Robust Adaptive Control with Applications to Multi-Agent Systems and Mobile Robotics

This thesis deals with robust adaptive control and its applications, and it is divided into three main parts. The first part is about the design of robust estimation algorithms based on recursive least squares. First, we present an estimator for the frequencies of biased multi-harmonic signals, and then an algorithm for distributed estimation of an unknown parameter over a network of adaptive agents. In the second part of this thesis, we consider a cooperative control problem over uncertain networks of linear systems and Kuramoto systems, in which the agents have to track the reference generated by a leader exosystem. Since the reference signal is not available to each network node, novel distributed observers are designed so as to reconstruct the reference signal locally for each agent, and therefore decentralizing the problem. In the third and final part of this thesis, we consider robust estimation tasks for mobile robotics applications. In particular, we first consider the problem of slip estimation for agricultural tracked vehicles. Then, we consider a search and rescue application in which we need to drive an unmanned aerial vehicle as close as possible to the unknown (and to be estimated) position of a victim, who is buried under the snow after an avalanche event. In this thesis, robustness is intended as an input-to-state stability property of the proposed identifiers (sometimes referred to as adaptive laws), with respect to additive disturbances, and relative to a steady-state trajectory that is associated with a correct estimation of the unknown parameter to be found.

Seizure prediction and control in epilepsy

The first part of my thesis presents an overview of the different approaches used in the past two decades in the attempt to forecast epileptic seizure on the basis of intracranial and scalp EEG. Past research could reveal some value of linear and nonlinear algorithms to detect EEG features changing over different phases of the epileptic cycle. However, their exact value for seizure prediction, in terms of sensitivity and specificity, is still discussed and has to be evaluated. In particular, the monitored EEG features may fluctuate with the vigilance state and lead to false alarms. Recently, such a dependency on vigilance states has been reported for some seizure prediction methods, suggesting a reduced reliability. An additional factor limiting application and validation of most seizure-prediction techniques is their computational load. For the first time, the reliability of permutation entropy [PE] was verified in seizure prediction on scalp EEG data, contemporarily controlling for its dependency on different vigilance states. PE was recently introduced as an extremely fast and robust complexity measure for chaotic time series and thus suitable for online application even in portable systems. The capability of PE to distinguish between preictal and interictal state has been demonstrated using Receiver Operating Characteristics (ROC) analysis. Correlation analysis was used to assess dependency of PE on vigilance states. Scalp EEG-Data from two right temporal epileptic lobe (RTLE) patients and from one patient with right frontal lobe epilepsy were analysed. The last patient was included only in the correlation analysis, since no datasets including seizures have been available for him. The ROC analysis showed a good separability of interictal and preictal phases for both RTLE patients, suggesting that PE could be sensitive to EEG modifications, not visible on visual inspection, that might occur well in advance respect to the EEG and clinical onset of seizures. However, the simultaneous assessment of the changes in vigilance showed that: a) all seizures occurred in association with the transition of vigilance states; b) PE was sensitive in detecting different vigilance states, independently of seizure occurrences. Due to the limitations of the datasets, these results cannot rule out the capability of PE to detect preictal states. However, the good separability between pre- and interictal phases might depend exclusively on the coincidence of epileptic seizure onset with a transition from a state of low vigilance to a state of increased vigilance. The finding of a dependency of PE on vigilance state is an original finding, not reported in literature, and suggesting the possibility to classify vigilance states by means of PE in an authomatic and objectic way. The second part of my thesis provides the description of a novel behavioral task based on motor imagery skills, firstly introduced (Bruzzo et al. 2007), in order to study mental simulation of biological and non-biological movement in paranoid schizophrenics (PS). Immediately after the presentation of a real movement, participants had to imagine or re-enact the very same movement. By key release and key press respectively, participants had to indicate when they started and ended the mental simulation or the re-enactment, making it feasible to measure the duration of the simulated or re-enacted movements. The proportional error between duration of the re-enacted/simulated movement and the template movement were compared between different conditions, as well as between PS and healthy subjects. Results revealed a double dissociation between the mechanisms of mental simulation involved in biological and non-biologial movement simulation. While for PS were found large errors for simulation of biological movements, while being more acurate than healthy subjects during simulation of non-biological movements. Healthy subjects showed the opposite relationship, making errors during simulation of non-biological movements, but being most accurate during simulation of non-biological movements. However, the good timing precision during re-enactment of the movements in all conditions and in both groups of participants suggests that perception, memory and attention, as well as motor control processes were not affected. Based upon a long history of literature reporting the existence of psychotic episodes in epileptic patients, a longitudinal study, using a slightly modified behavioral paradigm, was carried out with two RTLE patients, one patient with idiopathic generalized epilepsy and one patient with extratemporal lobe epilepsy. Results provide strong evidence for a possibility to predict upcoming seizures in RTLE patients behaviorally. In the last part of the thesis it has been validated a behavioural strategy based on neurobiofeedback training, to voluntarily control seizures and to reduce there frequency. Three epileptic patients were included in this study. The biofeedback was based on monitoring of slow cortical potentials (SCPs) extracted online from scalp EEG. Patients were trained to produce positive shifts of SCPs. After a training phase patients were monitored for 6 months in order to validate the ability of the learned strategy to reduce seizure frequency. Two of the three refractory epileptic patients recruited for this study showed improvements in self-management and reduction of ictal episodes, even six months after the last training session.

