Multiple model adaptive control of functional electrical stimulation

This paper establishes the feasibility of multiple-model switched adaptive control to regulate functional electrical stimulation for upper limb stroke rehabilitation. An estimation-based multiple-model switched adaptive control (EMMSAC) framework for nonlinear time-invariant systems is described, and extensions are presented to enable application to time-varying Hammerstein structures that can accurately represent the stimulated arm. A principled design procedure is then developed to construct both a suitable set of candidate models from experimental data and a corresponding set of tracking controllers. The procedure is applied to a sample of able-bodied young participants to produce a general EMMSAC controller. This is then applied to a different sample of the population during an isometric nonvoluntary trajectory tracking task. The results show that it is possible to eliminate model identification while employing closed-loop controllers that maintain high performance in the presence of rapidly changing system dynamics. This paper hence addresses critical limitations to effective stroke rehabilitation in a clinical setting

Identification of nonlinear interconnected systems

This thesis was submitted for the degree of Master of Philosophy and awarded by Brunel University.In this work we address the problem of identifying a discrete-time nonlinear system composed of a linear dynamical system connected to a static nonlinear component. We use linear fractional representation to provide a united framework for the identification of two classes of such systems. The first class consists of discrete-time systems consists of a linear time invariant system connected to a continuous nonlinear static component. The identification problem of estimating the unknown parameters of the linear system and simultaneously fitting a math order spline to the nonlinear data is addressed. A simple and tractable algorithm based on the separable least squares method is proposed for estimating the parameters of the linear and the nonlinear components. We also provide a sufficient condition on data for consistency of the identification algorithm. Numerical examples illustrate the performance of the algorithm. Further, we examine a second class of systems that may involve a nonlinear static element of a more complex structure. The nonlinearity may not be continuous and is approximated by piecewise a±ne maps defined on different convex polyhedra, which are defined by linear combinations of lagged inputs and outputs. An iterative identification procedure is proposed, which alternates the estimation of the linear and the nonlinear subsystems. Standard identification techniques are applied to the linear subsystem, whereas recently developed piecewise affine system identification techniques are employed for the estimation of the nonlinear component. Numerical examples show that the proposed procedure is able to successfully profit from the knowledge of the interconnection structure, in comparison with a direct black box identification of the piecewise a±ne system.Funding was obtained as a Marie Curie Early Stage Researcher Training fellowship, under the NET-ACE project (MEST-CT-2004-6724)

Adaptive Input Reconstruction with Application to Model Refinement, State Estimation, and Adaptive Control.

Input reconstruction is the process of using the output of a system to estimate its input. In some cases, input reconstruction can be accomplished by determining the output of the inverse of a model of the system whose input is the output of the original system. Inversion, however, requires an exact and fully known analytical model, and is limited by instabilities arising from nonminimum-phase zeros. The main contribution of this work is a novel technique for input reconstruction that does not require model inversion. This technique is based on a retrospective cost, which requires a limited number of Markov parameters. Retrospective cost input reconstruction (RCIR) does not require knowledge of nonminimum-phase zero locations or an analytical model of the system. RCIR provides a technique that can be used for model refinement, state estimation, and adaptive control. In the model refinement application, data are used to refine or improve a model of a system. It is assumed that the difference between the model output and the data is due to an unmodeled subsystem whose interconnection with the modeled system is inaccessible, that is, the interconnection signals cannot be measured and thus standard system identification techniques cannot be used. Using input reconstruction, these inaccessible signals can be estimated, and the inaccessible subsystem can be fitted. We demonstrate input reconstruction in a model refinement framework by identifying unknown physics in a space weather model and by estimating an unknown film growth in a lithium ion battery. The same technique can be used to obtain estimates of states that cannot be directly measured. Adaptive control can be formulated as a model-refinement problem, where the unknown subsystem is the idealized controller that minimizes a measured performance variable. Minimal modeling input reconstruction for adaptive control is useful for applications where modeling information may be difficult to obtain. We demonstrate adaptive control of a seeker-guided missile with unknown aerodynamics.Ph.D.Aerospace EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/91520/1/amdamato_1.pd

