Nonlinear adaptive estimation with application to sinusoidal identification

Parameter estimation of a sinusoidal signal in real-time is encountered in applications in numerous areas of engineering. Parameters of interest are usually amplitude, frequency and phase wherein frequency tracking is the fundamental task in sinusoidal estimation. This thesis deals with the problem of identifying a signal that comprises n (n ≥ 1) harmonics from a measurement possibly affected by structured and unstructured disturbances. The structured perturbations are modeled as a time-polynomial so as to represent, for example, bias and drift phenomena typically present in applications, whereas the unstructured disturbances are characterized as bounded perturbation. Several approaches upon different theoretical tools are presented in this thesis, and classified into two main categories: asymptotic and non-asymptotic methodologies, depending on the qualitative characteristics of the convergence behavior over time. The first part of the thesis is devoted to the asymptotic estimators, which typically consist in a pre-filtering module for generating a number of auxiliary signals, independent of the structured perturbations. These auxiliary signals can be used either directly or indirectly to estimate—in an adaptive way—the frequency, the amplitude and the phase of the sinusoidal signals. More specifically, the direct approach is based on a simple gradient method, which ensures Input-to-State Stability of the estimation error with respect to the bounded-unstructured disturbances. The indirect method exploits a specific adaptive observer scheme equipped with a switching criterion allowing to properly address in a stable way the poor excitation scenarios. It is shown that the adaptive observer method can be applied for estimating multi-frequencies through an augmented but unified framework, which is a crucial advantage with respect to direct approaches. The estimators’ stability properties are also analyzed by Input-to-State-Stability (ISS) arguments. In the second part we present a non-asymptotic estimation methodology characterized by a distinctive feature that permits finite-time convergence of the estimates. Resorting to the Volterra integral operators with suitably designed kernels, the measured signal is processed, yielding a set of auxiliary signals, in which the influence of the unknown initial conditions is annihilated. A sliding mode-based adaptation law, fed by the aforementioned auxiliary signals, is proposed for deadbeat estimation of the frequency and amplitude, which are dealt with in a step-by-step manner. The worst case behavior of the proposed algorithm in the presence of bounded perturbation is studied by ISS tools. The practical characteristics of all estimation techniques are evaluated and compared with other existing techniques by extensive simulations and experimental trials.Open Acces

Parameter Estimation for a Sinusoidal Signal with a Time-Varying Amplitude

This paper addresses the parameter estimation problem of a non-stationary sinusoidal signal with a timevarying amplitude, which is given by a known function of time multiplied by an unknown constant coefficient. A robust estimation algorithm is proposed for identifying the unknown frequency and the amplitude coefficient in real-time. The estimation algorithm is constructed based on the Volterra integral operator with suitably designed kernels and sliding mode adaptation laws. It is shown that the parameter estimation error converges to zero within an arbitrarily small finite time, and the robustness against bounded additive disturbances is certified by bounded-input-bounded-output arguments. The effectiveness of the estimation technique is evaluated and compared with other existing tools through numerical simulations

Hyperbolic Interaction Model For Hierarchical Multi-Label Classification

Different from the traditional classification tasks which assume mutual exclusion of labels, hierarchical multi-label classification (HMLC) aims to assign multiple labels to every instance with the labels organized under hierarchical relations. Besides the labels, since linguistic ontologies are intrinsic hierarchies, the conceptual relations between words can also form hierarchical structures. Thus it can be a challenge to learn mappings from word hierarchies to label hierarchies. We propose to model the word and label hierarchies by embedding them jointly in the hyperbolic space. The main reason is that the tree-likeness of the hyperbolic space matches the complexity of symbolic data with hierarchical structures. A new Hyperbolic Interaction Model (HyperIM) is designed to learn the label-aware document representations and make predictions for HMLC. Extensive experiments are conducted on three benchmark datasets. The results have demonstrated that the new model can realistically capture the complex data structures and further improve the performance for HMLC comparing with the state-of-the-art methods. To facilitate future research, our code is publicly available

Event-triggered distributed MPC for resilient voltage control of an islanded microgrid

This paper addresses the problem of distributed secondary voltage control of an islanded microgrid (MG) from a cyber-physical perspective. An event-triggered distributed model predictive control (DMPC) scheme is designed to regulate the voltage magnitude of each distributed generators (DGs) in order to achieve a better trade-off between the control performance and communication and computation burdens. By using two novel event triggering conditions that can be easily embedded into the DMPC for the application of MG control, the computation and communication burdens are significantly reduced with negligible compromise of control performance. In addition, to reduce the sensor cost and to eliminate the negative effects of non-linearity, an adaptive non-asymptotic observer is utilized to estimate the internal and output signals of each DG. Thanks to the deadbeat observation property, the observer can be applied periodically to cooperate with the DMPC-based voltage regulator. Finally, the effectiveness of the proposed control method has been tested on a simple configuration with 4 DGs and the modified IEEE-13 test system through several representative scenarios

