# Hiro Ono visit, February 2012

Masahiro (Hiro) Ono, who recently got his PhD with Brian Williams at MIT, will visit CDS on 7 Feb 2012 (Tue).

### Schedule

- 10:30 am: Richard Murray, 109 Steele Lab
- 11:00 am: CDS seminar, 114 Steele
- 12:00 pm: Lunch with Necmiye Ozay + 2
- Richard will join at ~1 pm (so try for a table on the patio -:)

- 1:30 pm: Eric
- 2:15 pm: Necmiye
- 3:00 pm: Scott Livingston (...can move time to 16:30 if needed)
- 3:45 pm: Open
- 4:30 pm: Open

### Abstract

**Risk Allocation Approach to Chance-constrained Model Predictive Control**

Steele Library, 11 am

This talk presents solutions to two problems in the domain of chance-constrained model predictive control. A chance-constrained MPC problem requires that a set of state constraints are satisfied with a user-specified probability, in the presence of unbounded additive uncertainty.

First, we consider decentralized finite-horizon optimal control for multi-agent systems. The problem is particularly difficult when agents are coupled through a joint chance constraint, which limits the probability of constraint violation by any of the agents in the system. We propose a dual decomposition-based algorithm, namely Market-based Iterative Risk Allocation (MIRA), that solves the multi-agent problem in a decentralized manner. The algorithm addresses the issue of scalability by letting each agent optimize its own control input given a fixed value of a dual variable, which is shared among agents. A central module optimizes the dual variable by solving a root-finding problem iteratively. MIRA gives exactly the same optimal solution as the centralized optimization approach since it reproduces the KKT conditions of the centralized approach. Our approach is analogous to a price adjustment process in a competitive market called tatonnement or Walrasian auction: each agent optimizes its demand for risk at a given price, while the central module (or the market) optimizes the price of risk, which corresponds to the dual variable.

Second, we consider receding horizon control of dynamic systems under unbounded uncertainty. Resolvability or recursive feasibility is an essential property for robust model predictive controllers. However, when an unbounded stochastic uncertainty is present, it is generally impossible to guarantee resolvability. We propose a new concept called probabilistic resolvability. A model predictive control (MPC) algorithm is probabilistically resolvable if it has feasible solutions at future time steps with a certain probability, given a feasible solution at the current time. We propose a joint chance-constrained MPC algorithm that guarantees probabilistic resolvability. The proposed algorithm also guarantees the satisfaction of a joint chance constraint, which specifies a lower bound on the probability of satisfying a set of state constraints over a finite horizon. Furthermore, with moderate conditions, the finite-horizon optimal control problem solved at each time step in the proposed algorithm is a convex optimization problem.

#### Biography

Masahiro Ono received a B.S. degree in Aeronautics and Astronautics at the University of Tokyo, an M.S. degree in Technology and Policy, and M.S. and Ph.D. degrees in Aeronautics and Astronautics at MIT. His research is in chance-constrained model predictive control and its applications to multiagent systems and smart buildings. He recently accepted a faculty position at Keio University in Japan.