The Classical Continuous Mixed Optimal Control of Couple Nonlinear Parabolic Partial Differential Equations with State Constraints

In this work, the classical continuous mixed optimal control vector (CCMOPCV) problem of couple nonlinear partial differential equations of parabolic (CNLPPDEs) type with state constraints (STCO) is studied. The existence and uniqueness theorem (EXUNTh) of the state vector solution (SVES) of the CNLPPDEs for a given CCMCV is demonstrated via the method of Galerkin (MGA). The EXUNTh of the CCMOPCV ruled with the CNLPPDEs is proved. The Frechet derivative (FÉDE) is obtained. Finally, both the necessary and the sufficient theorem conditions for optimality (NOPC and SOPC) of the CCMOPCV with state constraints (STCOs) are proved through using the Kuhn-Tucker-Lagrange (KUTULA) multipliers theorem (KUTULATH).

Robust Self-Triggered Control for Nonlinear Cyber-Physical Systems with State Constraints under DoS Attacks

This paper is concerned with the event-based control problem for nonlinear cyber-physical systems (CPSs) with state constraints. A novel security control strategy consisting of a self-triggered mechanism is developed to decrease the network communication loads to the most extent on the basis of ensuring system safety and stability. The maximum capability of the designed self-triggered mechanism to resist denial-of-service (DoS) attacks occurring in controller-actuator (C-A) and sensor-controller (S-C) channels synchronously is also analyzed. In particular, we prove that the security control strategy guarantees the system safety and stability without resulting in Zeno behavior. Finally, a numerical example is provided to demonstrate the prominent effectiveness and the advantages over the existing results.