Adaptive output regulation for multivariable linear systems via slow identifiers

open3noThis paper deals with the problem of adaptive output regulation for linear multivariable systems. The proposed solution employs a continuous-time identifier that adapts the parameters of the internal model to match the (unknown) exosystem frequencies. Boundedness of the closed-loop trajectories is established and, under a persistence of excitation condition, asymptotic regulation is shown.openMelis A.; Bin M.; Marconi L.Melis A.; Bin M.; Marconi L

Approximate Nonlinear Regulation via Identification-Based Adaptive Internal Models

This article concerns the problem of adaptive output regulation for multivariable nonlinear systems in normal form. We present a regulator employing an adaptive internal model of the exogenous signals based on the theory of nonlinear Luenberger observers. Adaptation is performed by means of discrete-time system identification schemes, in which every algorithm fulfilling some optimality and stability conditions can be used. Practical and approximate regulation results are given relating the prediction capabilities of the identified model to the asymptotic bound on the regulated variables, which become asymptotic whenever a “right” internal model exists in the identifier's model set. The proposed approach, moreover, does not require “high-gain” stabilization actions

Robust controllers design for unknown error and exosystem: a hybid optimization and output regulation approach

This thesis addresses the problem of robustness in control in two main topics: linear output regulation when no knowledge is assumed of the modes of the exosystem, and hybrid gradient-free optimization. A framework is presented for the solution of the first problem, in which asymptotic regulation is achieved in case of a persistence of excitation condition. The stability properties of the closed-loop system are proved under a small-gain argument with no minimum phase assumption. The second part of the thesis addresses, and proposes, a solution to the gradientfree optimization problem, solved by a discrete-time direct search algorithm. The algorithm is shown to convergence to the set of minima of a particular class of non convex functions. It is, then, applied considering it coupled with a continuous-time dynamical system. A hybrid controller is developed in order to guarantee convergence to the set of minima and stability of the interconnection of the two systems. Almost global asymptotic is proven for the proposed hybrid controller. Shown to not be robust to any bounded measurement noise, a robust solution is also proposed. The aim of this thesis is to lay the ground for a solution of the output regulation problem in case the error is unknown, but a proxy optimization function is available. A controller embedding the characteristics of the two proposed approaches, as a main solution to the aforementioned problem, will be the focus of future studies

Adaptive output regulation via nonlinear Luenberger observers

open3noIn Marconi et al. 2007, it was shown that a solution to the output regulation problem for minimum-phase normal forms always exists. That approach, however, yields only an existence result, and no general analytic procedure is known to actually choose the regulator’s degrees of freedom, even for simple problems. In this paper we propose an adaptive regulator that, leveraging the aforementioned existence result, self-tunes online according to an optimization policy. To this aim, the regulator may employ every system identification scheme that fulfills some given strong stability properties, and the asymptotic regulation error is proved to be directly related to the prediction capabilities of the identifier.openBin M.; Bernard P.; Marconi L.Bin M.; Bernard P.; Marconi L

Event-triggered near optimal adaptive control of interconnected systems

Increased interest in complex interconnected systems like smart-grid, cyber manufacturing have attracted researchers to develop optimal adaptive control schemes to elicit a desired performance when the complex system dynamics are uncertain. In this dissertation, motivated by the fact that aperiodic event sampling saves network resources while ensuring system stability, a suite of novel event-sampled distributed near-optimal adaptive control schemes are introduced for uncertain linear and affine nonlinear interconnected systems in a forward-in-time and online manner. First, a novel stochastic hybrid Q-learning scheme is proposed to generate optimal adaptive control law and to accelerate the learning process in the presence of random delays and packet losses resulting from the communication network for an uncertain linear interconnected system. Subsequently, a novel online reinforcement learning (RL) approach is proposed to solve the Hamilton-Jacobi-Bellman (HJB) equation by using neural networks (NNs) for generating distributed optimal control of nonlinear interconnected systems using state and output feedback. To relax the state vector measurements, distributed observers are introduced. Next, using RL, an improved NN learning rule is derived to solve the HJB equation for uncertain nonlinear interconnected systems with event-triggered feedback. Distributed NN identifiers are introduced both for approximating the uncertain nonlinear dynamics and to serve as a model for online exploration. Next, the control policy and the event-sampling errors are considered as non-cooperative players and a min-max optimization problem is formulated for linear and affine nonlinear systems by using zero-sum game approach for simultaneous optimization of both the control policy and the event based sampling instants. The net result is the development of optimal adaptive event-triggered control of uncertain dynamic systems --Abstract, page iv

