Guidance and Control strategies for aerospace vehicles

A neighboring optimal guidance scheme was devised for a nonlinear dynamic system with stochastic inputs and perfect measurements as applicable to fuel optimal control of an aeroassisted orbital transfer vehicle. For the deterministic nonlinear dynamic system describing the atmospheric maneuver, a nominal trajectory was determined. Then, a neighboring, optimal guidance scheme was obtained for open loop and closed loop control configurations. Taking modelling uncertainties into account, a linear, stochastic, neighboring optimal guidance scheme was devised. Finally, the optimal trajectory was approximated as the sum of the deterministic nominal trajectory and the stochastic neighboring optimal solution. Numerical results are presented for a typical vehicle. A fuel-optimal control problem in aeroassisted noncoplanar orbital transfer is also addressed. The equations of motion for the atmospheric maneuver are nonlinear and the optimal (nominal) trajectory and control are obtained. In order to follow the nominal trajectory under actual conditions, a neighboring optimum guidance scheme is designed using linear quadratic regulator theory for onboard real-time implementation. One of the state variables is used as the independent variable in reference to the time. The weighting matrices in the performance index are chosen by a combination of a heuristic method and an optimal modal approach. The necessary feedback control law is obtained in order to minimize the deviations from the nominal conditions

Hybrid global-local optimisation algorithms for the layout design of tidal turbine arrays

Tidal stream power generation represents a promising source of renewable energy. In order to extract an economically useful amount of power, tens to hundreds of tidal turbines need to be placed within an array. The layout of these turbines can have a significant impact on the power extracted and hence on the viability of the site. Funke et al. formulated the question of the best turbine layout as an optimisation problem constrained by the shallow water equations and solved it using a local, gradient-based optimisation algorithm. Given the local nature of this approach, the question arises of how optimal the layouts actually are. This becomes particularly important for scenarios with complex bathymetry and layout constraints, both of which typically introduce locally optimal layouts. Optimisation algorithms which find the global optima generally require orders of magnitude more iterations than local optimisation algorithms and are thus infeasible in combination with an expensive flow model. This paper presents an analytical wake model to act as an efficient proxy to the shallow water model. Based upon this, a hybrid global-local two-stage optimisation approach is presented in which turbine layouts are first optimised with the analytical wake model via a global optimisation algorithm, and further optimised with the shallow water model via a local gradient-based optimisation algorithm. This procedure is applied to a number of idealised cases and a more realistic case with complex bathymetry in the Pentland Firth, Scotland. It is shown that in cases where bathymetry is considered, the two-stage optimisation procedure is able to improve the power extracted from the array by as much as 25% compared to local optimisation for idealised scenarios and by as much as 12% for the more realistic Pentland Firth scenario whilst in many cases reducing the overall computation time by approximately 35%

Overcoming the timescale barrier in molecular dynamics: Transfer operators, variational principles and machine learning

One of the main challenges in molecular dynamics is overcoming the ‘timescale barrier’: in many realistic molecular systems, biologically important rare transitions occur on timescales that are not accessible to direct numerical simulation, even on the largest or specifically dedicated supercomputers. This article discusses how to circumvent the timescale barrier by a collection of transfer operator-based techniques that have emerged from dynamical systems theory, numerical mathematics and machine learning over the last two decades. We will focus on how transfer operators can be used to approximate the dynamical behaviour on long timescales, review the introduction of this approach into molecular dynamics, and outline the respective theory, as well as the algorithmic development, from the early numerics-based methods, via variational reformulations, to modern data-based techniques utilizing and improving concepts from machine learning. Furthermore, its relation to rare event simulation techniques will be explained, revealing a broad equivalence of variational principles for long-time quantities in molecular dynamics. The article will mainly take a mathematical perspective and will leave the application to real-world molecular systems to the more than 1000 research articles already written on this subject

A variational approach to linear control structure problems

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