http://hdl.handle.net/1721.1/37332 2013-05-21T16:48:22Z http://hdl.handle.net/1721.1/77933 Supplementary material for nonparameteric adaptive control of time varying systems using gaussian processes Chowdhary, Girish; Kingravi, Hassan A.; How, Jonathan P.; Vela, Patricio A. Real-world dynamical variations make adaptive control of time-varying systems highly relevant. However, most adaptive control literature focuses on analyzing systems where the uncertainty is represented as a weighted linear combination of fixed number of basis functions, with constant weights. One approach to modeling time variations is to assume time varying ideal weights, and use difference integration to accommodate weight variation. However, this approach reactively suppresses the uncertainty, and has little ability to predict system behavior locally. We present an alternate formulation by leveraging Bayesian nonparametric Gaussian Process adaptive elements. We show that almost surely bounded adaptive controllers for a class of nonlinear time varying system can be formulated by incorporating time as an additional input to the Gaussian kernel. Analysis and simulations show that the learning-enabled local predictive ability of our adaptive controllers significantly improves performance. This technical report has supplementary material for "Bayesian Nonparametric Adaptive Control of Time-varying Systems using Gaussian Processes" American Control Conference paper 2013-03-15T04:00:00Z http://hdl.handle.net/1721.1/77931 Bayesian Nonparametric Adaptive Control using Gaussian Processes Chowdhary, Girish; Kingravi, Hassan A.; How, Jonathan P.; Vela, Patricio A. Most current Model Reference Adaptive Control (MRAC) methods rely on parametric adaptive elements, in which the number of parameters of the adaptive element are fixed a priori, often through expert judgment. An example of such an adaptive element are Radial Basis Function Networks (RBFNs), with RBF centers pre-allocated based on the expected operating domain. If the system operates outside of the expected operating domain, this adaptive element can become non-effective in capturing and canceling the uncertainty, thus rendering the adaptive controller only semi-global in nature. This paper investigates a Gaussian Process (GP) based Bayesian MRAC architecture (GP-MRAC), which leverages the power and flexibility of GP Bayesian nonparametric models of uncertainty. GP-MRAC does not require the centers to be preallocated, can inherently handle measurement noise, and enables MRAC to handle a broader set of uncertainties, including those that are defined as distributions over functions. We use stochastic stability arguments to show that GP-MRAC guarantees good closed loop performance with no prior domain knowledge of the uncertainty. Online implementable GP inference methods are compared in numerical simulations against RBFN-MRAC with preallocated centers and are shown to provide better tracking and improved long-term learning. This technical report is a preprint of an article submitted to a journal. 2013-03-15T04:00:00Z http://hdl.handle.net/1721.1/77915 Efficient Distributed Sensing Using Adaptive Censoring-Based Inference Mu, Beipeng; Chowdhary, Girish; How, Jonathan P. In many distributed sensing applications it is likely that only a few agents will have valuable information at any given time. Since wireless communication between agents is resource-intensive, it is important to ensure that the communication effort is focused on communicating valuable information from informative agents. This paper presents communication efficient distributed sensing algorithms that avoid network cluttering by having only agents with high Value of Information (VoI) broadcast their measurements to the network, while others censor themselves. A novel contribution of the presented distributed estimation algorithm is the use of an adaptively adjusted VoI threshold to determine which agents are informative. This adaptation enables the team to better balance between the communication cost incurred and the long-term accuracy of the estimation. Theoretical results are presented establishing the almost sure convergence of the communication cost and estimation error to zero for distributions in the exponential family. Furthermore, validation through numerical simulations and real datasets show that the new VoI-based algorithms can yield improved parameter estimates than those achieved by previously published hyperparameter consensus algorithms while incurring only a fraction of the communication cost. This technical report is a preprint of work submitted to a journal. 2013-03-15T04:00:00Z http://hdl.handle.net/1721.1/71875 Efficient distributed information fusion using value of information based censoring Mu, Beipeng; How, Jonathan P.; Chowdhary, Girish In many distributed sensing applications, not all agents have valuable information at all times. Therefore, requiring all agents to communicate at all times can be resource intensive. In this work, the notion of Value of Information (VoI) is used to improve the efficiency of distributed sensing algorithms. Particularly, only agents with high VoI broadcast their measurements to the network, while others censor their measurements. New VoI realized data fusion algorithms are introduced, and an in depth analysis of the costs incurred by these algorithms and conventional distributed data fusion algorithms is presented. Numerical simulations are used to compare the performance of the VoI realized algorithms with traditional data fusion algorithms. A VoI based algorithm that adaptively adjusts the criterion for being informative is presented and shown to strike a good balance between reduced communication cost and increased accuracy. 2012-07-27T04:00:00Z