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.     

On state observers for nonlinear systems

For linear systems, it is known that there exists a state observer if and only if the system is detectable, or in other words, asymptotically stabilizable by output injection. In this paper, it is shown that asymptotic stabilizability by output injections is neither necessary nor sufficient for the construction of a nonlinear observer which may not have an exponential error decay rate. The concept of uniform observers is introduced and necessary conditions and sufficient conditions are given for the construction of uniform observers.     

Sonar-based robot navigation using nonlinear robust observers

This paper addresses the sonar-based navigation of mobile robots. The extended Kalman filtering (EKF) technique is considered, but from a deterministic, nonstochastic, point of view. For this problem, new results are presented on the robustness of the nonlinear observation scheme. The original feature is that the region-of-convergence question is posed in its complete nonlinear framework, that is, considering the dynamics not only of the estimation error ζ(t), but also of the covariance matrix P(t). In this way the approach followed makes less conservative the treatment and improves the convergence analysis. The proposed ideas were tested successfully on simulation experiments of a mobile platform.     

A diagnosis-based approach for tire-road forces and maximum friction estimation

A new approach to estimate vehicle tire forces and road maximum adherence is presented. Contrarily to most of the previous works on this subject, it is not an asymptotic observer-based estimation, but a combination of elementary diagnosis tools and new algebraic techniques for filtering and estimating derivatives of noisy signals. In a first step, instantaneous friction and lateral forces will be computed within this framework. Then, extended braking stiffness concept is exploited to detect which braking efforts allow to distinguish a road type from another. A weighted Dugoff model is used during these ‘distinguishable’ intervals to estimate the maximum friction coefficient. Very promising results have been obtained in noisy simulations and real experimentations for most of the driving situations.     

A nonlinear observer for on-line estimation of the cerebrospinal fluid outflow resistance

Accurate estimates of the outflow resistance of the human cerebrospinal fluid system are important for the diagnosis of a medical condition known as hydrocephalus. In this paper we design a nonlinear observer which provides on-line estimates of the outflow resistance, to the best of our knowledge the first method to do so. The output of the observer is proven to globally converge to an unbiased estimate. Its performance is experimentally verified using the same apparatus used to perform actual patient diagnoses and a specially-designed physical model of the human cerebrospinal fluid system.     

Adaptive observers for time-delay nonlinear systems in triangular form

A simple nonlinear observer with a dynamic gain is proposed for a class of bounded-state nonlinear systems subject to state delay. By saturating the states of the observer nonlinearities with either symmetric or non-symmetric saturation functions, we show that the observer exists, whatever the delay is. Furthermore, it will be highlighted that the observer design is free from any preliminary analysis of the time-delay system such as estimating the Lipschitz constants of nonlinearities. The proposed design encompasses a wide class of nonlinear and time-delay systems written in triangular form and generalizes previous results on delayless nonlinear systems.     

Lyapunov-based switching control of nonlinear systems using high-gain observers

We consider output feedback stabilization of uniformly observable uncertain nonlinear systems when the uncertain parameters belong to a known but comparably large compact set. In a previous paper, we proposed a new logic-based switching control to improve the performance of continuous high-gain-observer-based sliding mode controllers. Our main goal here is to show that similar techniques can be exploited for solving challenging control problems for a more general class of uncertain nonlinear systems. We require neither the sign of the high-frequency gain to be known nor the system to be minimum-phase. The key idea is to split the set of parameters into smaller subsets, design a controller for each of them, and switch the controller if, after a dwell-time period, the derivative of the Lyapunov function does not satisfy a certain inequality. A high-gain observer is used to estimate the derivatives of the output as well as the derivative of the Lyapunov function. Another goal of this paper is to introduce a switching strategy that uses on-line information to decide on the controller to switch to, instead of using a pre-sorted list as in our previous work. The new strategy can improve the transient performance of the system.     

Adaptive observers as nonlinear internal models

This paper shows how the theory of nonlinear adaptive observers can be effectively used in the design of internal models for nonlinear output regulation. The theory substantially enhances the existing results in the context of adaptive output regulation, by allowing for not necessarily stable zero dynamics of the controlled plant and by weakening the standard assumption of having the steady-state control input generated by a linear system.     

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.     

Nonlinear observers comprising high-gain observers and extended Kalman filters

A full order observer is designed for a class of nonlinear systems that can potentially admit unstable zero dynamics. The structure of the observer is composed of an Extended High Gain Observer (EHGO), for the estimation of the derivatives of the output, augmented with an Extended Kalman Filter (EKF) for the estimation of the states of the internal dynamics. The EHGO is also utilized to estimate a signal that is used as a virtual output to an auxiliary system comprised of the internal dynamics. In the special case of the system being linear in the states of the internal dynamics, we achieve semi-global asymptotic convergence of the estimation error. We demonstrate the efficacy of the observer in two examples; namely, a synchronous generator connected to an infinite bus and a Translating Oscillator with a Rotating Actuator (TORA) system.     

