In this study, we develop an adaptive-critic-based controller to steer an agile missile that has a constraint on the minimum flight Mach number from various initial Mach numbers to a given final Mach number in minimum time while completely reversing its flightpath angle. This class of bounded state space, free final time problems is very difficult to solve due to discontinuities in costates at the constraint boundaries.We use a two-neural-network structure called "adaptive critic" in this study to carry out the optimization process. This structure obtains an optimal controller through solving optimal control-related equations resulting from a Hamiltonian formulation. Detailed derivations of equations and conditions on the constraint boundary are provided. For numerical experiments, we consider vertical plane scenarios. Flight Mach number and the flightpath angle are the states and the aerodynamic angle of attack is treated as the control. Numerical results bring out some attractive features of the adaptive critic approach and show that this formulation works very well in guiding the missile to its final conditions for this state constrained optimization problem from an envelope of initial conditions.
A mobile edge computing (MEC)-enabled blockchain system is proposed in this study for secure data storage and sharing in internet of things (IoT) networks, with the MEC acting as an overlay system to provide dynamic computation offloading services. Considering latency-critical, resource-limited, and dynamic IoT scenarios, an adaptive system resource allocation and computation offloading scheme is designed to optimize the scalability performance for MEC-enabled blockchain systems, wherein the scalability is quantified as MEC computational efficiency and blockchain system throughput. Specifically, we jointly optimize the computation offloading policy and block generation strategy to maximize the scalability of MEC-enabled blockchain systems and meanwhile guarantee data security and system efficiency. In contrast to existing works that ignore frequent user movement and dynamic task requirements in IoT networks, the joint performance optimization scheme is formulated as a Markov decision process (MDP). Furthermore, we design a deep deterministic policy gradient (DDPG)-based algorithm to solve the MDP problem and define the multiple and variable number of consecutive time slots as a decision epoch to conduct model training. Specifically, DDPG can solve an MDP problem with a continuous action space and it only requires a straightforward actor–critic architecture, making it suitable for tackling the dynamics and complexity of the MEC-enabled blockchain system. As demonstrated by simulations, the proposed scheme can achieve performance improvements over the deep Q network (DQN)-based scheme and some other greedy schemes in terms of long-term transactional throughput.
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