Switching observer design, consensus management, and time-delayed control with applications for rigid-body attitude dynamics
This dissertation addresses three diverse research problems pertaining to rigid body attitude stabilization and control. The problems addressed result in theoretical development for the topics of cooperative control, delayed feedback, and state estimation, through the formulation of a novel class of switching observers.
In the area of consensus management for cooperative control, the problem of designing torque control laws that synchronize the attitude of a team of rigid bodies under constant, unknown communication time delays is addressed. Directed communication graphs are considered, which encompass both leader-follower and leaderless architectures. A feedback linearization result involving the Modified Rodrigues parameter (MRP) representation of attitude kinematics reduces the attitude dynamics equations to double integrator agents and the remainder of the control effort achieves position consensus. New necessary and sufficient delay dependent stability conditions for the system of double integrator agents are presented.
This dissertation also considers the problem of stabilizing attitude dynamics with unknown piecewise-constant delayed feedback. The problem is addressed through stability analysis of switched linear time-invariant and nonlinear timedelay systems. In the case of linear systems with switched delay feedback, a new sufficiency condition for average dwell time result is presented using a complete type Lyapunov-Krasovskii (L-K) functional approach. Further, the corresponding switched system with nonlinear perturbations is proven to be exponentially stable inside a well characterized region of attraction for an appropriately chosen average dwell time.
Finally, this dissertation provides a new switching angular velocity observer formulation to the classical problem of rigid body attitude tracking in the absence of angular rate measurements. Exponential convergence of the angular velocity state estimation errors is proven independent of control design by using a novel error signal definition through this switching-type observer. The switching ensures C0 continuity for all the estimated states. Further, the maximum number of switches required by the observer is shown to be finite and that zeno-type behavior cannot occur. A “separation property” type result in the absence of actual angular rate measurements is established, wherein a linear and nonlinear controller utilizes angular velocity estimates from the proposed observer to achieve attitude tracking.