Nonlinear predictive control of irregularly sampled multirate systems using blackbox observers

This work aims the development of an inferential nonlinear model predictive control (NMPC) scheme based on a nonlinear fast rate model that is identified from irregularly sampled multirate data, which is corrupted with unmeasured disturbances and measurement noise. The model identification is carried out in two steps. In the first step, a MISO fast rate nonlinear output error (NOE) model is identified from the irregularly sampled output data. In the second step, a time varying nonlinear auto-regressive (NAR) type model is developed using the residuals generated in the first step. The deterministic and stochastic components of the observer are parameterized using generalized ortho-normal basis filters (GOBF). The identified NOE and NAR models are combined to form MISO state observers. We then proceed to use these identified observers to formulate a nonlinear MPC strategy for controlling irregularly sampled multirate systems. The identified observers are used to generate inter-sample estimates of the irregularly sampled outputs and for performing future trajectory predictions. The efficacy of the proposed modeling and control scheme is demonstrated using simulations on a benchmark continuous fermentation process. This process exhibits input multiplicity and change in the sign of steady state gain in the operating region. The validity of the proposed modeling and control scheme is also established by conducting identification and control experiments on a laboratory scale heater-mixer setup. The proposed NMPC gives satisfactory regulatory as well as servo performance over a wide operating range in the irregularly sampled multirate scenario.     

Semi-global finite-time observers for nonlinear systems

It is well known that high gain observers exist for single output nonlinear systems that are uniformly observable and globally Lipschitzian. Under the same conditions, we show that these systems admit semi-global and finite-time converging observers. This is achieved with a derivation of a new sufficient condition for local finite-time stability, in conjunction with applications of geometric homogeneity and Lyapunov theories.     

Structured estimation of tire forces and the ground slope using SM observers

In agricultural context, the principal cause of serious accidents for all-terrain vehicles(ATVs) is rollover. The most important parameters related to this risk is the ground slope. In this paper, we propose a structured observer to estimate the system states and the longitudinal tire forces using only wheel angular velocities measurement. The robust estimation is based on a second order sliding mode observer. This estimation is then used to build up a ground slope estimation. The algorithm is composed by two cascaded estimators. This structured estimation is then applied to the model of an agricultural vehicle G7(GregoireTM) integrated in the driving simulation environment SCANeRTM-Studio.     

Active state estimation of nonlinear systems

In this paper, state observers for control systems with nonlinear outputs are studied. For such systems, the observability does not only depend on the initial conditions, but also on the exciting control used. Thus, for such systems, design of active control is an integral part of the design for state observers. Here some sufficient conditions are given for the convergence of an observer. It is also discussed, via a camera example, how to actively excite a system in order to improve the observability.     

Discrete nonlinear observers for inertial navigation

We derive an exact deterministic nonlinear observer to compute the continuous state of an inertial navigation system based on partial discrete measurements, the so-called strap-down problem. Nonlinear contraction is used as the main analysis tool, and the hierarchical structure of the system physics is systematically exploited. The paper also discusses the use of nonlinear measurements, such as distances to time-varying reference points.     

Use of observers for the inversion of nonlinear maps

In this paper we deal with the problem of the inversion of nonlinear maps. The first contribution of the paper is the definition, in a formal framework, of some problems related to map inversion, which are already present in the literature, for instance in the robotics area and in observer theory. The second and the main contribution consists in the solution of such problems by means of observers, for which some structures are proposed, for the state estimation of a time-varying nonlinear system associated with the given map and reference trajectory.     

The global existence of nonlinear observers with linear error dynamics: A topological point of view

In this paper we show that under suitable assumptions, there exists a global homeomorphism Ψ(=Φ^-1) of which maps a nonlinear system onto a linear system with output injection . Thus, an observer for state x can be directly constructed as , which is a generalized version of Luenberger observer. An important feature of the obtained result is that there is no need to find the corresponding change of coordinates Ψ explicitly, which is different from current various existing approaches.     

Vehicle state estimation for anti-lock control with nonlinear observer

Vehicle state estimation during anti-lock braking is considered. A novel nonlinear observer based on a vehicle dynamics model and a simplified Pacejka tire model is introduced in order to provide estimates of longitudinal and lateral vehicle velocities and the tire-road friction coefficient for vehicle safety control systems, specifically anti-lock braking control. The approach differs from previous work on vehicle state estimation in two main respects. The first is the introduction of a switched nonlinear observer in order to deal with the fact that in some driving situations the information provided by the sensor is not sufficient to carry out state estimation (i.e., not all states are observable). This is shown through an observability analysis. The second contribution is the introduction of tire-road friction estimation depending on vehicle longitudinal motion. Stability properties of the observer are analyzed using a Lyapunov function based method. Practical applicability of the proposed nonlinear observer is shown by means of experimental results.     

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.