Approximation techniques for parameter estimation and feedback control for distributed models of large flexible structures

Approximation ideas are discussed that can be used in parameter estimation and feedback control for Euler-Bernoulli models of elastic systems. Focusing on parameter estimation problems, ways by which one can obtain convergence results for cubic spline based schemes for hybrid models involving an elastic cantilevered beam with tip mass and base acceleration are outlined. Sample numerical findings are also presented

Pilot Signal and Channel Estimator Co-Design for Hybrid-Field XL-MIMO

This paper addresses the intricate task of hybrid-field channel estimation in extremely large-scale MIMO (XL-MIMO) systems, critical for the progression of 6G communications. Within these systems, comprising a line-of-sight (LoS) channel component alongside far-field and near-field scattering channel components, our objective is to tackle the channel estimation challenge. We encounter two central hurdles for ensuring dependable sparse channel recovery: the design of pilot signals and channel estimators tailored for hybrid-field communications. To overcome the first challenge, we propose a method to derive optimal pilot signals, aimed at minimizing the mutual coherence of the sensing matrix within the context of compressive sensing (CS) problems. These optimal signals are derived using the alternating direction method of multipliers (ADMM), ensuring robust performance in sparse channel recovery. Additionally, leveraging the acquired optimal pilot signal, we introduce a two-stage channel estimation approach that sequentially estimates the LoS channel component and the hybrid-field scattering channel components. Simulation results attest to the superiority of our co-designed approach for pilot signal and channel estimation over conventional CS-based methods, providing more reliable sparse channel recovery in practical scenarios

Hysteresis-based switching observers for linear systems using quadratic boundedness

Switched-gain observers are investigated for the purpose of estimating the state of linear systems affected by bounded noises. Under mild assumptions, hybrid observers with switching gains are proposed and provided with stability analysis based on quadratic boundedness for the estimation error. Such observers are designed by solving optimization problems aimed at minimizing upper bounds on the estimation error in such a way as to get the smallest invariant set. The effectiveness of the proposed approach is evaluated with some numerical case studies

Hybrid Persistency of Excitation in Adaptive Estimation for Hybrid Systems

We propose a framework to analyze stability for a class of linear non-autonomous hybrid systems, where the continuous evolution of solutions is governed by an ordinary differential equation and the instantaneous changes are governed by a difference equation. Furthermore, the jumps are triggered by the influence of an external hybrid signal. The proposed framework builds upon a generalization of the well-known persistency of excitation (PE) and uniform observability (UO) notions to the realm of hybrid systems. That is, we establish conditions, under which, hybrid PE implies hybrid UO and, in turn, uniform exponential stability (UES) and input-to-state stability (ISS). Our proofs rely on an original statement for hybrid systems, expressed in terms of Lp bounds on the solutions. We demonstrate the utility of our results on generic adaptive estimation problems. The first one concerns the so-called gradient systems, reminiscent of the popular gradient-descent algorithm. The second one pertains to designing adaptive observers/identifiers for a class of hybrid systems that are nonlinear in the input and the output, and linear in the unknown parameters. In both cases, we illustrate through examples that the proposed hybrid framework succeeds when the classic purely continuous- or discrete-time counterparts fail.Comment: 30 pages, 6 figures. This is v2. Some corrections were added, relative to v

Adaptive Estimation and Detection Techniques with Applications

Hybrid systems have been identified as one of the main directions in control theory and attracted increasing attention in recent years due to their huge diversity of engineering applications. Multiplemodel (MM) estimation is the state-of-the-art approach to many hybrid estimation problems. Existing MM methods with fixed structure usually perform well for problems that can be handled by a small set of models. However, their performance is limited when the required number of models to achieve a satisfactory accuracy is large due to time evolution of the true mode over a large continuous space. In this research, variable-structure multiple model (VSMM) estimation was investigated, further developed and evaluated. A fundamental solution for on-line adaptation of model sets was developed as well as several VSMM algorithms. These algorithms have been successfully applied to the fields of fault detection and identification as well as target tracking in this thesis. In particular, an integrated framework to detect, identify and estimate failures is developed based on the VSMM. It can handle sequential failures and multiple failures by sensors or actuators. Fault detection and target maneuver detection can be formulated as change-point detection problems in statistics. It is of great importance to have the quickest detection of such mode changes in a hybrid system. Traditional maneuver detectors based on simplistic models are not optimal and are computationally demanding due to the requirement of batch processing. In this presentation, a general sequential testing procedure is proposed for maneuver detection based on advanced sequential tests. It uses a likelihood marginalization technique to cope with the difficulty that the target accelerations are unknown. The approach essentially utilizes a priori information about the accelerations in typical tracking engagements and thus allows improved detection performance. The proposed approach is applicable to change-point detection problems under similar formulation, such as fault detection

