Synthesis and Computer Study of Population Dynamics Controlled Models Using Methods of Numerical Optimization, Stochastization and Machine Learning

The problems of synthesis and analysis of multidimensional controlled models of population dynamics are of both theoretical and applied interest. The need to solve numerical optimization problems for such a class of models is associated with the expansion of ecosystem control requirements. The need to solve the problem of stochastization is associated with the emergence of new problems in the study of ecological systems properties under the influence of random factors. The aim of the work is to develop a new approach to studying the properties of population dynamics systems using methods of numerical optimization, stochastization and machine learning. The synthesis problems of nonlinear three-dimensional models of interconnected species number dynamics, taking into account trophic chains and competition in prey populations, are studied. Theorems on the asymptotic stability of equilibrium states are proved. A qualitative and numerical study of the models is carried out. Using computational experiments, the results of an analytical stability and permanent coexistence study are verified. The search for equilibrium states belonging to the stability and permanent coexistence region is made using the developed intelligent algorithm and evolutionary calculations. The transition is made from the model specified by the vector ordinary differential equation to the corresponding stochastic model. A comparative analysis of deterministic and stochastic models with competition and trophic chains is carried out. New effects are revealed that are characteristic of three-dimensional models, taking into account the competition in populations of prey. The formulation of the optimal control problem for a model with competition and trophic chains is proposed. To find optimal trajectories, new generalized algorithms for numerical optimization are developed. A methods for the synthesis of controllers based on the use of artificial neural networks and machine learning are developed. The results on the search for optimal trajectories and generation of control functions are presented.The obtained results can be used in modeling problems of ecological, demographic, socio-economic and chemical kinetics systems.

CMAC Trained Optimum Mid course Guidance for Tactical Flight Vehicle

This paper discusses design and validation of neural network based mid-course guidance law of a surface to air flight vehicle. In present study, initially different optimal trajectories have been generated off-line of different pursuer-evader engagements by ensuring minimum flight time, maximum terminal velocity and favorable handing over conditions for seeker based terminal guidance. These optimal trajectories have been evolved by nonlinear programming based direct method of optimisation. The kinematic information of both pursuer and evader, generated based on these trajectories have been used to train cerebellar model articulate controller (CMAC) neural network. Later for a given engagement scenario an on-line near optimal mid-course guidance law has been evolved based on output of trained network. Training has been carried out by CMAC type supervisory neural network. The tested engagement condition is within input/output training space of neural network. Seeker based homing guidance has been used for terminal phase. Complete methodology has been validated along pitch plane of pursuer-evader engagement. During mid-course phase, the guidance demand has been tracked by attitude hold autopilot and during terminal phase, the guidance demanded lateral acceleration has been tracked by acceleration autopilot. System robustness has been studied in presence of plant parameter variations and sensor noise under Monte Carlo Platform.

Optimal Trajectory Synthesis for Spacecraft Asteroid Rendezvous

Several researchers are considering the plausibility of being able to rapidly launch a mission to an asteroid, which would fly in close proximity of the asteroid to deliver an impulse in a particular direction so as to deflect the asteroid from its current orbit. Planetary motion, in general, and the motion of asteroids, in particular, are subject to planetary influences that are characterised by a kind of natural symmetry, which results in an asteroid orbiting in a stable and periodic or almost periodic orbit exhibiting a number of natural orbital symmetries. Tracking and following an asteroid, in close proximity, is the subject of this paper. In this paper, the problem of synthesizing an optimal trajectory to a NEO such as an asteroid is considered. A particular strategy involving the optimization of a co-planar trajectory segment that permits the satellite to approach and fly alongside the asteroid is chosen. Two different state space representations of the Hill–Clohessy–Wiltshire (HCW) linearized equations of relative motion are used to obtain optimal trajectories for a spacecraft approaching an asteroid. It is shown that by using a state space representation of HCW equations where the secular states are explicitly represented, the optimal trajectories are not only synthesized rapidly but also result in lower magnitudes of control inputs which must be applied continuously over extended periods of time. Thus, the solutions obtained are particularly suitable for low thrust control of the satellites orbit which can be realized by electric thrusters.

Penalty function method for the minimal time crisis problem

In this note, we propose a new method to approximate the minimal time crisis problem using an auxiliary control and a penalty function, and show its convergence to a solution to the original problem. The interest of this approach is illustrated on numerical examples for which optimal trajectories can leave and enter the crisis set tangentially.

Sustainable Groundwater Management in A Two-Cell Aquifer Model

The design of optimal water policies between farmers, municipalities and groundwaterdependent ecosystem is analysed in a hydro-economic model with physical interactions between a confined aquifer and a shallow aquifer having a natural drainage. Based on the Pecos Basin case study, we analyse the optimal trajectories of the water tables and the water allocation between users and environment flows for the ecosystems. We also explore the consequences for the water manager to use a one-cell model instead of the two-cell model. Our results show the importance to consider hydraulic conductivities for the preservation of groundwater-dependent ecosystems.

Time-optimal planning for quadrotor waypoint flight

Quadrotors are among the most agile flying robots. However, planning time-optimal trajectories at the actuation limit through multiple waypoints remains an open problem. This is crucial for applications such as inspection, delivery, search and rescue, and drone racing. Early works used polynomial trajectory formulations, which do not exploit the full actuator potential because of their inherent smoothness. Recent works resorted to numerical optimization but require waypoints to be allocated as costs or constraints at specific discrete times. However, this time allocation is a priori unknown and renders previous works incapable of producing truly time-optimal trajectories. To generate truly time-optimal trajectories, we propose a solution to the time allocation problem while exploiting the full quadrotor’s actuator potential. We achieve this by introducing a formulation of progress along the trajectory, which enables the simultaneous optimization of the time allocation and the trajectory itself. We compare our method against related approaches and validate it in real-world flights in one of the world’s largest motion-capture systems, where we outperform human expert drone pilots in a drone-racing task.

Revisiting a Three-Player Pursuit-Evasion Game

We consider the game of a holonomic evader passing between two holonomic pursuers. The optimal trajectories of this game are known. We give a detailed explanation of the game of kind’s solution and present a computationally efficient way to obtain trajectories numerically by integrating the retrograde path equations. Additionally, we propose a method for calculating the partial derivatives of the Value function in the game of degree. This latter result applies to differential games with homogeneous Value.