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

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

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

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

Adaptive Optimal Control The Thinking Man's GPC

Exploring connections between adaptive control theory and practice, this book treats the techniques of linear quadratic optimal control and estimation (Kalman filtering), recursive identification, linear systems theory and robust arguments

Contributions to automated realtime underwater navigation

Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy at the Massachusetts Institute of Technology and the Woods Hole Oceanographic Institution February 2012This dissertation presents three separate–but related–contributions to the art of underwater navigation. These methods may be used in postprocessing with a human in the loop, but the overarching goal is to enhance vehicle autonomy, so the emphasis is on automated approaches that can be used in realtime. The three research threads are: i) in situ navigation sensor alignment, ii) dead reckoning through the water column, and iii) model-driven delayed measurement fusion. Contributions to each of these areas have been demonstrated in simulation, with laboratory data, or in the field–some have been demonstrated in all three arenas. The solution to the in situ navigation sensor alignment problem is an asymptotically stable adaptive identifier formulated using rotors in Geometric Algebra. This identifier is applied to precisely estimate the unknown alignment between a gyrocompass and Doppler velocity log, with the goal of improving realtime dead reckoning navigation. Laboratory and field results show the identifier performs comparably to previously reported methods using rotation matrices, providing an alignment estimate that reduces the position residuals between dead reckoning and an external acoustic positioning system. The Geometric Algebra formulation also encourages a straightforward interpretation of the identifier as a proportional feedback regulator on the observable output error. Future applications of the identifier may include alignment between inertial, visual, and acoustic sensors. The ability to link the Global Positioning System at the surface to precision dead reckoning near the seafloor might enable new kinds of missions for autonomous underwater vehicles. This research introduces a method for dead reckoning through the water column using water current profile data collected by an onboard acoustic Doppler current profiler. Overlapping relative current profiles provide information to simultaneously estimate the vehicle velocity and local ocean current–the vehicle velocity is then integrated to estimate position. The method is applied to field data using online bin average, weighted least squares, and recursive least squares implementations. This demonstrates an autonomous navigation link between the surface and the seafloor without any dependence on a ship or external acoustic tracking systems. Finally, in many state estimation applications, delayed measurements present an interesting challenge. Underwater navigation is a particularly compelling case because of the relatively long delays inherent in all available position measurements. This research develops a flexible, model-driven approach to delayed measurement fusion in realtime Kalman filters. Using a priori estimates of delayed measurements as augmented states minimizes the computational cost of the delay treatment. Managing the augmented states with time-varying conditional process and measurement models ensures the approach works within the proven Kalman filter framework–without altering the filter structure or requiring any ad-hoc adjustments. The end result is a mathematically principled treatment of the delay that leads to more consistent estimates with lower error and uncertainty. Field results from dead reckoning aided by acoustic positioning systems demonstrate the applicability of this approach to real-world problems in underwater navigation.I have been financially supported by: the National Defense Science and Engineering Graduate (NDSEG) Fellowship administered by the American Society for Engineering Education, the Edwin A. Link Foundation Ocean Engineering and Instrumentation Fellowship, and WHOI Academic Programs office

Tyre curve estimation in slip-controlled braking

Progress in reducing actuator delays in pneumatic brake systems creates an opportunity for advanced anti-lock braking algorithms to be used on heavy goods vehicles. However, these algorithms require knowledge of variables that are impractical to measure directly. This paper introduces a braking force observer and road surface identification algorithms to support a sliding-mode slip controller for air-braked heavy vehicles. Both the force observer and the slip controller are shown to operate robustly under a variety of conditions in quarter-car simulations. A non-linear least-squares algorithm was found to be capable of performing regressions on all the parameters of the tyre model from the University of Michigan Transportation Research Institute when used ‘in the loop’ with the controller and the observer. A recursive least-squares algorithm that is less computationally expensive than the non-linear algorithm was also investigated but gave only reasonable estimates of the tyre model parameters on high-friction smooth roads. The authors would like to thank the members of the Cambridge Vehicle Dynamics Consortium (CVDC), and the Gates Cambridge Trust for their parts in funding this work.This is the author accepted manuscript. The final version is available from Sage via http://dx.doi.org/10.1177/095440701558593

An on-line equivalent system identification scheme for adaptive control

A prime obstacle to the widespread use of adaptive control is the degradation of performance and possible instability resulting from the presence of unmodeled dynamics. The approach taken is to explicitly include the unstructured model uncertainty in the output error identification algorithm. The order of the compensator is successively increased by including identified modes. During this model building stage, heuristic rules are used to test for convergence prior to designing compensators. Additionally, the recursive identification algorithm as extended to multi-input, multi-output systems. Enhancements were also made to reduce the computational burden of an algorithm for obtaining minimal state space realizations from the inexact, multivariate transfer functions which result from the identification process. A number of potential adaptive control applications for this approach are illustrated using computer simulations. Results indicated that when speed of adaptation and plant stability are not critical, the proposed schemes converge to enhance system performance