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

Robust output stabilization: improving performance via supervisory control

We analyze robust stability, in an input-output sense, of switched stable systems. The primary goal (and contribution) of this paper is to design switching strategies to guarantee that input-output stable systems remain so under switching. We propose two types of {\em supervisors}: dwell-time and hysteresis based. While our results are stated as tools of analysis they serve a clear purpose in design: to improve performance. In that respect, we illustrate the utility of our findings by concisely addressing a problem of observer design for Lur'e-type systems; in particular, we design a hybrid observer that ensures ``fast'' convergence with ``low'' overshoots. As a second application of our main results we use hybrid control in the context of synchronization of chaotic oscillators with the goal of reducing control effort; an originality of the hybrid control in this context with respect to other contributions in the area is that it exploits the structure and chaotic behavior (boundedness of solutions) of Lorenz oscillators.Comment: Short version submitted to IEEE TA

Teleoperation control based on combination of wave variable and neural networks

In this paper, a novel control scheme is developed for a teleoperation system, combining the radial basis function (RBF) neural networks (NNs) and wave variable technique to simultaneously compensate for the effects caused by communication delays and dynamics uncertainties. The teleoperation system is set up with a TouchX joystick as the master device and a simulated Baxter robot arm as the slave robot. The haptic feedback is provided to the human operator to sense the interaction force between the slave robot and the environment when manipulating the stylus of the joystick. To utilize the workspace of the telerobot as much as possible, a matching process is carried out between the master and the slave based on their kinematics models. The closed loop inverse kinematics method and RBF NN approximation technique are seamlessly integrated in the control design. To overcome the potential instability problem in the presence of delayed communication channels, wave variables and their corrections are effectively embedded into the control system, and Lyapunov-based analysis is performed to theoretically establish the closed-loop stability. Comparative experiments have been conducted for a trajectory tracking task, under the different conditions of various communication delays. Experimental results show that in terms of tracking performance and force reflection, the proposed control approach shows superior performance over the conventional methods

On observer design for a class of impulsive switched systems

In this thesis, the problem of state observation for a class of impulsive switched systems is addressed. Corresponding to each subsystem, an identity Luenberger observer is employed and a switching observer is constructed accordingly. The asymptotic stability property of the proposed switching observer is discussed and LMI-based algorithms are given which provide necessary conditions for the asymptotic stability of the switching observer for the switching signals with an average dwell time greater than a specific value. Since switched systems without impulse are a special case of impulsive switched systems, all the results in this work can be applied to design observers for switched systems without impulse. The design of finite time switching observers for a class of linear switched systems is another problem addressed in this work. The finite convergence time property of the proposed switching observer is discussed and the exponential stability of the observation error is investigated. An LMI-based algorithm is given which provides conditions for the exponential stability of the switching observer. Finally, the idea of finite time observers for linear continuous time systems is extended to linear time invariant discrete time systems. The main motivation for this extension is that unlike the famous dead-beat observers designed for discrete time systems, the proposed observer in this work need not place all the eigen-values at the origin, which leads to a much more flexible design compared to the existing techniques

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