Recursive State-Space Identification of Non-Uniformly Sampled-Data Systems Using QR Decomposition

A recursive least-squares (LS) state-space identification method based on the QR decomposition is proposed for non-uniformly sampled-data systems. Both cases of measuring all states and only the output(s) are considered for model identification. For the case of state measurement, a QR decomposition-based recursive LS (QRD-RLS) identification algorithm is given to estimate the state matrices. For the case of only output measurement, another identification algorithm is developed by combining the QRD-RLS approach with a hierarchical identification strategy. Both algorithms can guarantee fast convergence rate with low computation complexity. An illustrative example is shown to demonstrate the effectiveness of the proposed methods

Probabilistic Self-Localization and Mapping: An Asynchronous Multirate Approach

"© 2008 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works."[EN] In this paper, we present a set of robust and efficient algorithms with O(N) cost for the solution of the Simultaneous Localization And Mapping (SLAM) problem of a mobile robot. First, we introduce a novel object detection method, which is mainly based on multiple line fitting method for landmark detection with regular constrained angles. Second, a line-based pose estimation method is proposed, based on LeastSquares (LS). This method performs the matching of lines, providing the global pose estimation under assumption of known Data-Association. Finally, we extend the FastSLAM (FActored Solution To SLAM) algorithm for mobile robot self-localisation and mapping by considering the asynchronous sampling of sensors and actuators. In this sense, multi-rate asynchronous holds are used to interface signals with different sampling rates. Moreover, an asynchronous fusion method to predict and update mobile robot pose and map is also presented. In addition to this, FastSLAM 1.0 has been also improved by considering the estimated pose with the LS-approach to re-allocate each particle of the posterior distribution of the robot pose. This approach has a lower computational cost than the original Extended Kalman Filtering (EKF) approach in FastSLAM 2.0. All these methods have been combined in order to perform an efficient and robust self-localization and map building process. Additionally, these methods have been validated with experimental real data, in mobile robot moving on an unknown environment for solving the SLAM problem.This work has been supported by the Spanish Government (MCyT) research project BIA2005-09377-C03-02 and by the Italian Government (MIUR) research project PRIN2005097207.Armesto, L.; Ippoliti, G.; Longhi, S.; Tornero Montserrat, J. (2008). Probabilistic Self-Localization and Mapping: An Asynchronous Multirate Approach. IEEE Robotics & Automation Magazine. 15(2):77-88. https://doi.org/10.1109/M-RA.2007.907355S778815

MPC of constrained discrete-time linear periodic systems — A framework for asynchronous control: Strong feasibility, stability and optimality via periodic invariance

State-feedback model predictive control (MPC) of discrete-time linear periodic systems with time-dependent state and input dimensions is considered. The states and inputs are subject to periodically time-dependent, hard, convex, polyhedral constraints. First, periodic controlled and positively invariant sets are characterized, and a method to determine the maximum periodic controlled and positively invariant sets is derived. The proposed periodic controlled invariant sets are then employed in the design of least-restrictive strongly feasible reference-tracking MPC problems. The proposed periodic positively invariant sets are employed in combination with well-known results on optimal unconstrained periodic linear-quadratic regulation (LQR) to yield constrained periodic LQR control laws that are stabilizing and optimal. One motivation for systems with time-dependent dimensions is efficient control law synthesis for discrete-time systems with asynchronous inputs, for which a novel modeling framework resulting in low dimensional models is proposed. The presented methods are applied to a multirate nano-positioning system

MULTIRATE LQG CONTROL OF CONTINUOUS-TIME STOCHASTIC-SYSTEMS

The LQG problem for stochastic continuous-time systems subject to multirate sampling of both input and output variables is considered. By restating the problem as a discrete-time periodic LQG problem, a sufficient condition for the existence of an optimal stabilizing regulator is given in terms of the structural properties of the original system and the cost function. This improves on previous contributions, where optimal control schemes were proposed without addressing existence and/or stability issues. The possibility of incorporating an integral action within the optimal LQG regulator is also briefly discussed