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 {\em 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.
The relative degree limitation for adaptive observer-based synchronization schemes is overcome. The scheme is extended to nonpassifiable systems. Two synchronization methods are described and justified based on augmented error adaptive observer and high-order tuners. The solution is based on modern theory of nonlinear adaptive control, particularly on nonlinear observer structure and new classes of adaptation algorithms. Conditions of parametric convergence of the parameter estimation are established for the noiseless case. Robustness of the scheme to the bounded measurement error is establish…
The purpose of this paper is to deals with the problem of regional boundary asymptotic gradient full order observer (regional boundary asymptotic gradient full order observer) concept by using internal regional case. Thus, we study the relation between this notion and the corresponding asymptotic detectability and sensors. More precisely, various important results have been examined and explored concern an extension of an approach which enables to reconstruct the gradient of current state from internal region. In addition, it has been shown that the characterization of regional boundary asympt…
In this paper, we first present an adaptive distributed observer for a discrete-time leader system. This adaptive distributed observer will provide, to each follower, not only the estimation of the leader's signal, but also the estimation of the leader's system matrix. Then, based on the estimation of the matrix S, we devise a discrete adaptive algorithm to calculate the solution to the regulator equations associated with each follower, and obtain an estimated feedforward control gain. Finally, we solve the cooperative output regulation problem for discrete-time linear multi-agent systems by b…
This supplement illustrates application of adaptive observer design from (Tyukin et al, 2013) for systems which are not uniquely identifiable. It also provides an example of adaptive observer design for a magnetic bearings benchmark system (Lin, Knospe, 2000).
Observers are well known in control theory. Originally designed to estimate the hidden states of dynamical systems given some measurements, the observers scope has been recently extended to the estimation of some unknowns, for systems governed by partial differential equations. In this paper, observers are used to solve inverse source problem for a one-dimensional wave equation. An adaptive observer is designed to estimate the state and source components for a fully discretized system. The effectiveness of the method is emphasized in noise-free and noisy cases and an insight on the impact of m…
We consider the problem of adaptive observer design in the settings when the system is allowed to be nonlinear in the parameters, and furthermore they are to satisfy additional feasibility constraints. A solution to the problem is proposed that is based on the idea of universal observers and non-uniform small-gain theorem. The procedure is illustrated with an example.
We discuss a design approach for nonlinear discrete-time adaptive observer. This involves transforming a nonlinear system into a quasi-LPV (Linear Parameter Varying) polytopic model in Takagi-Sugeno (T-S) form using nonlinear embedding and sector nonlinearity (SNL) transformation. We then develop a discrete-time counterpart for a joint state and parameter estimation, based on design strategies developed for continuous time models in the existing literature. The design uses a Lyapunov approach and provides an error bounded by $\mathbb{L}_2$ gain. Based on this strategy, we propose a design for …
This paper proposes a multiple-model adaptive control methodology, using set-valued observers (MMAC-SVO) for the identification subsystem, that is able to provide robust stability and performance guarantees for the closed-loop, when the plant, which can be open-loop stable or unstable, has significant parametric uncertainty. We illustrate, with an example, how set-valued observers (SVOs) can be used to select regions of uncertainty for the parameters of the plant. We also discuss some of the most problematic computational shortcomings and numerical issues that arise from the use of this kind o…
Takagi-Sugeno (T-S) type of polytopic models have been used prominently in the literature to analyze nonlinear systems. With the sector nonlinearity approach, an exact representation of a nonlinear system within a sector could be obtained in a T-S form. Hence, a number of observer design strategies have been proposed for nonlinear systems using the T-S framework. In this work, a design strategy for adaptive observers is presented for a type of T-S systems with unknown parameters. The proposed approach improves upon the existing literature in two folds: reduce the computational burden and provi…
This article considers a model formulation and an adaptive observer design for the simultaneous estimation of the state of charge and crossover flux in disproportionation redox flow batteries. This novel nonaqueous battery chemistry allows a simple isothermal lumped parameter model to be formulated. The transport of vanadium through the porous separator is a key unknown function of battery variables and it is approximated in the space of continuous functions. The state and parameter observer adaptation laws are derived using Lyapunov analysis applied to the estimation error, the stability and …
Problem of an adaptive state observer design for nonlinear system with unknown time-varying parameters and under condition of delayed measurements is considered. State observation problem was raised by many researchers (see for example Sanx et al. (2019)). In this paper the results proposed in Bobtsov et al. (2021b), Bobtsov et al. (2021a), Bobtsov et al. (2022a), Bobtsov et al. (2022b) are developed. The problem is solved under assumption that the state matrix can be represented as sum of known and unknown parts. The output vector is measured with a known constant delay. An adaptive observer …
This paper shows how the theory of adaptive observers can be effectively used in the design internal models for nonlinear output regulation. The main result obtained in this way is a new method for the synthesis of adaptive internal models which substantially enhances the existing theory of adaptive output regulation, by allowing nonlinear internal models and more general classes of controlled plants.
