Register now After registration you will be able to apply for this opportunity online.
This opportunity is not published. No applications will be accepted.
Optimizing the design of sum-of-squares programs for stability regions of nonlinear systems
The aim of this project is to improve the performance of sum-of-squares programs used for stability region verification by rigorously assessing the effect of various objective functions on the obtained region and required runtime.
Keywords: computational methods, semidefinite programs, optimisation programs, sum-of-squares programs, Lyapunov methods, stability of nonlinear systems, region of attraction
Sum-of-squares (SOS) programs are polynomial optimisation programs used in a wide range of applications. For example, they can be used to compute stability regions of nonlinear systems. The conservativeness of the obtained region and computational runtime will depend on various parameters of the SOS program design. In particular, the choice of the cost function has significant influence on the result. While various cost functions have been employed for similar problems in the literature, no thorough comparison has been performed so far. A comparison includes the assessment on how the best choice of objective function depends on the properties of the dynamic system under consideration, and other parameters which enter the optimisation program.
Sum-of-squares (SOS) programs are polynomial optimisation programs used in a wide range of applications. For example, they can be used to compute stability regions of nonlinear systems. The conservativeness of the obtained region and computational runtime will depend on various parameters of the SOS program design. In particular, the choice of the cost function has significant influence on the result. While various cost functions have been employed for similar problems in the literature, no thorough comparison has been performed so far. A comparison includes the assessment on how the best choice of objective function depends on the properties of the dynamic system under consideration, and other parameters which enter the optimisation program.
The rigorous comparison and the assessment of the dependence of the objective function on dynamical system properties and program parameters are the principal aim of the project. Depending on the student's interest and preferences the project can optionally be extended to the comparison of software packages (Yalmip, Julia, CVX, SOSTOOLS, etc..) and other extended parameters of the SOS program.
**Requirements**
- Strong interest in computational methods
- Background in numerical optimisation methods
- Experience with different commercial and/or open source solver software preferred
To apply please send a CV and your transcripts as well as a brief motivation.
The rigorous comparison and the assessment of the dependence of the objective function on dynamical system properties and program parameters are the principal aim of the project. Depending on the student's interest and preferences the project can optionally be extended to the comparison of software packages (Yalmip, Julia, CVX, SOSTOOLS, etc..) and other extended parameters of the SOS program.
**Requirements**
- Strong interest in computational methods - Background in numerical optimisation methods - Experience with different commercial and/or open source solver software preferred
To apply please send a CV and your transcripts as well as a brief motivation.
- Eva Ahbe, ahbee@control.ee.ethz.ch
- Dr. Andrea Iannelli iannelli@control.ee.ethz.ch
- Eva Ahbe, ahbee@control.ee.ethz.ch - Dr. Andrea Iannelli iannelli@control.ee.ethz.ch