Adaptive Stochastic Systems: Estimation, Filtering, And Noise Attenuation

This dissertation investigates problems arising in identification and control of stochastic systems. When the parameters determining the underlying systems are unknown and/or time varying, estimation and adaptive filter- ing are invoked to to identify parameters or to track time-varying systems. We begin by considering linear systems whose coefficients evolve as a slowly- varying Markov Chain. We propose three families of constant step-size (or gain size) algorithms for estimating and tracking the coefficient parameter: Least-Mean Squares (LMS), Sign-Regressor (SR), and Sign-Error (SE) algorithms. The analysis is carried out in a multi-scale framework considering the relative size of the gain (rate of adaptation) to the transition rate of the Markovian system parameter. Mean-square error bounds are established, and weak convergence methods are employed to show the convergence of suitably interpolated sequences of estimates to solutions of systems of ordinary and stochastic differential equations with regime switching. Next we consider problems in noise attenuation in systems with unmodeled dynamics and stochastic signal errors. A robust two-phase design procedure is developed which first estimates the signal in a simplified form, and then applies a control to tune out the noise. Worst-case error bounds are derived in terms of the unmodeled dynamics and variances of the disturbance and measurement errors

Robustness, Weak Stability, and Stability in Distribution of Adaptive Filteringalgorithms Under Model Mismatch

This work is concerned with robustness, convergence, and stability of adaptive filtering (AF) type algorithms in the presence of model mismatch. The algorithms under consideration are recursive and have inherent multiscale structure. They can be considered as dynamic systems, in which the `state\u27 changes much more slowly than the perturbing noise. Beyond the existing results on adaptive algorithms, model mismatch significantly affects convergence properties of AF algorithms, raising issues of algorithm robustness. Weak convergence and weak stability (i.e., recurrence) under model mismatch are derived. Based on the limiting stochastic differential equations of suitably scaled iterates, stability in distribution is established. Then algorithms with decreasing step sizes and their convergence properties are examined. When input signals are large, identification bias due to model mismatch will become large and unacceptable. Methods for reducing such bias are introduced when the identified models are used in regulation problems

Modeling and identification of an RRR-robot

A dynamic model of a robot with 3 rotational degrees of freedom is derived in closed form. A systematic procedure for estimation of model dynamic parameters is suggested. It consists of the following steps: (i) identification of friction model parameters for each joint; (ii) calculation of optimal exciting trajectories, required for estimation of the remaining dynamic model parameters; (iii) estimation of these parameters using a least-squares method. The estimated model satisfactory reconstructs experimental control signals, justifying its use in model-based nonlinear control

Tools for Nonlinear Control Systems Design

This is a brief statement of the research progress made on Grant NAG2-243 titled "Tools for Nonlinear Control Systems Design", which ran from 1983 till December 1996. The initial set of PIs on the grant were C. A. Desoer, E. L. Polak and myself (for 1983). From 1984 till 1991 Desoer and I were the Pls and finally I was the sole PI from 1991 till the end of 1996. The project has been an unusually longstanding and extremely fruitful partnership, with many technical exchanges, visits, workshops and new avenues of investigation begun on this grant. There were student visits, long term.visitors on the grant and many interesting joint projects. In this final report I will only give a cursory description of the technical work done on the grant, since there was a tradition of annual progress reports and a proposal for the succeeding year. These progress reports cum proposals are attached as Appendix A to this report. Appendix B consists of papers by me and my students as co-authors sorted chronologically. When there are multiple related versions of a paper, such as a conference version and journal version they are listed together. Appendix C consists of papers by Desoer and his students as well as 'solo' publications by other researchers supported on this grant similarly chronologically sorted

Validation and Verification of Future Integrated Safety-Critical Systems Operating under Off-Nominal Conditions

Loss of control remains one of the largest contributors to aircraft fatal accidents worldwide. Aircraft loss-of-control accidents are highly complex in that they can result from numerous causal and contributing factors acting alone or (more often) in combination. Hence, there is no single intervention strategy to prevent these accidents and reducing them will require a holistic integrated intervention capability. Future onboard integrated system technologies developed for preventing loss of vehicle control accidents must be able to assure safe operation under the associated off-nominal conditions. The transition of these technologies into the commercial fleet will require their extensive validation and verification (V and V) and ultimate certification. The V and V of complex integrated systems poses major nontrivial technical challenges particularly for safety-critical operation under highly off-nominal conditions associated with aircraft loss-of-control events. This paper summarizes the V and V problem and presents a proposed process that could be applied to complex integrated safety-critical systems developed for preventing aircraft loss-of-control accidents. A summary of recent research accomplishments in this effort is also provided