Generalized recursive least squares: Stability, robustness, and excitation

We study a class of recursive least-squares estimators in an errors-in-variables setting where disturbances affect both the regressor and the regressand variables. We prove the existence and stability of an optimal steady state and robustness with respect to the disturbances in form of input-to-state and input–output stability relative to the unperturbed steady-state trajectories. Depending on the choice of some design parameters, different specific estimators can be realized within the considered class, each of which is associated with a different underlying optimization problem and with different excitation requirements for the unperturbed regressor. As expected, we find that persistence of excitation is associated with uniform, in fact exponential, convergence. In addition, we also show that choices of the design parameters are possible for which convergence and robustness hold without persistence of excitation and with the same asymptotic gain, the only difference being a loss of uniformity in the convergence rate

The reduced order model problem in distributed parameter systems adaptive identification and control

The research concerning the reduced order model problem in distributed parameter systems is reported. The adaptive control strategy was chosen for investigation in the annular momentum control device. It is noted, that if there is no observation spill over, and no model errors, an indirect adaptive control strategy can be globally stable. Recent publications concerning adaptive control are included

Model Identification and Adaptive State Observation for a Class of Nonlinear Systems

In this article, we consider the joint problems of state estimation and model identification for a class of continuous-time nonlinear systems in the output-feedback canonical form. An adaptive observer is proposed that combines an extended high-gain observer and a discrete-time identifier. The extended observer provides the identifier with a dataset permitting the identification of the system model and the identifier adapts the extended observer according to the new estimated model. The design of the identifier is approached as a system identification problem and sufficient conditions are presented that, if satisfied, allow different identification algorithms to be used for the adaptation phase. The cases of recursive least-squares and multiresolution black-box identification via wavelet-based identifiers are specifically addressed. Stability results are provided relating the asymptotic estimation error to the prediction capabilities of the identifier. Robustness with respect to additive disturbances affecting the system equations and measurements is also established in terms of an input-to-state stability property relative to the noiseless estimates

Advances and Trends in Mathematical Modelling, Control and Identification of Vibrating Systems

This book introduces novel results on mathematical modelling, parameter identification, and automatic control for a wide range of applications of mechanical, electric, and mechatronic systems, where undesirable oscillations or vibrations are manifested. The six chapters of the book written by experts from international scientific community cover a wide range of interesting research topics related to: algebraic identification of rotordynamic parameters in rotor-bearing system using finite element models; model predictive control for active automotive suspension systems by means of hydraulic actuators; model-free data-driven-based control for a Voltage Source Converter-based Static Synchronous Compensator to improve the dynamic power grid performance under transient scenarios; an exact elasto-dynamics theory for bending vibrations for a class of flexible structures; motion profile tracking control and vibrating disturbance suppression for quadrotor aerial vehicles using artificial neural networks and particle swarm optimization; and multiple adaptive controllers based on B-Spline artificial neural networks for regulation and attenuation of low frequency oscillations for large-scale power systems. The book is addressed for both academic and industrial researchers and practitioners, as well as for postgraduate and undergraduate engineering students and other experts in a wide variety of disciplines seeking to know more about the advances and trends in mathematical modelling, control and identification of engineering systems in which undesirable oscillations or vibrations could be presented during their operation