Fast Real-Time Online Optimization for Estimation and Control

Dr. Joao Hespanha

Professor, Electrical & Computer Engineering, Mechanical Engineering, and Center for Control, Dynamical-systems, and Computation, University of California, Santa Barbara

Seminar Information

Seminar Series
Dynamic Systems & Controls

Seminar Date - Time
April 21, 2023, 3:00 pm
-
4 PM

Seminar Location
EBU II 479, Von Karman-Penner Seminar Room

Dr. Joao Hespanha

Abstract

The widespread availability of low-cost, low-power embedded computation has made it possible to apply online optimization to solve nonlinear control problems with hard state and input constraints, leading to the increasing popularity of Model Predictive Control (MPC) in numerous industrial applications. Online optimization has also become popular in solving estimation problems by taking advantage of known constraints on the state, measurement noise, and disturbances. In particular, Moving Horizon Estimation (MHE) computes states estimates that are “maximally compatible” with measurements observed over a finite window of time.  Recently, MPC and MHE have been combined to solve output feedback control problems by combining state estimation and control into a single min-max optimization.

This talk addresses the use of second-order optimization methods to solve real-time estimation and control problems. Second-order methods utilize Newton’s root-finding algorithm to find solutions to first-order optimality conditions and can exhibit local superlinear convergence. However, these methods also present significant challenges and this talk addresses two of them: scalability and convergence.

In general, the computational effort required by second-order optimization methods scales poorly with respect to the number of optimization variables and constraints. However, this is generally not the case for optimizations arising in MPC and MHE, enabling the solution of problems with thousands of optimization variables in real-time control systems with sampling times on the order of just a few milliseconds.

Although second-order methods can exhibit superlinear convergence for convex problems, much less can be said for nonconvex optimizations. We discuss the design of second-order algorithms that modify the Hessian matrix to obtain a search direction that is a solution to a quadratic program that locally approximates the original optimization. By selecting this type of modification appropriately, we show that the only stable points of the resulting iterations are local minima, whereas all other stationary points become unstable equilibria. This type of modification can also be used to solve min-max optimizations that lack appropriate convexity-concavity properties.

Speaker Bio

João P. Hespanha received his Ph.D. degree in electrical engineering and applied science from Yale University, New Haven, Connecticut in 1998. From 1999 to 2001, he was Assistant Professor at the University of Southern California, Los Angeles. He moved to the University of California, Santa Barbara in 2002, where he currently holds a Distinguished Professor position with the Department of Electrical and Computer Engineering.

Dr. Hespanha is the recipient of the Yale University’s Henry Prentiss Becton Graduate Prize for exceptional achievement in research in Engineering and Applied Science, a National Science Foundation CAREER Award, the 2005 best paper award at the 2nd Int. Conf. on Intelligent Sensing and Information Processing, the 2005 Automatica Theory/Methodology best paper prize, the 2006 George S. Axelby Outstanding Paper Award, and the 2009 Ruberti Young Researcher Prize. Dr. Hespanha is a Fellow of the International Federation of Automatic Control (IFAC) and of the IEEE. He was an IEEE distinguished lecturer from 2007 to 2013.

His current research interests include hybrid and switched systems; multi-agent control systems; game theory; optimization; distributed control over communication networks (also known as networked control systems); the use of vision in feedback control; stochastic modeling in biology; and network security.