Target point‐based path‐following controller for a car‐type vehicle using bounded controls

In this paper, we have studied the control problem of target point‐based path following for car‐type vehicles. This special path‐following task arises from the needs of vision‐based guidance systems, where a given target point located ahead of the vehicle, in the visual range of the camera, must follow a specified path. A solution to this problem is developed through a nonlinear transformation of the path‐following problem into a reference trajectory tracking problem, by modeling the target point as a virtual vehicle. The use of target point complicates the control problem, as the development produces a first‐order nonlinear nonglobally Lipschitz differential equation with finite escape time. This problem is solved by using small control signals. Bounded feedback laws are designed to control the real vehicle's angular acceleration and the virtual vehicle's velocity, to achieve stability. The resulting controller is globally asymptotically stable with respect to the origin, the proof of which is derived from Lyapunov‐based arguments and a bootstrap argument. It is also shown that the use of exponentially convergent observers/differentiators does not affect the stability of the closed‐loop system. The effectiveness of this controller has been illustrated through simulations. Copyright © 2014 John Wiley & Sons, Ltd.     

Covariance Structure Maximum-Likelihood Estimates in Compound Gaussian Noise: Existence and Algorithm Analysis

Recently, a new adaptive scheme [Conte (1995), Gini (1997)] has been introduced for covariance structure matrix estimation in the context of adaptive radar detection under non-Gaussian noise. This latter has been modeled by compound-Gaussian noise, which is the product c of the square root of a positive unknown variable tau (deterministic or random) and an independent Gaussian vector x, c=radictaux. Because of the implicit algebraic structure of the equation to solve, we called the corresponding solution, the fixed point (FP) estimate. When tau is assumed deterministic and unknown, the FP is the exact maximum-likelihood (ML) estimate of the noise covariance structure, while when tau is a positive random variable, the FP is an approximate maximum likelihood (AML). This estimate has been already used for its excellent statistical properties without proofs of its existence and uniqueness. The major contribution of this paper is to fill these gaps. Our derivation is based on some likelihood functions general properties like homogeneity and can be easily adapted to other recursive contexts. Moreover, the corresponding iterative algorithm used for the FP estimate practical determination is also analyzed and we show the convergence of this recursive scheme, ensured whatever the initialization.     

Stabilisation of perturbed chains of integrators using Lyapunov-based homogeneous controllers

In this paper, we present a Lyapunov-based homogeneous controller for the stabilisation of a perturbed chain of integrators of arbitrary order r ≥ 1. The proposed controller is based on homogeneous controller for stabilisation of pure chain of integrators. The control of homogeneity degree is also introduced and various controllers are designed using this concept, namely a bounded-controller with minimum amplitude of discontinuous control and a controller with globally fixed-time convergence. The performance of the controller is validated through simulations.     

Velocity‐free attitude stabilization with inertial vector measurements

This paper deals with the attitude stabilization problem of a rigid body, where neither the angular velocity nor the attitude is used in the feedback; only body‐referenced vector measurements are needed. The proposed control scheme is based on an angular velocity observer‐like system relying solely on vector measurements. The proposed controller ensures almost global asymptotic stability and provides some interesting performance properties through an appropriate tuning of the control gains. The performance and effectiveness of the proposed control scheme are illustrated via simulation results where the control gains are adjusted using a nonlinear optimization. Copyright © 2015 John Wiley & Sons, Ltd.     

Involvement of the caudal medulla in negative feedback mechanisms triggered by spatial summation of nociceptive inputs

In the rat, applying noxious heat stimuli to the excitatory receptive fields and simultaneously to adjacent, much larger, areas of the body results in a surface-related reduction in the responses of lumbar dorsal horn convergent neurons. These inhibitory effects induced by spatial summation of nociceptive inputs have been shown to involve a supraspinally mediated negative feedback loop. The aim of the present study was to determine the anatomic level of integration of these controls and hence to ascertain what relationships they might share with other descending controls modulating the transmission of nociceptive signals. The responses of lumbar convergent neurons to noxious stimulation (15-s immersion in a 48 degrees C water bath) applied to increasing areas of the ipsilateral hindlimb were examined in several anesthetized preparations: sham-operated rats, rats with acute transections performed at various levels of the brain stem, and spinal rats. The effects of heterotopic noxious heat stimulation (tail immersion in a 52 degrees C water bath) on the C-fiber responses of these neurons also were analyzed. The electrophysiological properties of dorsal horn convergent neurons, including their responses to increasing stimulus surface areas, were not different in sham-operated animals and in animals the brain stems of which had been transected completely rostral to a plane -2. 8 mm remote from interaural line (200 micron caudal to the caudal end of the rostral ventromedial medulla). In these animals, increasing the stimulated area size from 4.8 to 18 cm2 resulted in a 35-45% reduction in the responses. In contrast, relative to responses elicited by 4.8 cm2 stimuli, responses to 18 cm2 were unchanged or even increased in animals with transections at more caudal level and in spinal animals. Inhibitions of the C-fiber responses elicited by heterotopic noxious heat stimulation were in the 70-80% range during conditioning in sham-operated animals and in animals with rostral brain stem transections. Such effects were reduced significantly (residual inhibitions in the 10-20% range) in animals with transections >500 micron caudal to the caudal end of the rostral ventromedial medulla and in spinal animals. It is concluded that the caudal medulla constitutes a key region for the expression of negative feed-back mechanisms triggered by both spatial summation of noxious inputs and heterotopic noxious inputs.     

Time-varying high-gain observers for numerical differentiation

In this paper, we propose high-gain numerical differentiators for estimating the higher derivatives of a given signal. We consider time varying high-gain vectors converging exponentially to the high-gain vectors introduced by F. Esfandiari and K.H. Khalil (1992) in an earlier paper. The dynamics of these time-varying high-gain vectors can be chosen in order to achieve specific objectives, such as peaking attenuation and low sensitivity with respect to noise disturbance. In particular, we show that the numerical differentiator introduced in an earlier paper avoids the peaking phenomenon in the sense of H.J. Sussmann and P.V. Kokotovic (1991), i.e., there is no unbounded overshoot of the error estimate during the initial times. We also propose another numerical differentiator which filters the reference signal with respect to a very simple quadratic cost.     

Path planning on compact Lie groups using a homotopy method

In this paper, we address the issue of solving the motion planning problems (MPP for short) for a class of left-invariant control systems Σ whose state spaces are semisimple compact Lie groups. The sub-Riemannian metrics induced by the dynamics of Σ admit nontrivial abnormal extremals. This fact a priori represents an obstruction for the procedure we use to tackle the MPP, which consists of a homotopy (or continuation) method. We are however able to provide complete answers for the MPP.