Hamiltonian Servo: Control and Estimation of a Large Team of Autonomous Robotic Vehicles

This paper proposes a novel Hamiltonian servo system, a combined modeling framework for control and estimation of a large team/fleet of autonomous robotic vehicles. The Hamiltonian servo framework represents high-dimensional, nonlinear and non-Gaussian generalization of the classical Kalman servo system. After defining the Kalman servo as a motivation, we define the affine Hamiltonian neural network for adaptive nonlinear control of a team of UGVs in continuous time. We then define a high-dimensional Bayesian particle filter for estimation of a team of UGVs in discrete time. Finally, we formulate a hybrid Hamiltonian servo system by combining the continuous-time control and the discrete-time estimation into a coherent framework that works like a predictor-corrector system.

Tensor-Centric Warfare V: Topology of Systems Confrontation

In this paper, as a new contribution to the tensor-centric warfare (TCW) series [1] [2] [3] [4], we extend the kinetic TCW-framework to include non-kinetic effects, by addressing a general systems confrontation [5], which is waged not only in the traditional physical Air-Land-Sea domains, but also simultaneously across multiple non-physical domains, including cyberspace and social networks. Upon this basis, this paper attempts to address a more general analytical scenario using rigorous topological methods to introduce a two-level topological representation of modern armed conflict;in doing so, it extends from the traditional red-blue model of conflict to a red-blue-green model, where green represents various neutral elements as active factions;indeed, green can effectively decide the outcomes from red-blue conflict. System confrontations at various stages of the scenario will be defined by the non-equilibrium phase transitions which are superficially characterized by sudden entropy growth. These will be shown to have the underlying topology changes of the systems-battlespace. The two-level topological analysis of the systems-battlespace is utilized to address the question of topology changes in the combined battlespace. Once an intuitive analysis of the combined battlespace topology is performed, a rigorous topological analysis follows using (co)homological invariants of the combined systems-battlespace manifold.

Tensor-Centric Warfare I: Tensor Lanchester Equations

We propose the basis for a rigorous approach to modeling combat, specifically under conditions of complexity and uncertainty. The proposed basis is a tensorial generalization of earlier Lanchester-type equations, inspired by the contemporary debate in defence and military circles around how to best utilize information and communications systems in military operations, including the distributed C4ISR system (Command, Control, Communications, Computing, Intelligence, Surveillance and Reconnaissance). Despite attracting considerable interest and spawning several efforts to develop sound theoretical frameworks for informing force design decision-making, the development of good frameworks for analytically modeling combat remains anything but decided. Using a simple combat scenario, we first develop a tensor generalization of the Lanchester square law, and then extend it to also include the Lanchester linear law, which represents the effect of suppressive fire. We also add on-off control inputs, and discuss the results of a simple simulation of the final model using our small scenario.

Tensor-Centric Warfare II: Entropic Uncertainty Modeling

In the first paper of the tensor-centric warfare (TCW) series [1], we proposed a tensor model of combat generalizing earlier Lanchester-type systems with a particular emphasis on contemporary military thinking, including the distributed C4ISR system (Command, Control, Communications, Computing, Intelligence, Surveillance and Reconnaissance). In the present paper, we extend this initial tensor combat model with entropic Lie-derivative machinery in order to capture some aspects of this deep uncertainty, while, in the process, formalizing into our model military notion of symmetry and asymmetry in warfare as a commutator, also known as a Lie bracket. In doing so, we have sought to shift the question from the prediction of outcomes of combat, upon which previous combat models such as the Lanchester-type equations have been typically constructed, towards determining the uncertainty outcomes, using a rigorous analytical basis.

Tensor-Centric Warfare VI: A Global Warfare Model

We propose a global warfare model that integrates the models of the whole tensor-centric warfare series, represented as a high-dimensional entangled warfare category. Its underpinning metaphysics is “entangled fusion”: this is the macroscopic entanglement concept inspired by high-dimensional (HD) quantum computation (the “quantum brain”), in which any number of entangled wave-functions can be highly correlated, with neuron-like signaling among them. From this entangled perspective, war and battle is seen essentially as a holistic phenomenon: if any one of a set of mutually entangled warring parties is removed from the equation, then the war as it is instantly stops, possibly to be replaced by a new conflict between the remaining parties but distinct from that which it supplants. The formal global warfare framework developed in this paper expresses this fundamental idea of arbitrary many interrelated/entangled conflicts, each of them defined by its own battle-manifold (with warfighting tensor fields acting on it) and occurring (more-or-less) simultaneously on the planet;we call this entangled

Tensor-Centric Warfare III: Combat Dynamics with Delta-Strikes

This paper is the third part of the complex combat dynamics series, called tensor-centric warfare (for the first two parts, see [1] [2]). In the present paper, we extend the tensor combat model from [1] and [2] to model the dynamics of delta-strikes/missiles , which are temporally confined strong kinetic effects . The scenarios analyzed here include both deterministic and random delta-strikes which mimic single, multiple and continuous-time missile attacks. We also look at the bidirectional random strike as well as the general Hamilton-Langevin dynamics framework and provide an interpretation of the results obtained through simulation.

Tensor-Centric Warfare IV:Kahler Dynamics of Battlefields

This paper presents the complex dynamics synthesis of the combat dy-namics series called tensor-centric warfare (TCW;for the first three parts of the series, see [1] [2] [3]), which includes tensor generalization of classical Lanchester-type combat equations, entropic Lie-dragging and commutators for modeling warfare uncertainty and symmetry, and various delta-strikes and missiles (both deterministic and random). The present paper gives a unique synthesis of the Red vs. Blue vectorfields into a single complex battle-vectorfield, using dynamics on Kähler manifolds as a rigorous framework for extending the TCW concept. The global Kähler dynamics framework, with its rigorous underpinning called the Kähler-Ricci flow, provides not only a new insight into the “geometry of warfare”, but also into the “physics of warfare”, in terms of Lagrangian and Hamiltonian structures of the battlefields. It also provides a convenient and efficient computational framework for entropic wargaming.