Various nonlinear models and their identification, equalization and linearization

System identification is a pre-requisite to analysis of a dynamic system and design of an appropriate controller for improving its performance. The more accurate the mathematical model identified for a system, the more effective will be the controller designed for it. The identification of nonlinear systems is a topic which has received considerable attention over the last two decades. Generally speaking, when it is difficult to model practical systems by mathematical analysis method, system identification may be an efficient way to overcome the shortage of mechanism analysis method. The goal of the modeling is to find a simple and efficient model which is in accord with the practical system. In many cases, linear models are not suitable to present these systems and nonlinear models have to be considered. Since there are nonlinear effects in practical systems, e.g. harmonic generation, intermediation, desensitization, gain expansion and chaos, we can infer that most control systems are nonlinear. Nonlinear models are more widely used in practice, because most phenomena are nonlinear in nature. Indeed, for many dynamic systems the use of nonlinear models is often of great interest and generally characterizes adequately physical processes over their whole operating range. Thus, accuracy and performance of the control law increase significantly. Therefore, nonlinear system modeling is much more important than linear system identification. We will deal with various nonlinear models and their processing

Pre-distortion algorithms implemented in fixed-point arithmetic

[SPA]En la actualidad se requiere que los sistemas de comunicaciones inal ambricas proporcionen altas tasas de datos junto con una gran calidad. A n de conseguir esto, se emplean t ecnicas de transmisi on y modulaci on espectralmente e cientes, lo que resulta en se~nales con grandes uctuaciones en la envolvente y, por tanto, un PAPR (Peak-to-Average Power Ratio) alto. Adem as, debido a exigencias de e ciencia de potencia, los ampli - cadores operan en las inmediaciones de la regi on de saturaci on. Desafortunadamente, esto conlleva un comportamiento no lineal del ampli cador, lo que introduce distorsiones no lineales. Estas distorsiones provocan, por un lado, una degradaci on de la se~nal transmitida y, por otro, un ensanchamiento en el espectro del ancho de banda del canal, y, consecuentemente una interferencia en los canales de transmisi on adyacentes. La pre-distorsi on digital es una t ecnica empleada para compensar las distorsiones introducidas por el ampli cador, de manera que el sistema resultante opere como una etapa de ampli caci on lineal y e ciente. Esta soluci on reduce el tama~no de la unidad de transmisi on y ayuda a reducir costes, especialmente si se combina con otras t ecnicas de linealizaci on. Como el pre-distorsionador ha de predecir la no linealidad introducida por el ampli cador, la pre-distorsi on puede considerarse un problema de modelado de comportamiento. En este proyecto se consideran varios esquemas de pre-distorsi on basados en modelado del comportamiento ya propuestos en la literatura. Desde el modelo de polinomios sin memoria hasta las series truncadas de Volterra, un modelo m as general y con mayor coste computacional, para terminar con decomposed piecewise Volterra series propuesto por Zhu en [1], el cual permite reducir el coste computacional mediante la poda selectiva de las series truncadas de Volterra. El objetivo principal de este trabajo es evaluar la implementaci on en coma ja de dichos algoritmos. Para ello, los algoritmos han sido implementados en MATLAB tanto en coma ja como en coma otante, donde la ultima se usa como referencia para la comparaci on de su rendimiento. Adem as, en el proyecto se presenta una revisi on detallada de la teor a de los modelos que se tratan. Los algoritmos han sido evaluados mediante un modelo de referencia no-lineal: el modelo Saleh para los algoritmos sin memoria y el modelo Hammerstein para los casos con memoria. Los resultados de las simulaciones muestran que el modelo decomposed piecewise Volterra utilizando el modelo de reducci on din amica de Volterra como sub-modelo, mejora el rendimiento de los modelos tradicionales. [ENG]Nowadays, wireless communications systems are required to provide high data-rates with high quality. In order to achieve this, spectrally e cient transmission techniques are employed which rely on signals with large envelope uctuations. Moreover, due to power e ciency demands power ampli ers have to work close to their saturation region. Unfortunately, their resulting nonlinear behaviour introduces nonlinear distortions. By this, on the one hand the transmitted signal is degraded, on the other hand, it causes spectral widening beyond the channel bandwidth, and consequently interference with neighbouring transmission channels. Digital pre-distortion is a technique used to compensate the distortions introduced by the power ampli er, so that the overall system operates as a linear yet e cient amplifying stage. This solution reduces the transmission unit size and allows for cutting energy costs, especially if combined with other linearization techniques. As the pre-distorter has to predict the nonlinearity introduced by the power ampli er, pre-distortion can be considered a behavioural modeling problem. In this thesis, we consider several pre-distortion schemes found in literature that are based on behavioural modeling. Starting with the memoryless polynomial model, we move on to the general but computationally expensive truncated Volterra series and, nally end up with the decomposed piecewise Volterra series proposed by Zhu in [1] that allow to reduce the computational complexity by selectively pruning of the truncated Volterra series. The main goal of this work is to evaluate the xed-point implementation of the algorithms. In order to do so the algorithms are implmented in MATLAB in xed-point arithmetic, as well as in oating-point arithmetic; where the latter is used as reference for a comparison of performance. In addition, a detailed review of the theory is presented in this work. The algorithms are evaluated with a nonlinear reference model: a saleh model for the memoryless case and a hammerstein model for the memory cases. Simulation results show that the decomposed piecewise Volterra model employing the dynamic deviation reduction-based Volterra model as sub-model outperforms the traditional models.Escuela Técnica Superior de Ingeniería de TelecomunicaciónUniversidad Politécnica de Cartagen

