techniques for NASA’s Deep Space Network antennas and compares different algorithms through numerical studies. As described in [1–3], the NASA Deep Space Network antennas have spacecraft trajectory programmed into them to form the antenna command. To compensate for disturbances and determine the true position of the spacecraft, circular movements are added to the antenna command trajectory in a technique known as conical scanning (ConScan). From the sinusoidal variations in the power of the signal received from the spacecraft by the antenna, the true spacecraft position can then be estimated. A least-squares method was reported in literature and used in practice for the batch processing mode. We compare this method with two other possible methods: the general linear method, which uses prior distribution of spacecraft position, and the MCMCmethod, which tries to solve the nonlinear problem directly by representing the desired distribution of spacecraft position with samples. Simulations show that for the amount of data collected for ConScan batch processing in practice, all three algorithms perform essentially the same. When we artificially reduce the amount of available data, performance improvement manifests itself but the amount is dependent upon the noise level. For a low level of noise, general linear is significantly better than least squares, whereas MCMC is marginally better than general linear. For a high level of noise, general linear is marginally better than least squares, whereas MCMC is significantly better than general linear.

Multi-environment NLF tracking assessment testbed (MENTAT): an update

In applications in which even the best EKFs and MHTs may perform poorly, the single-target and multi-target Bayes nonlinear filters become potentially important. In recent years, new implementation techniques such as sequential Monte Carlo (a.k.a. particle-system) have emerged that, when hosted on ever more inexpensive, smaller, and powerful computers, make these filters potentially computationally tractable for real-time applications. A methodology for preliminary test and evaluation (PT&E) of the relative strengths and weaknesses of these algorithms is becoming increasingly necessary. The purpose of PT&E is to (1) assess the broad strengths and weaknesses of various algorithms or algorithm types; (2) justify further algorithm development; and (3) provide guidance as to which algorithms are potentially useful for which applications. At last years conference we described our plans for the development of a PT&E tool, MENTAT. In this paper we report on current progress. Our implementation is MATLAB-based, and harnesses the GUI-building capabilities of the well-known MATLAB package, SIMULINK.