Abstract
We demonstrate applications of algebraic techniques that optimize and certify polynomial inequalities to problems of interest in the operations research and transportation engineering communities. Three problems are considered: (1) wireless coverage of targeted geographical regions with guaranteed signal quality and minimum transmission power, (2) computing real-time certificates of collision avoidance for a simple model of an unmanned vehicle (UV) navigating through a cluttered environment, and (3) designing a nonlinear hovering controller for a quadrotor UV, which has recently been used for load transportation. On our smaller-scale applications, we apply the sum of squares (SOS) relaxation and solve the underlying problems with semidefinite programming. On the larger-scale or real-time applications, we use our recently introduced “SDSOS Optimization” techniques which result in second order cone programs. To the best of our knowledge, this is the first study of real-time applications of sum of squares techniques in optimization and control. No knowledge in dynamics and control is assumed from the reader.
Original language | English (US) |
---|---|
Pages (from-to) | 709-729 |
Number of pages | 21 |
Journal | Optimization Letters |
Volume | 10 |
Issue number | 4 |
DOIs | |
State | Published - Apr 1 2016 |
All Science Journal Classification (ASJC) codes
- Business, Management and Accounting (miscellaneous)
- Control and Optimization
Keywords
- Algebraic techniques in optimization
- Lyapunov methods
- Polynomial optimization
- Real-time optimization
- Second order cone programming
- Semidefinite programming