Robust Nonlinear Output Regulation by Identification Tools

The present thesis focuses on the problem of robust output regulation for minimum phase nonlinear systems by means of identification techniques. Given a controlled plant and an exosystem (an autonomous system that generates eventual references or disturbances), the control goal is to design a proper regulator able to process the only measure available, i.e the error/output variable, in order to make it asymptotically vanishing. In this context, such a regulator can be designed following the well known “internal model principle” that states how it is possible to achieve the regulation objective by embedding a replica of the exosystem model in the controller structure. The main problem shows up when the exosystem model is affected by parametric or structural uncertainties, in this case, it is not possible to reproduce the exact behavior of the exogenous system in the regulator and then, it is not possible to achieve the control goal. In this work, the idea is to find a solution to the problem trying to develop a general framework in which coexist both a standard regulator and an estimator able to guarantee (when possible) the best estimate of all uncertainties present in the exosystem in order to give “robustness” to the overall control loop.

Symbolic Dynamics Analysis: a new methodology for foetal heart rate variability analysis

Cardiotocography (CTG) is a widespread foetal diagnostic methods. However, it lacks of objectivity and reproducibility since its dependence on observer's expertise. To overcome these limitations, more objective methods for CTG interpretation have been proposed. In particular, many developed techniques aim to assess the foetal heart rate variability (FHRV). Among them, some methodologies from nonlinear systems theory have been applied to the study of FHRV. All the techniques have proved to be helpful in specific cases. Nevertheless, none of them is more reliable than the others. Therefore, an in-depth study is necessary. The aim of this work is to deepen the FHRV analysis through the Symbolic Dynamics Analysis (SDA), a nonlinear technique already successfully employed for HRV analysis. Thanks to its simplicity of interpretation, it could be a useful tool for clinicians. We performed a literature study involving about 200 references on HRV and FHRV analysis; approximately 100 works were focused on non-linear techniques. Then, in order to compare linear and non-linear methods, we carried out a multiparametric study. 580 antepartum recordings of healthy fetuses were examined. Signals were processed using an updated software for CTG analysis and a new developed software for generating simulated CTG traces. Finally, statistical tests and regression analyses were carried out for estimating relationships among extracted indexes and other clinical information. Results confirm that none of the employed techniques is more reliable than the others. Moreover, in agreement with the literature, each analysis should take into account two relevant parameters, the foetal status and the week of gestation. Regarding the SDA, results show its promising capabilities in FHRV analysis. It allows recognizing foetal status, gestation week and global variability of FHR signals, even better than other methods. Nevertheless, further studies, which should involve even pathological cases, are necessary to establish its reliability.

Nonlinear Control Strategies for Cooperative Control of Multi-Robot Systems

This thesis deals with distributed control strategies for cooperative control of multi-robot systems. Specifically, distributed coordination strategies are presented for groups of mobile robots. The formation control problem is initially solved exploiting artificial potential fields. The purpose of the presented formation control algorithm is to drive a group of mobile robots to create a completely arbitrarily shaped formation. Robots are initially controlled to create a regular polygon formation. A bijective coordinate transformation is then exploited to extend the scope of this strategy, to obtain arbitrarily shaped formations. For this purpose, artificial potential fields are specifically designed, and robots are driven to follow their negative gradient. Artificial potential fields are then subsequently exploited to solve the coordinated path tracking problem, thus making the robots autonomously spread along predefined paths, and move along them in a coordinated way. Formation control problem is then solved exploiting a consensus based approach. Specifically, weighted graphs are used both to define the desired formation, and to implement collision avoidance. As expected for consensus based algorithms, this control strategy is experimentally shown to be robust to the presence of communication delays. The global connectivity maintenance issue is then considered. Specifically, an estimation procedure is introduced to allow each agent to compute its own estimate of the algebraic connectivity of the communication graph, in a distributed manner. This estimate is then exploited to develop a gradient based control strategy that ensures that the communication graph remains connected, as the system evolves. The proposed control strategy is developed initially for single-integrator kinematic agents, and is then extended to Lagrangian dynamical systems.

Nonlinear constrained and saturated control of power electronics and electromechanical systems

Power electronic converters are extensively adopted for the solution of timely issues, such as power quality improvement in industrial plants, energy management in hybrid electrical systems, and control of electrical generators for renewables. Beside nonlinearity, this systems are typically characterized by hard constraints on the control inputs, and sometimes the state variables. In this respect, control laws able to handle input saturation are crucial to formally characterize the systems stability and performance properties. From a practical viewpoint, a proper saturation management allows to extend the systems transient and steady-state operating ranges, improving their reliability and availability. The main topic of this thesis concern saturated control methodologies, based on modern approaches, applied to power electronics and electromechanical systems. The pursued objective is to provide formal results under any saturation scenario, overcoming the drawbacks of the classic solution commonly applied to cope with saturation of power converters, and enhancing performance. For this purpose two main approaches are exploited and extended to deal with power electronic applications: modern anti-windup strategies, providing formal results and systematic design rules for the anti-windup compensator, devoted to handle control saturation, and “one step” saturated feedback design techniques, relying on a suitable characterization of the saturation nonlinearity and less conservative extensions of standard absolute stability theory results. The first part of the thesis is devoted to present and develop a novel general anti-windup scheme, which is then specifically applied to a class of power converters adopted for power quality enhancement in industrial plants. In the second part a polytopic differential inclusion representation of saturation nonlinearity is presented and extended to deal with a class of multiple input power converters, used to manage hybrid electrical energy sources. The third part regards adaptive observers design for robust estimation of the parameters required for high performance control of power systems.