Title :
Minimum relative entropy state transitions in discrete time systems with statistically uncertain noise
Author :
Vladimirov, Igor G. ; Petersen, Ian R.
Author_Institution :
Sch. of Eng. & Inf. Technol., Univ. of New South Wales at ADFA, Canberra, ACT, Australia
Abstract :
We develop a stochastic dissipativity theory for discrete-time systems driven by an uncertain random noise. The deviation of the unknown probability law of the noise from a nominal white noise distribution is quantified by the conditional relative entropy given the initial state of the system.We establish a dissipation inequality and superadditivity property for the conditional relative entropy supply. The problem of minimizing the supply required to drive the system between given state distributions over a specified time horizon is considered. We obtain a dynamic programming Bellman equation for the minimum required relative entropy supply and show that the optimal noise is Markov with respect to the state of the system. For linear systems with Gaussian nominal noise and Gaussian initial and terminal state distributions, computing the minimum required supply is reduced to solving an algebraic Riccati equation.
Keywords :
Gaussian distribution; Markov processes; Riccati equations; discrete time systems; dynamic programming; linear systems; statistical analysis; uncertain systems; white noise; Bellman equation; Gaussian initial state distribution; Gaussian nominal noise; Gaussian terminal state distribution; Markov process; algebraic Riccati equation; conditional relative entropy; discrete time system; dissipation inequality; dynamic programming; linear system; minimum relative entropy state transition; probability law; statistically uncertain random noise; stochastic dissipativity theory; superadditivity property; white noise distribution; Covariance matrix; Drives; Entropy; Equations; Markov processes; Noise; Probability distribution;
Conference_Titel :
Decision and Control (CDC), 2010 49th IEEE Conference on
Conference_Location :
Atlanta, GA
Print_ISBN :
978-1-4244-7745-6
DOI :
10.1109/CDC.2010.5717654