Optimal and Adaptive Control of Stochastic Systems
Project Award Date: 07-01-2009
Fractional Brownian motion is a family of Gaussian processes that includes Brownian motion as well as some processes that have long-range dependence. These processes have been empirically identified for turbulence, flicker noise in electronic devices, Internet traffic, neural and coronary activity, and memory and reaction times, so they should serve as models for a variety of physical phenomena.
This research focuses on the control of stochastic systems driven by an arbitrary fractional Brownian motion (FBM) and by some discontinuous processes. The stochastic systems are primarily described by linear and bilinear stochastic differential equations which can be finite or infinite dimensional. The cost functionals for the control problems are quadratic in the state and the control with both finite and infinite time horizons. A contribution to an optimal control should arise from the prediction of the solution of the optimal system because all fractional Brownian motions have correlated increments except for the case of Brownian motion so such prediction problems will be further investigated.
Since systems are often only partially known, parameter identification of these stochastic control systems will be investigated to determine strongly consistent estimators of the unknown parameters using pseudo least squares and pseudo weighted least squares algorithms which are recursive and often strongly consistent.
The adaptive control of partially known linear and bilinear systems will be investigated because such problems naturally arise in the applications of optimal control to physical phenomena. Since distributed parameter systems are important models, stochastic equations in a Hilbert space and their control are proposed for investigation. Research topics will provide more general models and results for stochastic optimal controls and for strongly consistent identification schemes and self-optimizing adaptive controls.
Primary Sponsor(s): Air Force Office of Scientific Research