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.

Analysis of optimal control problems for the incompressible MHD equations and implementation in a finite element multiphysics code

This thesis deals with the study of optimal control problems for the incompressible Magnetohydrodynamics (MHD) equations. Particular attention to these problems arises from several applications in science and engineering, such as fission nuclear reactors with liquid metal coolant and aluminum casting in metallurgy. In such applications it is of great interest to achieve the control on the fluid state variables through the action of the magnetic Lorentz force. In this thesis we investigate a class of boundary optimal control problems, in which the flow is controlled through the boundary conditions of the magnetic field. Due to their complexity, these problems present various challenges in the definition of an adequate solution approach, both from a theoretical and from a computational point of view. In this thesis we propose a new boundary control approach, based on lifting functions of the boundary conditions, which yields both theoretical and numerical advantages. With the introduction of lifting functions, boundary control problems can be formulated as extended distributed problems. We consider a systematic mathematical formulation of these problems in terms of the minimization of a cost functional constrained by the MHD equations. The existence of a solution to the flow equations and to the optimal control problem are shown. The Lagrange multiplier technique is used to derive an optimality system from which candidate solutions for the control problem can be obtained. In order to achieve the numerical solution of this system, a finite element approximation is considered for the discretization together with an appropriate gradient-type algorithm. A finite element object-oriented library has been developed to obtain a parallel and multigrid computational implementation of the optimality system based on a multiphysics approach. Numerical results of two- and three-dimensional computations show that a possible minimum for the control problem can be computed in a robust and accurate manner.

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.

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.

Development and experimental validation of a knock induced damage model and real-time implementation of model-based strategies to control knock intensity in boosted gasoline engines

This PhD thesis reports the main activities carried out during the 3 years long “Mechanics and advanced engineering sciences” course, at the Department of Industrial Engineering of the University of Bologna. The research project title is “Development and analysis of high efficiency combustion systems for internal combustion engines” and the main topic is knock, one of the main challenges for boosted gasoline engines. Through experimental campaigns, modelling activity and test bench validation, 4 different aspects have been addressed to tackle the issue. The main path goes towards the definition and calibration of a knock-induced damage model, to be implemented in the on-board control strategy, but also usable for the engine calibration and potentially during the engine design. Ionization current signal capabilities have been investigated to fully replace the pressure sensor, to develop a robust on-board close-loop combustion control strategy, both in knock-free and knock-limited conditions. Water injection is a powerful solution to mitigate knock intensity and exhaust temperature, improving fuel consumption; its capabilities have been modelled and validated at the test bench. Finally, an empiric model is proposed to predict the engine knock response, depending on several operating condition and control parameters, including injected water quantity.