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Runners competing in races are looking to optimize their performance. In this paper, a runner's performance in a race, such as a marathon, is formulated as an optimal control problem where the controls are: the nutrition intake throughout…
This paper formulates optimal pacing of a cyclist on hilly terrain time-trials as a minimum-time optimal control problem. Maximal power of a cyclist serves as a time-varying constraint and depends on fatigue and recovery which are captured…
This paper introduces a nonlinear optimal guidance framework for guiding a pursuer to intercept a moving target, with an emphasis on real-time generation of optimal feedback control for a nonlinear optimal control problem. Initially,…
This paper presents an optimal control problem to analyze the efficacy of counter-terrorism tactics. We present an algorithm that efficiently combines the Minimum Principle of Pontryagin, the shooting method and the cyclic descent of…
In this paper, we present a framework for solving continuous optimal control problems when the true system dynamics are approximated through an imperfect model. We derive a control strategy by applying Pontryagin's Minimum Principle to the…
Our aim is to present a new model which encompasses pace optimization and motor control effort for a runner on a fixed distance. We see that for long races, the long term behaviour is well approximated by a turnpike problem. We provide…
We present a mathematical model for optimizing breakaway strategies in competitive cycling, balancing power expenditure, aerodynamic drag, and crashing. Our framework incorporates probabilistic crash dynamics, allowing a cyclist's risk…
In order to describe the velocity and the anaerobic energy of two runners competing against each other for middle-distance races, we present a mathematical model relying on an optimal control problem for a system of ordinary differential…
Conceptual view of fitness and fitness measurement of strategic decisions on information systems, technological systems and innovation are becoming more important in recent years. This paper determines some dynamics of fitness landscape…
With the advent of power-meters allowing cyclists to precisely track their power outputs throughout the duration of a race, devising optimal power output strategies for races has become increasingly important in competitive cycling. To do…
In this work we refer to motivations, applications, and relations of control theory with other areas of mathematics. We present a brief historical review of optimal control theory, from its roots in the calculus of variations and the…
Optimal Control Theory is a powerful mathematical tool, which has known a rapid development since the 1950s, mainly for engineering applications. More recently, it has become a widely used method to improve process performance in quantum…
In this note our aim is to give a proof of the Pontryagin maximum principle for a general optimal control problem with running state constraints and smooth dynamics. Our proof is based on the classical Ekeland variational principle. The…
This paper aims to address the nonlinear optimal guidance problem with impact-time and impact-angle constraints, which is fundamentally important for multiple pursuers to collaboratively achieve a target. Addressing such a guidance problem…
Quantum metrology comprises a set of techniques and protocols that utilize quantum features for parameter estimation which can in principle outperform any procedure based on classical physics. We formulate the quantum metrology in terms of…
Elucidating the fitness measures optimized during the evolution of complex biological systems is a major challenge in evolutionary theory. We present experimental evidence and an analytical framework demonstrating how biochemical networks…
We study an optimal control problem arising from a resource allocation problem in cellular metabolism. A minimalistic model that describes the production of enzymatic vs. non-enzymatic biomass components from a single nutrient source is…
The foraging behavior of animals is a paradigm of target search in nature. Understanding which foraging strategies are optimal and how animals learn them are central challenges in modeling animal foraging. While the question of optimality…
This paper consists of a detailed and novel stochastic optimal control analysis of a coupled non-linear dynamical system. The state equations are modeled as additional food provided prey-predator system with Holling Type-III functional…
Physicists seeking to understand complex biological systems often find it rewarding to create simple "toy models" that reproduce system behavior. Here a toy model is used to understand a puzzling phenomenon from the sport of track and…