Vehicle velocity estimation using nonlinear observers

Nonlinear observers for estimation of lateral and longitudinal velocity of automotive vehicles are proposed. The observers are based on a sensor suite that is standard in many new cars, consisting of acceleration and yaw rate measurements in addition to wheel speed and steering angle measurements. Two approaches are considered: first, a modular approach where the estimated longitudinal velocity is used as input to the observer for lateral velocity, and second, a combined approach where all states are estimated in the same observer. Both approaches use a tire-road friction model, which is assumed to be known. It is also assumed that the road is flat. Stability of the observers is proven in the form of input-to-state stability of the observer error dynamics, under a structural assumption on the friction model. The assumption on the friction model is discussed in detail, and the observers are validated on experimental data from cars.     

A nonlinear position and attitude observer on SE(3) using landmark measurements

This paper addresses the problem of position and attitude estimation, based on landmark readings and velocity measurements. A derivation of a nonlinear observer on SE(3) is presented, using a Lyapunov function conveniently expressed as a function of the difference between the estimated and the measured landmark coordinates. The resulting feedback laws are explicit functions of the landmark measurements and velocity readings, exploiting the sensor information directly in the observer. The proposed observer yields almost global asymptotic stabilization of the position and attitude errors and exponential convergence in any closed ball inside the region of attraction. Also, it is shown that the asymptotic convergence of the estimation error trajectories is shaped by the landmark geometry and observer design parameters. The problem of non-ideal velocity readings is also considered, and the observer is augmented to compensate for bias in the angular and linear velocity measurements. The resulting position, attitude, and bias estimation errors are shown to converge exponentially fast to the desired equilibrium points, for bounded initial estimation errors. Simulation results are presented to illustrate the stability and convergence properties of the observer.     

Hybrid dead-beat observers for a class of nonlinear systems

This paper studies both the full order and the reduced order dead-beat observer problem for a class of nonlinear systems, linear in the unmeasured states. A novel hybrid observer design strategy is proposed, with the help of the notion of strong observability in finite time. The proposed methodology is applied for the estimation of the frequency of a sinusoidal signal. The results show that accurate estimation can be provided even if the signal is corrupted by high frequency noise. A brief discussion of the robustness properties of the proposed observer with respect to measurement errors is also provided.     

Adaptive state observation of linear time-varying systems with delayed measurements and unknown parameters

In this article, we address the problem of adaptive state observation of linear time-varying systems with delayed measurements and unknown parameters. Our new developments extend the results reported in our recently works. The case with known parameters has been studied by many researchers. However in this article we show that the generalized parameter estimation-based observer design provides a very simple solution for the unknown parameter case. Moreover, when this observer design technique is combined with the dynamic regressor extension and mixing estimation procedure the estimated state and parameters converge in fixed-time imposing extremely weak excitation assumptions.     

An Adaptive and Optimized Switching Observer for Sensorless Control of an Electromagnetic Valve Actuator in Camless Internal Combustion Engines

In this paper, the design and operation of a special electromagnetic actuator as a variable engine valve actuator are presented. Further, this paper describes a feasible approximated velocity switching estimator based on measurements of current and input voltage to achieve sensorless control. The proposed concept allows a reduced‐order observer to be conceived and yields a specific control strategy with an acceptable performance. In general, this approach represents a viable strategy to build reduced‐order observers for estimating the velocity of systems through the measurement of input current and voltage. The robustness of the velocity tracking is explored using a minimum variance approach. The effect of the noise is minimized, and the position can be achieved through an adaptive and optimized structure by combining this particular velocity estimator and an observer based on the electromechanical system. Position control is achieved through an inversion of the model. This approach avoids a more complex structure for the observer and yields an acceptable performance as well as eliminating bulky position‐sensor systems. In addition, a control strategy is presented and discussed. Computer simulations of the sensorless control structure are presented in which the positive effects of the observer with optimized parameter setting are visible in the closed‐loop control.     

Observer forms for perspective systems

The estimation of three-dimensional position information from two-dimensional images in computer vision systems can be formulated as a state estimation problem for a nonlinear perspective dynamic system. The multi-output state estimation problem has been treated by several authors using methods for nonlinear observer design. This paper shows that a perspective system can be transformed to two observer forms, and provides constructive methods for arriving at the transformations. These observer forms lead to straightforward observer designs. First, it is shown that, using an output transformation, the system admits an observer form which leads to an observer with linear error dynamics. A second observer design is based on a time-scaled block triangular form. Both designs assume a commonly used observability condition. The designs are demonstrated in simulation.     

A robust observer for discrete time nonlinear systems

This paper extends the results developed in (Ciccarella et al., 1993) and presents a robust observer for discrete time nonlinear systems. A simple, robust and easy to implement algorithm is given whose convergence properties are guaranteed for autonomous and forced systems. Combined parameter and state estimation is made for a numerical example, which compares the robust observer to the observer given in (Ciccarella et al., 1993).     