In this paper, we study the leader-following consensus problem of multiple Euler-Lagrange systems subject to an uncertain leader system. We first establish an adaptive distributed observer for a neutrally stable linear leader system whose system matrix is not known exactly. Under standard assumptions, this adaptive distributed observer can estimate and pass the leader's state to each follower through the communication network of the system without knowing the leader's system matrix exactly. Under the additional assumption that the leader's state is persistently exciting, this adaptive distribu…
This paper develops an adaptive observation-based efficient reinforcement learning (RL) approach for systems with uncertain drift dynamics. A novel concurrent learning adaptive extended observer (CL-AEO) is first designed to jointly estimate the system state and parameter. This observer has a two-timescale structure and doesn't require any additional numerical techniques to calculate the state derivative information. The idea of concurrent learning (CL) is leveraged to use the recorded data, which leads to a relaxed verifiable excitation condition for the convergence of parameter estimation. B…
This paper considers the cooperative output regulation problem for linear multi-agent systems with a directed communication graph, heterogeneous linear subsystems, and an exosystem whose output is available to only a subset of subsystems. Both the cases with nominal and uncertain linear subsystems are studied. For the case with nominal linear subsystems, a distributed adaptive observer-based controller is designed, where the distributed adaptive observer is implemented for the subsystems to estimate the exogenous signal. For the case with uncertain linear subsystems, the proposed distributed o…
This paper introduces a new nonlinear observer for state estimation of linear time invariant systems. The proposed observer contains a (nonlinear) cubic term in its error dynamics. "For the final version of this article, please refer to the published version in Int. Jr. of Adaptive Control and Signal Processing. The differences between the published and arxiv version are substantial and significant"
We consider the problem of state and parameter estimation for a wide class of nonlinear oscillators. Observable variables are limited to a few components of state vector and an input signal. The problem of state and parameter reconstruction is viewed within the classical framework of observer design. This framework offers computationally-efficient solutions to the problem of state and parameter reconstruction of a system of nonlinear differential equations, provided that these equations are in the so-called adaptive observer canonic form. We show that despite typical neural oscillators being l…
This paper proposes a design methodology for non-linear state observers for invariant kinematic systems posed on finite dimensional connected Lie groups, and studies the associated fundamental system structure. The concept of synchrony of two dynamical systems is specialised to systems on Lie groups. For invariant systems this leads to a general factorisation theorem of a nonlinear observer into a synchronous (internal model) term and an innovation term. The synchronous term is fully specified by the system model. We propose a design methodology for the innovation term based on gradient-like t…
Designing Robust Software Sensors for Nonlinear Systems via Neural Networks and Adaptive Sliding Mode Control
TICLab, International University of Rabat（国际拉巴特大学TIC实验室）；CNRS–CRAN–7039, University of Lorraine（法国洛林大学CNRS-CRAN-7039机构）；INRIA Nancy–LARSEN（INRIA南尼ce-LARSEN机构）；Mohammed VI Polytechnic University, College of Computing（穆莱·易卜拉欣六世理工大学计算机学院）；Faculty of Engineering, University of Leeds（利兹大学工程学院）
This paper studies cooperative tracking problem of heterogeneous Euler-Lagrange systems with an uncertain leader. Different from most existing works, system dynamic knowledge of the leader node is unaccessible to any follower node in our paper. Distributed adaptive observers are designed for all follower nodes, simultaneously estimate the state and parameters of the leader node. The observer design does not rely on the frequency knowledge of the leader node, and the estimation errors are shown to converge to zero exponentially. Moreover, the results are applied to general directed graphs, wher…
This paper deals with the design of a model-based rapid fault detection and isolation strategy using sliding mode observers. To address this problem, a new scheme is proposed by adaptively combining the information provided by a bank of observers. In this regard, a new structure for sliding mode observers is considered. Then, the well-known recursive least square algorithm is utilized to merge individual state estimations suitably such that the system fault is detected faster. The required condition for enhancing perfect state estimation is derived, and the stability of the overall system is p…
In this paper, we study the leader-following consensus problem for a class of uncertain nonlinear multi-agent systems under jointly connected directed switching networks. The uncertainty includes constant unbounded parameters and external disturbances. We first extend the recent result on the adaptive distributed observer from global asymptotical convergence to global exponential convergence. Then, by integrating the conventional adaptive control technique with the adaptive distributed observer, we present our solution by a distributed adaptive state feedback control law. Our result is illustr…
We propose a new model of the oculomotor system, particularly the vestibulo-ocular reflex, gaze fixation, and smooth pursuit. Our key insight is to exploit recent developments on adaptive internal models. The outcome is a simple model that includes the interactions between the brainstem and the cerebellum and that recovers behaviors from more than 15 oculomotor experiments. In addition, we put forward a thesis that the cerebellum embodies internal models of all persistent, exogenous reference and disturbance signals acting on the body and observable through the error signals it receives.
This paper considers the safety-critical control design problem with output measurements. An observer-based safety control framework that integrates the estimation error quantified observer and the control barrier function (CBF) approach is proposed. The function approximation technique is employed to approximate the uncertainties introduced by the state estimation error, and an adaptive CBF approach is proposed to design the safe controller which is obtained by solving a convex quadratic program (QP). Theoretical results for CBFs with a relative degree 1 and a higher relative degree are given…
Model predictive control (MPC) for uncertain systems in the presence of hard constraints on state and input is a non-trivial problem, and the challenge is increased manyfold in the absence of state measurements. In this paper, we propose an adaptive output feedback MPC technique, based on a novel combination of an adaptive observer and robust MPC, for single-input single-output discrete-time linear time-invariant systems. At each time instant, the adaptive observer provides estimates of the states and the system parameters that are then leveraged in the MPC optimization routine while robustly …