Bayes meets Bach: applications of Bayesian statistics to audio restoration

Memoryless nonlinear distortion can be present in audio signals, from recording to reproduction: bad quality or amateurishly operated equipments, physically degraded media and low quality reproducing devices are some examples where nonlinearities can naturally appear. Another quite common defect in old recordings are the long pulses, caused in general by the reproduction of disks with deep scratches or severely degraded magnetic tapes. Such defects are characterized by an initial discontinuity in the waveform, followed by a low-frequency transient of long duration. In both cases audible artifacts can be created, causing an unpleasant experience to the listener. It is then important to develop techniques to mitigate such defects, having at hand only the degraded signal, in a way to recover the original signal. In this thesis, techniques to deal with both problems are presented: the restoration of nonlinearly degraded recordings is tackled in a Bayesian context, considering both autoregressive models and sparsity in the DCT domain for the original signal, as well as through a deterministic solution also based on sparsity; for the suppression of long pulses, a parametric approach is revisited with the addition of an efficient initialization procedure, and a nonparametric modeling via Gaussian process is also presented.Distorções não-lineares podem aparecer em sinais de áudio desde o momento da sua gravação até a posterior reprodução: equipamentos precários ou operados de maneira indevida, mídias fisicamente degradadas e baixa qualidade dos aparelhos de reprodução são somente alguns exemplos onde não-linearidades podem aparecer de modo natural. Outro defeito bastante comum em gravações antigas são os pulsos longos, em geral causados pela reprodução de discos com arranhões muito profundos ou fitas magnéticas severamente degradadas. Tais defeitos são caracterizados por uma descontinuidade inicial na forma de onda, seguida de um transitório de baixa frequência e longa duração. Em ambos os casos, artefatos auditivos podem ser criados, causando assim uma experiência ruim para o ouvinte. E importante então desenvolver técnicas para mitigar tais efeitos, tendo como base somente uma versão do sinal degradado, de modo a recuperar o sinal original não degradado. Nessa tese são apresentadas técnicas para lidar com esses dois problemas: o problema de restaurar gravações corrompidas com distorções não-lineares é abordado em um contexto bayesiano, considerando tanto modelos autorregressivos quanto de esparsidade no domínio da DCT para o sinal original, bem como por uma solução determinística também em usando esparsidade; para a supressão de pulsos longos, uma abordagem paramétrica é revisitada, junto com o acréscimo de um eficiente procedimento de inicialização, sendo também apresentada uma abordagem não-paramétricausando processos gaussianos