This paper presents a class of Dynamic Multi-Armed Bandit problems where the reward can be modele... more This paper presents a class of Dynamic Multi-Armed Bandit problems where the reward can be modeled as the noisy output of a time varying linear stochastic dynamic system that satisfies some boundedness constraints. The class allows many seemingly different problems with time varying option characteristics to be considered in a single framework. It also opens up the possibility of considering many new problems of practical importance. For instance it affords the simultaneous consideration of temporal option unavailabilities and the depen- dencies between options with time varying option characteristics in a seamless manner. We show that, for this class of problems, the combination of any Upper Confidence Bound type algorithm with any efficient reward estimator for the expected reward ensures the logarithmic bounding of the expected cumulative regret. We demonstrate the versatility of the approach by the explicit consideration of a new example of practical interest.
This work presents an intrinsic formulation of an observer for an important class of simple mecha... more This work presents an intrinsic formulation of an observer for an important class of simple mechanical systems on a Lie group. Recently, Aghannan and Rouchon have formulated an observer for a simple mechanical system on a general Riemannian manifold. The current paper specializes their result to the case where the manifold is a Lie group, the kinetic energy is left
his paper extends the powerful and intuitive framework of PID control to fully actuated, left-inv... more his paper extends the powerful and intuitive framework of PID control to fully actuated, left-invariant, mechanical systems on a general Lie group. The class of problems solved includes tracking of a smoothly time-varying desired orientation for a rigid body with fully actuated attitude dynamics in two or three dimensions. If the reference velocity and unmodeled disturbance forces converge to constant values, then the closed-loop system will be almost-globally exponentially stable. The controller is robust to errors or variations in the inertial parameters and the actuator parameters. We explicitly construct the controller on the group of rigid body rotations and demonstrate its performance in quadrotor attitude tracking.
This paper presents a class of Dynamic Multi-Armed Bandit problems where the reward can be modele... more This paper presents a class of Dynamic Multi-Armed Bandit problems where the reward can be modeled as the noisy output of a time varying linear stochastic dynamic system that satisfies some boundedness constraints. The class allows many seemingly different problems with time varying option characteristics to be considered in a single framework. It also opens up the possibility of considering many new problems of practical importance. For instance it affords the simultaneous consideration of temporal option unavailabilities and the depen- dencies between options with time varying option characteristics in a seamless manner. We show that, for this class of problems, the combination of any Upper Confidence Bound type algorithm with any efficient reward estimator for the expected reward ensures the logarithmic bounding of the expected cumulative regret. We demonstrate the versatility of the approach by the explicit consideration of a new example of practical interest.
This work presents an intrinsic formulation of an observer for an important class of simple mecha... more This work presents an intrinsic formulation of an observer for an important class of simple mechanical systems on a Lie group. Recently, Aghannan and Rouchon have formulated an observer for a simple mechanical system on a general Riemannian manifold. The current paper specializes their result to the case where the manifold is a Lie group, the kinetic energy is left
his paper extends the powerful and intuitive framework of PID control to fully actuated, left-inv... more his paper extends the powerful and intuitive framework of PID control to fully actuated, left-invariant, mechanical systems on a general Lie group. The class of problems solved includes tracking of a smoothly time-varying desired orientation for a rigid body with fully actuated attitude dynamics in two or three dimensions. If the reference velocity and unmodeled disturbance forces converge to constant values, then the closed-loop system will be almost-globally exponentially stable. The controller is robust to errors or variations in the inertial parameters and the actuator parameters. We explicitly construct the controller on the group of rigid body rotations and demonstrate its performance in quadrotor attitude tracking.
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Papers by Sanjeeva Maithripala