Circumnavigation on Multiple Circles Around a Nonstationary Target With Desired Angular Spacing.

In this article, the objective for a group of nonholonomic agents is to achieve multicircular circumnavigation with any desired angular spacing around a nonstationary target. A cooperative protocol is proposed to achieve this objective and, additionally, generalizes the circumnavigation problem of unicycle vehicles around a target (moving and stationary). Due to the nonholonomic constraints, existing protocols cannot be extended directly to achieve this objective. Thus, the proposed algorithm is worked out from the desired geometry to achieve the objective. A fixed-time consensus estimator is designed under a cyclic digraph to arrive at the desired interagent angular separation in the target-centric frame. The target information and desired formation parameters are assumed to be known to only one agent partially. Due to uncertainty in the target's motion, it is assumed that the target's acceleration and angular velocity are unknown. Fixed-time estimators under a digraph address the lack of information. The tracking controller drives the agents to the desired position around the target, thus making the errors go to zero instead of any finite bounds. The controller guarantees the bounded control effort irrespective of the error magnitude. The numerical examples are presented to show the effectiveness of the algorithm.

An optimal dynamic inversion-based neuro-adaptive approach for treatment of chronic myelogenous leukemia.

Combining the advanced techniques of optimal dynamic inversion and model-following neuro-adaptive control design, an innovative technique is presented to design an automatic drug administration strategy for effective treatment of chronic myelogenous leukemia (CML). A recently developed nonlinear mathematical model for cell dynamics is used to design the controller (medication dosage). First, a nominal controller is designed based on the principle of optimal dynamic inversion. This controller can treat the nominal model patients (patients who can be described by the mathematical model used here with the nominal parameter values) effectively. However, since the system parameters for a realistic model patient can be different from that of the nominal model patients, simulation studies for such patients indicate that the nominal controller is either inefficient or, worse, ineffective; i.e. the trajectory of the number of cancer cells either shows non-satisfactory transient behavior or it grows in an unstable manner. Hence, to make the drug dosage history more realistic and patient-specific, a model-following neuro-adaptive controller is augmented to the nominal controller. In this adaptive approach, a neural network trained online facilitates a new adaptive controller. The training process of the neural network is based on Lyapunov stability theory, which guarantees both stability of the cancer cell dynamics as well as boundedness of the network weights. From simulation studies, this adaptive control design approach is found to be very effective to treat the CML disease for realistic patients. Sufficient generality is retained in the mathematical developments so that the technique can be applied to other similar nonlinear control design problems as well.