Adaptive Estimation and Detection Techniques with Applications

Hybrid systems have been identified as one of the main directions in control theory and attracted increasing attention in recent years due to their huge diversity of engineering applications. Multiplemodel (MM) estimation is the state-of-the-art approach to many hybrid estimation problems. Existing MM methods with fixed structure usually perform well for problems that can be handled by a small set of models. However, their performance is limited when the required number of models to achieve a satisfactory accuracy is large due to time evolution of the true mode over a large continuous space. In this research, variable-structure multiple model (VSMM) estimation was investigated, further developed and evaluated. A fundamental solution for on-line adaptation of model sets was developed as well as several VSMM algorithms. These algorithms have been successfully applied to the fields of fault detection and identification as well as target tracking in this thesis. In particular, an integrated framework to detect, identify and estimate failures is developed based on the VSMM. It can handle sequential failures and multiple failures by sensors or actuators. Fault detection and target maneuver detection can be formulated as change-point detection problems in statistics. It is of great importance to have the quickest detection of such mode changes in a hybrid system. Traditional maneuver detectors based on simplistic models are not optimal and are computationally demanding due to the requirement of batch processing. In this presentation, a general sequential testing procedure is proposed for maneuver detection based on advanced sequential tests. It uses a likelihood marginalization technique to cope with the difficulty that the target accelerations are unknown. The approach essentially utilizes a priori information about the accelerations in typical tracking engagements and thus allows improved detection performance. The proposed approach is applicable to change-point detection problems under similar formulation, such as fault detection

Novel metaheuristic for parameter estimation in nonlinear dynamic biological systems

BACKGROUND: We consider the problem of parameter estimation (model calibration) in nonlinear dynamic models of biological systems. Due to the frequent ill-conditioning and multi-modality of many of these problems, traditional local methods usually fail (unless initialized with very good guesses of the parameter vector). In order to surmount these difficulties, global optimization (GO) methods have been suggested as robust alternatives. Currently, deterministic GO methods can not solve problems of realistic size within this class in reasonable computation times. In contrast, certain types of stochastic GO methods have shown promising results, although the computational cost remains large. Rodriguez-Fernandez and coworkers have presented hybrid stochastic-deterministic GO methods which could reduce computation time by one order of magnitude while guaranteeing robustness. Our goal here was to further reduce the computational effort without loosing robustness. RESULTS: We have developed a new procedure based on the scatter search methodology for nonlinear optimization of dynamic models of arbitrary (or even unknown) structure (i.e. black-box models). In this contribution, we describe and apply this novel metaheuristic, inspired by recent developments in the field of operations research, to a set of complex identification problems and we make a critical comparison with respect to the previous (above mentioned) successful methods. CONCLUSION: Robust and efficient methods for parameter estimation are of key importance in systems biology and related areas. The new metaheuristic presented in this paper aims to ensure the proper solution of these problems by adopting a global optimization approach, while keeping the computational effort under reasonable values. This new metaheuristic was applied to a set of three challenging parameter estimation problems of nonlinear dynamic biological systems, outperforming very significantly all the methods previously used for these benchmark problems

Measurement errors in visual servoing

Abstract — In recent years, a number of hybrid visual servoing control algorithms have been proposed and evaluated. For some time now, it has been clear that classical control approaches — image and position based —- have some inherent problems. Hybrid approaches try to combine them in order to overcome these problems. However, most of the proposed approaches concentrate mainly on the design of the control law, neglecting the issue of errors resulting from the sensory system. This work deals with the effect of measurement errors in visual servoing. The particular contribution of this paper is the analysis of the propagation of image error through pose estimation and visual servoing control law. We have chosen to investigate the properties of the vision system and their effect to the performance of the control system. Two approaches are evaluated: i) position, and ii) 2 1/2 D visual servoing. We believe that our evaluation offers a valid tool to build and analyze hybrid control systems based on, for example, switching [1] or partitioning [2]. I