Allerton 2015 Paper Abstract

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Hariyoshi, Ena (University of California, Berkeley), Ranade, Gireeja (University of California, Berkeley), Sahai, Anant (UC Berkeley)

Vector Control Systems with Unpredictable Actuation

Scheduled for presentation during the Invited Session "Recent Developments in Information Theory, Statistics and Probability II" (ThD2), Thursday, October 1, 2015, 16:50−17:10, Solarium

53rd Annual Allerton Conference on Communication, Control, and Computing, Sept 29-Oct 2, 2015, Allerton Park and Retreat Center, Monticello, IL, USA

This information is tentative and subject to change. Compiled on November 19, 2019

Keywords Stochastic Systems and Control, Networked Control Systems

Abstract

Vector systems are fundamentally different from scalar systems since the dynamics of a vector system can both spin and stretch the system state. The magnitude and direction of control actions for multi-dimensional systems can be coordinated across time. Hence, planning future actions is important. System predictability, and the related ability to plan, can affect system stabilizability.

This paper considers a simple d-dimensional state-space model for an unpredictable "spinning" control system. The spinning controller has a particular restriction: it may only apply a scalar control in a direction that is randomly chosen by nature at each time. This model is related to the classically studied models for intermittent Kalman filtering and intermittent control problems, but is simpler to analyze. The simplicity of the spinning model lets us use dynamic programming to characterize the decay rate of the system and thus understand the fundamental limitations imposed by the fact that future control directions are unpredictable. We can reduce the unpredictability of the model by providing non-causal side information about the future control directions, and further calculate how this affects the decay rate of the system. With k-steps of lookahead on the random control direction, the d-dimensional system decays as fast as a d-k dimensional system with no lookahead on the control action. This model is a first step to understand unpredictability in more general networked control systems.

 

 

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