Cooperative control of a network of multi-vehicle unmanned systems

Development of unmanned systems network is currently among one of the most important areas of activity and research with implications in variety of disciplines, such as communications, controls, and multi-vehicle systems. The main motivation for this interest can be traced back to practical applications wherein direct human involvement may not be possible due to environmental hazards or the extraordinary complexity of the tasks. This thesis seeks to develop, design, and analyze techniques and solutions that would ensure and guarantee the fundamental stringent requirements that are envisaged for these dynamical networks. In this thesis, the problem of team cooperation is solved by using synthesis-based approaches. The consensus problem is defined and solved for a team of agents having a general linear dynamical model. Stability of the team is guaranteed by using modified consensus algorithms that are achieved by minimizing a set of individual cost functions. An alternative approach for obtaining an optimal consensus algorithm is obtained by invoking a state decomposition methodology and by transforming the consensus seeking problem into a stabilization problem. In another methodology, the game theory approach is used to formulate the consensus seeking problem in a "more" cooperative framework. For this purpose, a team cost function is defined and a min-max problem is solved to obtain a cooperative optimal solution. It is shown that the results obtained yield lower cost values when compared to those obtained by using the optimal control technique. In game theory and optimal control approaches that are developed based on state decomposition, linear matrix inequalities are used to impose simultaneously the decentralized nature of the problem as well as the consensus constraints on the designed controllers. Moreover, performance and stability properties of the designed cooperative team is analyzed in presence of actuator anomalies corresponding to three types of faults. Steady state behavior of the team members are analyzed under faulty scenarios. Adaptability of the team members to the above unanticipated circumstances is demonstrated and verified. Finally, the assumption of having a fixed and undirected network topology is relaxed to address and solve a more realistic and practical situation. It is shown that the stability and consensus achievement of the network with a switching structure and leader assignment can still be achieved. Moreover, by introducing additional criteria, the desirable performance specifications of the team can still be ensured and guaranteed

Indefinite metric spaces in estimation, control and adaptive filtering

The goal of this thesis is two-fold: first to present a unified mathematical framework (based upon optimization in indefinite metric spaces) for a wide range of problems in estimation and control, and second, to motivate and introduce the problem of robust estimation and control, and to study its implications to the area of adaptive signal processing. Robust estimation (and control) is concerned with the design of estimators (and controllers that have acceptable performance in the face of model uncertainties and lack of statistical information, and can be considered an outgrowth and extension of (the now classical) LQG theory, developed in the 1950's and 1960's which assumed perfect models and complete statistical knowledge. It has particular significance in adaptive signal processing where one needs to cope with time-variations of system parameters and to compensate for lack of a priori knowledge of the statistics of the input data and disturbances. One method of addressing the above problem is the so-called H∞ approach, which was introduced by G. Zames in 1980 and that has been recently solved by various authors. Despite the "fundamental differences" between the philosophies of the H∞ and LQG approaches to control and estimation, there are striking "formal similarities" between the controllers and estimators obtained from these two methodologies. In an attempt to explain these similarities, we shall describe a new approach to H∞ estimation (and control), different from the existing (e.g., interpolation-theoretic-based, game-theoretic-based, etc) approaches, that is based upon setting up estimation (and control problems) not in the usual Hilbert space of random variables, but in an indefinite (so-called Krein) space

Distributed Control of Networked Nonlinear Euler-Lagrange Systems

Motivated by recent developments in formation and cooperative control of networked multi-agent systems, the main goal of this thesis is development of efficient synchronization and formation control algorithms for distributed control of networked nonlinear systems whose dynamics can be described by Euler-Lagrange (EL) equations. One of the main challenges in the design of the formation control algorithm is its optimality and robustness to parametric uncertainties, external disturbances and ability to reconfigure in presence of component, actuator, or sensor faults. Furthermore, the controller should be capable of handling switchings in the communication network topology. In this work, nonlinear optimal control techniques are studied for developing distributed controllers for networked EL systems. An individual cost function is introduced to design a controller that relies on only local information exchanges among the agents. In the development of the controller, it is assumed that the communication graph is not fixed (in other words the topology is switching). Additionally, parametric uncertainties and faults in the EL systems are considered and two approaches, namely adaptive and robust techniques are introduced to compensate for the effects of uncertainties and actuator faults. Next, a distributed H_infinity performance measure is considered to develop distributed robust controllers for uncertain networked EL systems. The developed distributed controller is obtained through rigorous analysis and by considering an individual cost function to enhance the robustness of the controllers in presence of parametric uncertainties and external bounded disturbances. Moreover, a rigorous analysis is conducted on the performance of the developed controllers in presence of actuator faults as well as fault diagnostic and identification (FDI) imperfections. Next, synchronization and set-point tracking control of networked EL systems are investigated in presence of three constraints, namely, (i) input saturation constraints, (ii) unavailability of velocity feedback, and (iii) lack of knowledge on the system parameters. It is shown that the developed distributed controllers can accomplish the desired requirements and specification under the above constraints. Finally, a quaternion-based approach is considered for the attitude synchronization and set-point tracking control problem of formation flying spacecraft. Employing the quaternion in the control law design enables handling large rotations in the spacecraft attitude and, therefore, any singularities in the control laws are avoided. Furthermore, using the quaternion also enables one to guarantee boundedness of the control signals both with and without velocity feedback