Cyber-Resilient Self-Triggered Distributed Control of Networked Microgrids Against Multi-Layer DoS Attacks

Networked microgrids with high penetration of distributed generators have ubiquitous remote information exchange, which may be exposed to various cyber security threats. This paper, for the first time, addresses a consensus problem in terms of frequency synchronisation in networked microgrids subject to multi-layer denial of service (DoS) attacks, which could simultaneously affect communication, measurement and control actuation channels. A unified notion of Persistency-of-Data-Flow (PoDF) is proposed to characterise the data unavailability in different information network links, and further quantifies the multi-layer DoS effects on the hierarchical system. With PoDF, we provide a sufficient condition of the DoS attacks under which the consensus can be preserved with the proposed edgebased self-triggered distributed control framework. In addition, to mitigate the conservativeness of offline design against the worst-case attack across all agents, an online self-adaptive scheme of the control parameters is developed to fully utilise the latest available information of all data transmission channels. Finally, the effectiveness of the proposed cyber-resilient self-triggered distributed control is verified by representative case studies

Fixed-Time Convergent Distributed Observer Design of Linear Systems: A Kernel-Based Approach

The robust distributed state estimation for a class of continuous-time linear time-invariant systems is achieved by a novel kernel-based distributed observer, which, for the first time, ensures fixed-time convergence properties. The communication network between the agents is prescribed by a directed graph in which each node involves a fixed-time convergent estimator. The local observer estimates and broadcasts the observable states among neighbours so that the full state vector can be recovered at each node and the estimation error reaches zero after a predefined fixed time in the absence of perturbation. This represents a new distributed estimation framework that enables faster convergence speed and further reduced information exchange compared to a conventional Luenberger-like approach. The ubiquitous timevarying communication delay across the network is suitably compensated by a prediction scheme. Moreover, the robustness of the algorithm in the presence of bounded measurement and process noise is characterised. Numerical simulations and comparisons demonstrate the effectiveness of the observer and its advantages over the existing methods

Robust Adaptive Learning-based Path Tracking Control of Autonomous Vehicles under Uncertain Driving Environments

This paper investigates the path tracking control problem of autonomous vehicles subject to modelling uncertainties and external disturbances. The problem is approached by employing a 2-degree of freedom vehicle model, which is reformulated into a newly defined parametric form with the system uncertainties being lumped into an unknown parametric vector. On top of the parametric system representation, a novel robust adaptive learning control (RALC) approach is then developed, which estimates the system uncertainties through iterative learning while treating the external disturbances by adopting a robust term. It is shown that the proposed approach is able to improve the lateral tracking performance gradually through learning from previous control experiences, despite only partial knowledge of the vehicle dynamics being available. It is noteworthy that a novel technique targeting at the non-square input distribution matrix is employed so as to deal with the under-actuation property of the vehicle dynamics, which extends the adaptive learning control theory from square systems to non-square systems. Moreover, the convergence properties of the RALC algorithm are analysed under the framework of Lyapunov-like theory by virtue of the composite energy function and the λ-norm. The effectiveness of the proposed control scheme is verified by representative simulation examples and comparisons with existing methods

Distributed Model Predictive Control for Heterogeneous Vehicle Platoon with Inter-Vehicular Spacing Constraints

This paper proposes a distributed control scheme for a platoon of heterogeneous vehicles based on the mechanism of model predictive control (MPC). The platoon composes of a group of vehicles interacting with each other via inter-vehicular spacing constraints, to avoid collision and reduce communication latency, and aims to make multiple vehicles driving on the same lane safely with a close range and the same velocity. Each vehicle is subject to both state constraints and input constraints, communicates only with neighboring vehicles, and may not know a priori desired setpoint. We divide the computation of control inputs into several local optimization problems based on each vehicle’s local information. To compute the control input of each vehicle based on local information, a distributed computing method must be adopted and thus the coupled constraint is required to be decoupled. This is achieved by introducing the reference state trajectories from neighboring vehicles for each vehicle and by employing the interactive structure of computing local problems of vehicles with odd indices and even indices. It is shown that the feasibility of MPC optimization problems is achieved at all time steps based on tailored terminal inequality constraints, and the asymptotic stability of each vehicle to the desired trajectory is guaranteed even under a single iteration between vehicles at each time. Finally, a comparison simulation is conducted to demonstrate the effectiveness of the proposed distributed MPC method for heterogeneous vehicle control with respect to normal and extreme scenarios