A Linear Active Disturbance Rejection Control for a Ball and Rigid Triangle System

This paper proposes an application of linear flatness control along with active disturbance rejection control (ADRC) for the local stabilization and trajectory tracking problems in the underactuated ball and rigid triangle system. To this end, an observer-based linear controller of the ADRC type is designed based on the flat tangent linearization of the system around its corresponding unstable equilibrium rest position. It was accomplished through two decoupled linear extended observers and a single linear output feedback controller, with disturbance cancelation features. The controller guarantees locally exponentially asymptotic stability for the stabilization problem and practical local stability in the solution of the tracking error. An advantage of combining the flatness and the ADRC methods is that it possible to perform online estimates and cancels the undesirable effects of the higher-order nonlinearities discarded by the linearization approximation. Simulation indicates that the proposed controller behaves remarkably well, having an acceptable domain of attraction

Discrete Adaptive Second Order Sliding Mode Controller Design with Application to Automotive Control Systems with Model Uncertainties

Sliding mode control (SMC) is a robust and computationally efficient solution for tracking control problems of highly nonlinear systems with a great deal of uncertainty. High frequency oscillations due to chattering phenomena and sensitivity to data sampling imprecisions limit the digital implementation of conventional first order continuous-time SMC. Higher order discrete SMC is an effective solution to reduce the chattering during the controller software implementation, and also overcome imprecisions due to data sampling. In this paper, a new adaptive second order discrete sliding mode control (DSMC) formulation is presented to mitigate data sampling imprecisions and uncertainties within the modeled plant's dynamics. The adaptation mechanism is derived based on a Lyapunov stability argument which guarantees asymptotic stability of the closed-loop system. The proposed controller is designed and tested on a highly nonlinear combustion engine tracking control problem. The simulation test results show that the second order DSMC can improve the tracking performance up to 80% compared to a first order DSMC under sampling and model uncertainties.Comment: 6 pages, 6 figures, 2017 American Control Conferenc

Asymptotic and finite-time almost global attitude tracking: representations free approach

In this paper, the attitude tracking problem is considered using the rotation matrices. Due to the inherent topological restriction, it is impossible to achieve global attractivity with any continuous attitude control system on $SO(3)$. Hence in this work, we propose some control protocols achieve almost global tracking asymptotically and in finite time, respectively. In these protocols, no world frame is needed and only relative state informations are requested. For finite-time tracking case, Filippov solutions and non-smooth analysis techniques are adopted to handle the discontinuities. Simulation examples are provided to verify the performances of the control protocols designed in this paper.Comment: arXiv admin note: text overlap with arXiv:1705.0282

Iterative learning control for constrained linear systems

This paper considers iterative learning control for linear systems with convex control input constraints. First, the constrained ILC problem is formulated in a novel successive projection framework. Then, based on this projection method, two algorithms are proposed to solve this constrained ILC problem. The results show that, when perfect tracking is possible, both algorithms can achieve perfect tracking. The two algorithms differ however in that one algorithm needs much less computation than the other. When perfect tracking is not possible, both algorithms can exhibit a form of practical convergence to a "best approximation". The effect of weighting matrices on the performance of the algorithms is also discussed and finally, numerical simulations are given to demonstrate the e®ectiveness of the proposed methods

On generalized terminal state constraints for model predictive control

This manuscript contains technical results related to a particular approach for the design of Model Predictive Control (MPC) laws. The approach, named "generalized" terminal state constraint, induces the recursive feasibility of the underlying optimization problem and recursive satisfaction of state and input constraints, and it can be used for both tracking MPC (i.e. when the objective is to track a given steady state) and economic MPC (i.e. when the objective is to minimize a cost function which does not necessarily attains its minimum at a steady state). It is shown that the proposed technique provides, in general, a larger feasibility set with respect to existing approaches, given the same computational complexity. Moreover, a new receding horizon strategy is introduced, exploiting the generalized terminal state constraint. Under mild assumptions, the new strategy is guaranteed to converge in finite time, with arbitrarily good accuracy, to an MPC law with an optimally-chosen terminal state constraint, while still enjoying a larger feasibility set. The features of the new technique are illustrated by three examples.Comment: Part of the material in this manuscript is contained in a paper accepted for publication on Automatica and it is subject to Elsevier copyright. The copy of record is available on http://www.sciencedirect.com

Minimax rank estimation for subspace tracking

Rank estimation is a classical model order selection problem that arises in a variety of important statistical signal and array processing systems, yet is addressed relatively infrequently in the extant literature. Here we present sample covariance asymptotics stemming from random matrix theory, and bring them to bear on the problem of optimal rank estimation in the context of the standard array observation model with additive white Gaussian noise. The most significant of these results demonstrates the existence of a phase transition threshold, below which eigenvalues and associated eigenvectors of the sample covariance fail to provide any information on population eigenvalues. We then develop a decision-theoretic rank estimation framework that leads to a simple ordered selection rule based on thresholding; in contrast to competing approaches, however, it admits asymptotic minimax optimality and is free of tuning parameters. We analyze the asymptotic performance of our rank selection procedure and conclude with a brief simulation study demonstrating its practical efficacy in the context of subspace tracking.Comment: 10 pages, 4 figures; final versio

Integral curves of noisy vector fields and statistical problems in diffusion tensor imaging: nonparametric kernel estimation and hypotheses testing

Let $v$ be a vector field in a bounded open set $G\subset {\mathbb {R}}^d$. Suppose that $v$ is observed with a random noise at random points $X_i, i=1,...,n,$ that are independent and uniformly distributed in $G.$ The problem is to estimate the integral curve of the differential equation $$\frac{dx(t)}{dt}=v(x(t)),\qquad t\geq 0,x(0)=x_0\in G,$$ starting at a given point $x(0)=x_0\in G$ and to develop statistical tests for the hypothesis that the integral curve reaches a specified set $\Gamma\subset G.$ We develop an estimation procedure based on a Nadaraya--Watson type kernel regression estimator, show the asymptotic normality of the estimated integral curve and derive differential and integral equations for the mean and covariance function of the limit Gaussian process. This provides a method of tracking not only the integral curve, but also the covariance matrix of its estimate. We also study the asymptotic distribution of the squared minimal distance from the integral curve to a smooth enough surface $\Gamma\subset G$. Building upon this, we develop testing procedures for the hypothesis that the integral curve reaches $\Gamma$. The problems of this nature are of interest in diffusion tensor imaging, a brain imaging technique based on measuring the diffusion tensor at discrete locations in the cerebral white matter, where the diffusion of water molecules is typically anisotropic. The diffusion tensor data is used to estimate the dominant orientations of the diffusion and to track white matter fibers from the initial location following these orientations. Our approach brings more rigorous statistical tools to the analysis of this problem providing, in particular, hypothesis testing procedures that might be useful in the study of axonal connectivity of the white matter.Comment: Published in at http://dx.doi.org/10.1214/009053607000000073 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

A family of asymptotically stable control laws for flexible robots based on a passivity approach

A general family of asymptotically stabilizing control laws is introduced for a class of nonlinear Hamiltonian systems. The inherent passivity property of this class of systems and the Passivity Theorem are used to show the closed-loop input/output stability which is then related to the internal state space stability through the stabilizability and detectability condition. Applications of these results include fully actuated robots, flexible joint robots, and robots with link flexibility