Decentralized state observers for range‐based position and velocity estimation in acyclic formations with fixed topologies

This paper addresses the problem of decentralized position and velocity estimation in formations of autonomous vehicles. A limited number of vehicles in the formation have access to absolute position measurements, while the rest must rely on range measurements to neighboring agents, local sensor data, and limited communication capabilities to estimate their own position and velocity. The contribution is threefold: (i) a method for designing local state observers for each agent in the formation that rely only on locally available information is presented; (ii) the stability of the continuous‐time linear time‐varying Kalman filter subject to exponentially decaying perturbations in some variables is studied; and (iii) the stability of the error dynamics of the resulting decentralized state observer is analyzed for acyclic formations with fixed topologies, and it is shown that the error converges exponentially fast to the origin for all initial conditions. Simulation results are presented and discussed to validate the proposed solution, as well as assessing its performance under the influence of measurement noise. Copyright © 2015 John Wiley & Sons, Ltd.     

Adaptive interconnected observer for sensorless induction motor

An adaptive interconnected observer for induction motor (IM) drive without mechanical sensors (speed sensor and load torque sensor) is presented. The observer estimates the fluxes, the angular velocity, the load torque and the stator resistance even under or near unobservable conditions. Practical stability based on Lyapunov theory is proved to guarantee the strongly uniformly practical stability of the estimation error dynamics. A contribution of this article is the experimental validation of the observer on reference trajectories of a sensorless IM observer benchmark. The trajectories of this benchmark are chosen to test the motor near and under conditions of unobservability. Robustness with respect to parameters variations is proved and experimentally verified.     

Finite‐time angular velocity observers for rigid‐body attitude tracking with bounded inputs

The attitude tracking of a rigid body without angular velocity measurements is addressed. A continuous angular velocity observer with fractional power functions is proposed to estimate the angular velocity via quaternion attitude information. The fractional power gains can be properly tuned according to a homogeneous method such that the estimation error system is uniformly almost globally finite‐time stable, irrespective of control inputs. To achieve output feedback attitude tracking control, a quaternion‐based nonlinear proportional‐derivative controller using full‐state feedback is designed first, yielding uniformly almost globally finite‐time stable of the attitude tracking system as well as bounded control torques a priori. It is then shown that the certainty equivalent combination of the observer and nonlinear proportional‐derivative controller ensures finite‐time convergence of the attitude tracking error for almost all initial conditions. The proposed methods not only avoid high‐gain injection, as opposed to the semi‐global results, but also overcome the unwinding problem associated with some quaternion‐based observers and/or controllers. Numerical simulations are presented to verify the effectiveness of the proposed methods. Copyright © 2016 John Wiley & Sons, Ltd.     

OBSERVER LINEARIZATION OF NONLINEAR SYSTEMS BY GENERALIZED TANSFORMATIONS

In this paper, we study the problem of observer linearization for single output dynamical systems in the presence of an output‐dependent time‐scaling transformation and a simultaneous output diffeomorphism. The approach, based on an exterior calculus approach, provides a constructive approach to the problem of equivalence of a locally observable nonlinear system to a linear observer form by means of an output dependent time‐scale transformation, an output diffeomorphism and a state‐space diffeomorphism. A generalization of existing results is obtained which allows the treatment of a larger class of locally observable nonlinear systems.     

Globally exponentially stable attitude observer with Earth velocity estimation

This paper presents a novel observer for attitude estimation based on a triad of high‐grade rate gyros aided by a body‐fixed vector measurement of a constant inertial vector, departing from the majority of solutions that consider at least two of these vectors. A cascade approach is proposed, where the first block estimates a vector that is related to the angular velocity of the Earth and a second block estimates the attitude. While the topological characteristics are relaxed in the attitude observer so that global exponential stability is achieved, an additional stage is also devised that yields estimates directly on the special orthogonal group, preserving global convergence of the estimation error. Simulation results with realistic sensor noise were performed, including extensive Monte Carlo runs. These results illustrate the convergence of the proposed solution, as well as the achievable performance and robustness to sensor noise.     

Nonlinear vehicle side-slip estimation with friction adaptation

A nonlinear observer for estimation of the longitudinal velocity, lateral velocity, and yaw rate of a vehicle, designed for the purpose of vehicle side-slip estimation, is modified and extended in order to work for different road surface conditions. The observer relies on a road-tire friction model and is therefore sensitive to changes in the adhesion characteristics of the road surface. The friction model is parametrized with a single friction parameter, and an update law is designed. The adaptive observer is proven to be uniformly globally asymptotically stable and uniformly locally exponentially stable under a persistency-of-excitation condition and a set of technical assumptions, using results related to Matrosov's theorem. The observer is tested on recorded data from two test vehicles and shows good results on a range of road surfaces.     

Finite-time observer-based output-feedback control for the global stabilisation of the PVTOL aircraft with bounded inputs

In this work, an output-feedback scheme for the global stabilisation of the planar vertical take-off and landing aircraft with bounded inputs is developed taking into account the positive nature of the thrust. The global stabilisation objective is proven to be achieved avoiding input saturation and by exclusively considering the system positions in the feedback. To cope with the lack of velocity measurements, the proposed algorithm involves a finite-time observer. The generalised versions of the involved finite-time stabilisers have not only permitted to solve the output-feedback stabilisation problem avoiding input saturation, but also provide additional flexibility in the control design that may be used in aid of performance improvements. With respect to previous approaches, the developed finite-time observer-based scheme guarantees the global stabilisation objective disregarding velocity measurements in a bounded input context. Simulation tests corroborate the analytical developments. The study includes further experimental results on an actual flying device.     

