Identification of dynamic systems, theory and formulation

The problem of estimating parameters of dynamic systems is addressed in order to present the theoretical basis of system identification and parameter estimation in a manner that is complete and rigorous, yet understandable with minimal prerequisites. Maximum likelihood and related estimators are highlighted. The approach used requires familiarity with calculus, linear algebra, and probability, but does not require knowledge of stochastic processes or functional analysis. The treatment emphasizes unification of the various areas in estimation in dynamic systems is treated as a direct outgrowth of the static system theory. Topics covered include basic concepts and definitions; numerical optimization methods; probability; statistical estimators; estimation in static systems; stochastic processes; state estimation in dynamic systems; output error, filter error, and equation error methods of parameter estimation in dynamic systems, and the accuracy of the estimates

Application of control theory to dynamic systems simulation

The application of control theory is applied to dynamic systems simulation. Theory and methodology applicable to controlled ecological life support systems are considered. Spatial effects on system stability, design of control systems with uncertain parameters, and an interactive computing language (PARASOL-II) designed for dynamic system simulation, report quality graphics, data acquisition, and simple real time control are discussed

Simulating dynamic systems using Linear Time Calculus theories

To appear in Theory and Practice of Logic Programming (TPLP). Dynamic systems play a central role in fields such as planning, verification, and databases. Fragmented throughout these fields, we find a multitude of languages to formally specify dynamic systems and a multitude of systems to reason on such specifications. Often, such systems are bound to one specific language and one specific inference task. It is troublesome that performing several inference tasks on the same knowledge requires translations of your specification to other languages. In this paper we study whether it is possible to perform a broad set of well-studied inference tasks on one specification. More concretely, we extend IDP3 with several inferences from fields concerned with dynamic specifications

Constructing a General Theory of Life: The Dynamics of Human and Non-human Systems

The ultimate objective of theorists studying living systems is to construct a general theory of life that can explain and predict the dynamics of both human and nonhuman systems. Yet little progress has been made in this endeavour. Why? Because of the inappropriate methods adopted by complexity theorists. By assuming that the supply-side physics model – in which local interactions are said to give rise to the emergence of order and complexity – could be transferred either entirely (social physics) or partially (agent-based models, or ABMs) from the physical to the life sciences, we have distorted reality and, thereby, delayed the construction of a general dynamic theory of living systems. Is there a solution? Yes, but only if we abandon the deductive and analogical methods of complexity theorists and adopt the inductive method. With this approach it is possible to construct a realist and demand-side general dynamic theory, as in the case of the dynamic-strategy theory presented in this paper.complex living systems, unified theory, general theory of life, dynamics. Demand-side, methodology

Adaptive Complex Contagions and Threshold Dynamical Systems

A broad range of nonlinear processes over networks are governed by threshold dynamics. So far, existing mathematical theory characterizing the behavior of such systems has largely been concerned with the case where the thresholds are static. In this paper we extend current theory of finite dynamical systems to cover dynamic thresholds. Three classes of parallel and sequential dynamic threshold systems are introduced and analyzed. Our main result, which is a complete characterization of their attractor structures, show that sequential systems may only have fixed points as limit sets whereas parallel systems may only have period orbits of size at most two as limit sets. The attractor states are characterized for general graphs and enumerated in the special case of paths and cycle graphs; a computational algorithm is outlined for determining the number of fixed points over a tree. We expect our results to be relevant for modeling a broad class of biological, behavioral and socio-technical systems where adaptive behavior is central.Comment: Submitted for publicatio

Dynamic Phase Transitions in PVT Systems

The main objective of this article are two-fold. First, we introduce some general principles on phase transition dynamics, including a new dynamic transition classification scheme, and a Ginzburg-Landau theory for modeling equilibrium phase transitions. Second, apply the general principles and the recently developed dynamic transition theory to study dynamic phase transitions of PVT systems. In particular, we establish a new time-dependent Ginzburg-Landau model, whose dynamic transition analysis is carried out. It is worth pointing out that the new dynamic transition theory, along with the dynamic classification scheme and new time-dependent Ginzburg Landau models for equilibrium phase transitions can be used in other phase transition problems, including e.g. the ferromagnetism and superfluidity, which will be reported elsewhere. In addition, the analysis for the PVT system in this article leads to a few physical predications, which are otherwise unclear from the physical point of view

Dissipative periodic processes

General theory of dissipative periodic systems for dynamic systems defined by differential equation