Dynamic system evolution and markov chain approximation

Abstract

In this paper computational aspects of the mathematical modelling of dynamic system evolution have been considered as a problem in information theory. The construction of mathematical models is treated as a decision making process with limited available information.The solution of the problem is associated with a computational model based on heuristics of a Markov Chain in a discrete space–time of events. A stable approximation of the chain has been derived and the limiting cases are discussed. An intrinsic interconnection of constructive, sequential, and evolutionary approaches in related optimization problems provides new challenges for future work

Energy-Delay Evaluation and Optimization for NB-IoT PSM With Periodic Uplink Reporting

“…An optimization model of the PSM parameters that offers maximized energy saving and simultaneously minimizing the communication delay is presented in this section. We used the priori method [23] in a multi-objective optimization technique to formulate a problem that can simultaneously solve the two parameters i.e. delay and energy saving.…”

Coupling control and human factors in mathematical models of complex systems

“…If we include these constraints into the definition of the Hamiltonian/Lagrangian, the analysis cannot be reduced to only those five case discussed previously in this section. In the general case, the number of speed holding phases for the entire trip can be determined by a posteriori estimations based on a sequential algorithm of information processing accounting for human factors [27]. Recall that in conventional methodologies this number is postulated a priori.…”

“…Naturally, it cannot be reduced to the five cases discussed before. Instead, a sequential (in real time) algorithm is required to incorporate human factors into the model via sequential estimations of a time-perturbed Hamiltonian approximation [26,27] for each time subinterval t ≤ τ ≤ t + ∆t with t ∈ [0, T ]. This formulation is more general than those resulted from conventional methodologies.…”

“…Computational methodologies for solving the problem for each Hamiltonian estimation are known as they were developed for the numerical solution of HJBbased models (e.g., [16,29,7,28]). Finally, a general approach to the analysis of such models (obtained via a decision making process with limited information available) using tools of information theory and the Markov chain approximation method can be found in [26,27].…”

“…Now, we are in a position to highlight major difficulties in applications of conventional methodologies to the above problem. First, we note that in reality the control variable of this problem cannot vary continuously due to the discrete character of the information [27] obtained in this specific case by the moving vehicle in a dynamically changing environment. Therefore, if we consider a finite (possibly very large) set of control settings, for example, throttle settings as it was originally proposed in [13]…”