Invariant template matching in systems with spatiotemporal coding: a vote for instability

We consider the design of a pattern recognition that matches templates to images, both of which are spatially sampled and encoded as temporal sequences. The image is subject to a combination of various perturbations. These include ones that can be modeled as parameterized uncertainties such as image blur, luminance, translation, and rotation as well as unmodeled ones. Biological and neural systems require that these perturbations be processed through a minimal number of channels by simple adaptation mechanisms. We found that the most suitable mathematical framework to meet this requirement is that of weakly attracting sets. This framework provides us with a normative and unifying solution to the pattern recognition problem. We analyze the consequences of its explicit implementation in neural systems. Several properties inherent to the systems designed in accordance with our normative mathematical argument coincide with known empirical facts. This is illustrated in mental rotation, visual search and blur/intensity adaptation. We demonstrate how our results can be applied to a range of practical problems in template matching and pattern recognition.Comment: 52 pages, 12 figure

Model Reference Adaptive Control Laws: Application to Nonlinear Aeroelastic Systems

Nonlinear Aeroelastic Control has been a research topic of great interest for the past few decades. Dierent approaches has been attempted aiming to obtain better accuracy in the model dynamics description and better control performance. As far as the aeroelastic mathematical model is concerned, the scientic world converged in the use of a bi-dimension, two degree of freedom, plunging and pitching, wing section model, of which the bigger advantages are to be reproducible experimentally with an appropriate wind tunnel apparatus and to allow LCO (Limit Cycle Oscillation) exhibition at low values of wind speed, facilitating parametric studies of the nonlinear aeroelastic system and its control architecture. A parametric analysis of the linearized system, typical of aircraft ight dynamic studies, is employed to verify and validate the model dynamic properties dependency, focusing in particular to the eect of stiness reduction as means of failure simulation. In fact, despite of the recent years ourishing literature on aeroelastic adaptive controls, there is a noted lack of robustness and sensitivity analysis with respect to structural proprieties degradation which might be associated with a structural failure. Structural mode frequencies and aeroelastic response, including Limit Cycle Oscillations (LCOs) characteristics, are signicantly aected by changes in stiness. This leads to a great interest in evaluating and comparing the adaptation capabilities of dierent control architectures subjected to large plant uncertainties and unmodeled dynamics. Motivated by the constantly increasing diusion of the new L adaptive control theory, developed for the control of uncertain non-autonomous nonlinear systems, and by the fact that its application to aeroelasticity is in its infancy, a deep investigation of this control scheme properties and performance drew our attention. The new control theory is conceptually similar to the Model Reference Adaptive Control (MRAC) theory to which has often been compared indeed for performance evaluation purpose. In this dissertation, a comprehensive analysis of the new control theory is obtained by performance evaluation and comparison of four dierent control schemes, two MRAC and two L 1 , focusing the attention on the states and control input time response, adaptive law parameters' convergence, transient evolution and fastness, and robustness in terms of tolerance of uncertainties in o-design conditions. The objective is pursued by re- writing the aeroelastic model nonlinear equations of motion in an amenable form to the development of the four dierent control laws. The control laws are then derived for the appropriate class of plant which the system belongs to, and design parameter obtained, when necessary, following the mathematical formulation of the control theories developers. A simulation model is employed to carry out the numerical analysis and to outline pros and cons of each architecture, to obtain as nal result the architecture that better ts the nonlinear aeroelastic problem proposed. This methodology is used to guarantee a certain robustness in controlling a novel actuation architecture, developed for utter suppression of slender/highly exible wing, based on a coordinated multiple spoiler stripe, located at fteen percent of the mean aerodynamic chord. The control actuation system design, manufacturing and experimental wind tunnel test is part of the dissertation. Two dierent experimental setup are developed for two dierent purpose. First, a six-axis force balance test is carried out to validate the numerical aerodynamic results obtained during the validation process, and to collect the aerodynamic coecient date base useful for the development of the simulation model of the novel architecture. The second experimental apparatus, is a two degree of freedom, plunging/pitching, system on which the prototyped wing section is mounted to obtain LCO aeroelastic response during wind tunnel experiment. The nonlinear aeroelastic mathematical formulation is modied to take into account of the novel actuation architecture and, coupled with the more robust MRAC control laws derived for the previous model, serves as benchmark for properties assessment of the overall architecture, for utter suppression. The novel control actuation architecture proposed, is successfully tested in wind tunnel experimentation conrming the validity of the proposed solution. This dissertation provides a step forward to the denition of certain MRAC control schemes properties, and together provides a novel actuation solution for utter suppression which demonstrates to be a viable alternative to classical leading and/or trailing-edge ap architecture or to be used as redundancy to them

