Controllability of linear deterministic and stochastic systems
Necessary and sufficient conditions, which are formulated in terms of convergence of a certain sequence of operators involving the resolvent of the negative of the controllability operator, are found for deterministic linear stationary control systems to be completely and approximately controllable, respectively. It is shown that the S-controllability of partially observable linear stationary control systems with additive Gaussian white noise disturbance, that is a property of attaining an arbitrarily small neighborhood of each point in the state space with a probability arbitrarily close to one, is equivalent to the approximate controllability of their deterministic part. Also, it is shown that the C-controllability of the same kind of systems, that is defined as S-controllability improved with some uniformity conditions, is equivalent to the complete controllability of their deterministic part.
Stage stunt system is an automatic steeve system orchestrated by PLC. Security and fault-recover are two important properties of the system. In this paper, we analyze and verify the stage stunt system formally. We adopt hybrid automata to model the system. The forward reachability is used to verify the properties on the reachable states. We present a case study to illustrate the feasibility of the proposed verification.