QPSO算法在非线性观测器设计中的应用*

具有量子行为的粒子群优化(Quantum-behaved Particle Swarm Optimization,QPSO)算法是继粒子群优化算法(Particle Swarm Optimization,PSO)后,最新提出的一种新型、高效的进化算法.提出了运用QPSO算法设计的非线性观测器方法.该方法属于滚动时域估计方法,利用具有量子行为的粒子群算法优化获得系统状态的最优估计.仿真结果显示该方法对初始条件不敏感,具有很强的跟踪能力.     

Nonlinear observer design for state and disturbance estimation

A new systematic framework for nonlinear observer design that allows the concurrent estimation of the process state variables together with key unknown process or sensor disturbances is proposed. The nonlinear observer design problem is addressed within a similar methodological framework as the one introduced in [N. Kazantzis, C. Kravaris, Nonlinear observer design using Lyapunov's auxiliary theorem, Systems Control Lett. 34 (1998) 241; A.J. Krener, M. Xiao, Nonlinear observer design in the Siegel domain, SIAM J. Control Optim. 41 (2002) 932.] for state estimation purposes only. From a mathematical standpoint, the problem under consideration is addressed through a system of first-order singular PDEs for which a rather general set of solvability conditions is derived. A nonlinear observer is then designed with a state-dependent gain that is computed from the solution of the system of singular PDEs. Under the aforementioned conditions, both state and disturbance estimation errors converge to zero with assignable rates. The convergence properties of the proposed nonlinear observer are tested through simulation studies in an illustrative example involving a biological reactor.     

基于Uni-Tire轮胎模型的车辆质心侧偏角估计

针对车辆质心侧偏角估计的准确性和实时性能问题,提出了车辆质心侧偏角估计的非线性全维观测器设计方法.首先基于车辆动力学模型及纵滑-侧偏联合工况下的Uni-Tire轮胎模型,利用车载传感器测量车辆状态;观测器利用这些状态估计出车辆的纵向速度、侧向速度及横摆角速度,并由此得到车辆的质心侧偏角估计.其次利用输入-状态稳定(input-to-state stability,ISS)理论对观测器的稳定性进行了分析.最后采用红旗CA7180A3E型轿车的车辆参数使用车辆仿真软件veDYNA对极限工况下的估计结果进行了离线仿真研究,并利用xPC-Target仿真环境和dSPACE实时仿真系统搭建仿真平台,对非线性全维观测器的实时性进行验证.仿真结果表明,非线性估计方法估计精度较高,实时性较好,可以满足工程应用的要求.     

A sliding mode observer for monitoring and fault estimation in a network of dynamical systems

In this paper, a novel fault estimation strategy is proposed for a network of dynamical systems at a supervisory monitoring level. The network nodes include linear and Lipschitz nonlinear dynamics and time‐varying coupling strength. The aim is to enhance the autonomy level of this class of systems by means of this inherently robust, nonlinear strategy based on sliding mode ideas. The faults are reconstructed from the equivalent output error injection signal which is used to maintain sliding. A key facet of the strategy is that the synthesis of the sliding mode observer for the network depends solely on the dynamics of an individual node of the network. The theoretical results developed in the paper are demonstrated with an example consisting of a network of pendulums. Copyright © 2013 John Wiley & Sons, Ltd.     

Interval estimation for uncertain systems with time-varying delays

The estimation problem for uncertain time-delay systems is addressed. A design method of reduced-order interval observers is proposed. The observer estimates the set of admissible values (the interval) for the state at each instant of time. The cases of known fixed delays and uncertain time-varying delays are analysed. The proposed approach can be applied to linear delay systems and nonlinear time-delay systems in the output canonical form. It involves the properties of quasi-monotone/Metzler/cooperative systems. In this framework, it is shown that if under a suitable coordinate transformation the delay-free subsystem is cooperative, then the delayed estimation error dynamics inherits this property. The conditions to find the observer gains are formulated in the form of LMI. The framework efficiency is demonstrated on examples of nonlinear systems.     

Position tracking in delayed bilateral teleoperators without velocity measurements

This work considers the control of nonlinear bilateral teleoperators with variable time delays without the need of velocity measurements. The recently proposed Immersion and Invariance observer is used to obtain an exponentially convergent estimate of the unmeasured velocities. Under the classical assumption that the human operator and the environment define passive, velocity to force, maps, it is proved that with this observer and a Proportional plus damping controller, velocities and position error are globally bounded. Finally, in the case that the human operator and the environment do not exert forces on the local and remote manipulators, respectively, global asymptotic convergence of velocities and of position error to zero is achieved. The theoretical results are sustained with simulations using a couple of two degrees‐of‐freedom nonlinear manipulators. Copyright © 2015 John Wiley & Sons, Ltd.