Large deviations of stochastic systems and applications

This dissertation focuses on large deviations of stochastic systems with applications to optimal control and system identification. It encompasses analysis of two-time-scale Markov processes and system identification with regular and quantized data. First, we develops large deviations principles for systems driven by continuous-time Markov chains with twotime scales and related optimal control problems. A distinct feature of our setup is that the Markov chain under consideration is time dependent or inhomogeneous. The use of two time-scale formulation stems from the effort of reducing computational complexity in a wide variety of applications in control, optimization, and systems theory. Starting with a rapidly fluctuating Markovian system, under irreducibility conditions, both large deviations upper and lower bounds are established first for a fixed terminal time and then for time-varying dynamic systems. Then the results are applied to certain dynamic systems and LQ control problems. Second, we study large deviations for identifications systems. Traditional system identification concentrates on convergence and convergence rates of estimates in mean squares, in distribution, or in a strong sense. For system diagnosis and complexity analysis, however, it is essential to understand the probabilities of identification errors over a finite data window. This paper investigates identification errors in a large deviations framework. By considering both space complexity in terms of quantization levels and time complexity with respect to data window sizes, this study provides a new perspective to understand the fundamental relationship between probabilistic errors and resources that represent data sizes in computer algorithms, sample sizes in statistical analysis, channel bandwidths in communications, etc. This relationship is derived by establishing the large deviations principle for quantized identification that links binary-valued data at one end and regular sensors at the other. Under some mild conditions, we obtain large deviations upper and lower bounds. Our results accommodate independent and identically distributed noise sequences, as well as more general classes of mixing-type noise sequences. Numerical examples are provided to illustrate the theoretical results

Investigations of Model-Free Sliding Mode Control Algorithms including Application to Autonomous Quadrotor Flight

Sliding mode control is a robust nonlinear control algorithm that has been used to implement tracking controllers for unmanned aircraft systems that are robust to modeling uncertainty and exogenous disturbances, thereby providing excellent performance for autonomous operation. A significant advance in the application of sliding mode control for unmanned aircraft systems would be adaptation of a model-free sliding mode control algorithm, since the most complex and time-consuming aspect of implementation of sliding mode control is the derivation of the control law with incorporation of the system model, a process required to be performed for each individual application of sliding mode control. The performance of four different model-free sliding mode control algorithms was compared in simulation using a variety of aerial system models and real-world disturbances (e.g. the effects of discretization and state estimation). The two best performing algorithms were shown to exhibit very similar behavior. These two algorithms were implemented on a quadrotor (both in simulation and using real-world hardware) and the performance was compared to a traditional PID-based controller using the same state estimation algorithm and control setup. Simulation results show the model-free sliding mode control algorithms exhibit similar performance to PID controllers without the tedious tuning process. Comparison between the two model-free sliding mode control algorithms showed very similar performance as measured by the quadratic means of tracking errors. Flight testing showed that while a model-free sliding mode control algorithm is capable of controlling realworld hardware, further characterization and significant improvements are required before it is a viable alternative to conventional control algorithms. Large tracking errors were observed for both the model-free sliding mode control and PID based flight controllers and the performance was characterized as unacceptable for most applications. The poor performance of both controllers suggests tracking errors could be attributed to errors in state estimation, which effectively introduce unknown dynamics into the feedback loop. Further testing with improved state estimation would allow for more conclusions to be drawn about the performance characteristics of the model-free sliding mode control algorithms