Bayesian Nonparametric Adaptive Control using Gaussian Processes

The problem of making control decisions over time for acheiving a desired behavior goal for a dynamical systems has been widely studied in control systems literature. The paradigm of Model Reference Adaptive control is concerned with guaranteeing stability of the dynamical system being controlled and en- suring that it behaves like a designer chosen reference model in presence of uncertainty. Most current model reference adaptive control methods rely on parametric adaptive elements, in which the number of parame- ters of the adaptive element are fixed a-priori, often through expert judgment. Examples of such adaptive elements are the commonly used Radial Basis Function (RBF) Neural Networks (NNs) with pre- allocated centers allocated based on the expected operating domain. If the system operates outside of the expected operating domain, such adaptive elements can become non-effective, thus rendering the adaptive controller only semi-global in nature. This paper investigates Gaussian Process based adaptive elements which gen- eralize the notion of Gaussian distributions to function approximation. We show that these nonparametric adaptive elements guarantee good closed loop performance with minimal prior domain knowledge of the un- certainty through stochastic stability arguments. Online implementable GP inference method are evaluated in simulations and compared with RBF-NN adaptive controllers with pre-allocated centers.

Authors

• Girish Chowdhary
• Hassan Kingravi
• Jonathan How
• Patricio Vela Georgia Institute of Technology

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