Reachable Set Analysis Of Dynamic Systems Subject To State Constraints

Reachable set estimation of dynamic systems is to derive some closed bounded set to bound all the states from the origin by inputs with bounded peak value, which has various applications in states and parameters estimation, peak-to-peak gain minimization and control systems with actuator saturation.In practical engineering, every physical state is subject to a certain constraint, the violation of the constraint may cause severe damages or destroy a device. Thus, it is important to have a clear constraint of the range of the key quantities during the operation of the device without violating it. Undoubtedly, state constraint considerably affects the scope of a system's reachable set. Our aim is to excavate an accurate description of the reachable set of a system in the presence of state constraint.First, the problem of reachable set estimation for linear systems with state constraint is studied. The maximal Lyapunov functional, combined with the state constraint is utilized to give a non-ellipsoidal description of the reachable set which is referred to as a truncated ellipsoid. Since there exist non-differential points, we introduce the concept of sub-differential and sub-gradient to handle them. Both theory and numerical simulation demonstrate the effectiveness of our proposed method.Second, the problem of reachable set estimation for systems with state constraint and time-varying delay is studied. The maximal Lyapunov-Razumikhin functional is designed to give a sufficient condition to the reachable set estimation of the aforementioned system. The new method could significantly simplify the analyses procedure and give a more accurate description of the reachable set at the same time.Finally, we consider singular systems subject to time-varying delay and state constraint. By using the maximal Lyapunov-Krasovskii functional, the intersections of polyhedrons and state constraint are obtained to bound all the states of the singular system. The method of reciprocally convex combination, delay partition and free weighting matrix are introduced to lessen the conservatism which is caused by time-varying delay.