Validating Noncooperative Control Designs Through a Lyapunov Approach

A decentralized verification procedure is proposed to verify stability and performance for systems with multiple controllers designed by noncooperative agents. The key concept is to use Lyapunov functions as measure of the influence of each controller on the system. Sum of squares programming is used to verify Lyapunov derivative conditions, thus providing a sufficient condition for the specification. Dual decomposition is then used to decentralize the algorithm with the guarantee that decentralized verification is equivalent to centralized verification. The verification procedure is extended to decentralized control synthesis. To reduce the conservatism caused by improper choice of Lyapunov candidate, a perturbation algorithm is proposed to modify the Lyapunov candidate such that it better suits the purpose of verification.