Decision and Control Lecture Series
Decision and Control Laboratory, Coordinated Science Laboratory
Stochastic Estimation and Control for Vector Linear Systems with Cauchy Noise
Jason L. Speyer
Ronald and Valerie Sugar Distinguished Professor in Engineering
Mechanical and Aerospace Engineering Department and Electrical Engineering Department
University of California, Los Angeles
Wednesday, September 18, 2013
3:00 p.m. to 4:00 p.m.
B02 CSL Auditorium
The Gaussian paradigm has dominated the foundation of estimation and control algorithms. The assumed Gaussian probability density functions (pdf) have very light tails where almost all of its uncertainty evolves near its mean value. However, in many realistic applications the system can experience large impulsive noises far more often then the Gaussian would admit. Here, I with Moshe Idan of the Technion have suggested using the Cauchy pdf for the development of a new class of estimation and control algorithms. I begin our research overview by introducing the vector Cauchy estimation problem and the generation of the characteristic function of the unnormalized conditional probability density function (ucpdf). Once the characteristic function of the unnormalized cpdf is obtained, the conditional mean and variance are easily computed from its first and second derivatives. Two-state and three-state dynamic system examples demonstrates the vector-state Cauchy estimator's performance and are compared to a conditional mean Gaussian estimator (Kalman filter). Next, based on the characteristic function of the cpdf, a model predictive (MP) optimal controller is developed and compared to a comparable Gaussian controller. This Cauchy MP controller naturally mitigates outliers generated in the Cauchy simulation whereas the Gaussian performance degenerates significantly. Scalar-state and two-state controller performance demonstrate the controller properties.
Jason L. Speyer received the B.S. in Aeronautics and Astronautics from MIT, and the Ph.D. in applied mathematics from Harvard University. He is the Ronald and Valerie Sugar Distinguished Professor in Engineering within the Mechanical and Aerospace Engineering Department and the Electrical Engineering Department, UCLA. He coauthored, with W. H. Chung, Stochastic Processes, Estimation, and Control (SIAM, 2008), and coauthored, with D. H. Jacobson, Primer on Optimal Control Theory (SIAM, 2010). He is a life fellow of the IEEE and a fellow of the AIAA and was awarded the AIAA Mechanics and Control of Flight Award, AIAA Dryden Lectureship in Research, Air Force Exceptional Civilian Decoration (1991 and 2001), IEEE Third Millennium Medal, the AIAA Aerospace Guidance, Navigation, and Control Award, and membership in the National Academy of Engineering.