Abstract
We present a parameter inference algorithm for autonomous stochastic linear hybrid systems, which computes a maximum-likelihood model, given only a set of continuous output data of the system. We overcome the potentially intractable problem of identifying the sequence of discrete modes by using dynamic programming; we then compute the maximum-likelihood continuous models using an Expectation Maximization technique. This allows us to find a maximum-likelihood model in time that is polynomial in the number of discrete modes as well as in the length of the data series. We prove local convergence of the algorithm. We also propose a novel initialization technique to derive good initial conditions for the model parameters. Finally, we demonstrate our algorithm on some examples – two simple one-dimensional examples with simulated data, and an application to real flight test data from a dual-vehicle demonstration of the Stanford DragonFly Unmanned Aerial Vehicles.
This work is supported by ONR under MURI contract N00014-02-1-0720, by DARPA under Software Enabled Control (AFRL contract F33615-99-C-3014) and by an NSF Career Award. H. Balakrishnan is supported by a Stanford Graduate Fellowship.
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Balakrishnan, H., Hwang, I., Jang, J.S., Tomlin, C.J. (2004). Inference Methods for Autonomous Stochastic Linear Hybrid Systems. In: Alur, R., Pappas, G.J. (eds) Hybrid Systems: Computation and Control. HSCC 2004. Lecture Notes in Computer Science, vol 2993. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24743-2_5
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DOI: https://doi.org/10.1007/978-3-540-24743-2_5
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