Bounds for Deterministic and Stochastic Dynamical Systems using Sum-of-Squares Optimization
Bounds for Deterministic and Stochastic Dynamical Systems using Sum-of-Squares Optimization
We describe methods for proving upper and lower bounds on infinite-time averages in deterministic dynamical systems and on stationary expectations in stochastic systems. The dynamics and the quantities to be bounded are assumed to be polynomial functions of the state variables. The methods are computer-assisted, using sum-of-squares polynomials to formulate …