Geometric optimal control and applications to aerospace

Zhu, Jihong; Trélat, Emmanuel; Cerf, Max

doi:10.1186/s40736-017-0033-4

Cited by 23 publications

(13 citation statements)

References 78 publications

(176 reference statements)

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“…8. This result is also in line with popular litereture position (Wang Jian, 2016;Zhu et al, 2017). Our first novel controller, LQGi,1, used updated values of kalman gain all through the regime of simulation to arrive at the result dipicted in Fig.…”

Section: Discussion Of Resultssupporting

confidence: 79%

Pitch Control of a Rocket with a Novel LQG/LTR Control Algorithm

Kisabo¹,

Adebimpe²,

Sholiyi³

2019

Journal of Aircraft and Spacecraft Technology

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This paper presents the design, simulation and analysis of a novel LQG and LQG/LTR control algorithm for the pitch angle of a sounding rocket. These improved LQG and LQG/LTR control algorithms stem from the fact that a Riccati Differential Equation (RDE) rather than the popular Algebraic Riccati Equation (ARE) is used to obtaining the Kalman gain in the observer of the traditional Linear Quadratic Gaussian (LQG) control algorithm. Thus, eight (8) different controllers were design, simulated and analysed, three (3) of such controllers are novel and two out of these novel controllers were able to recover completely the robustness lost in the traditional LQG controller. All controllers synthesized were analysed using time response characteristics of closed-loop system and compared with the LQR and LQG control system. Using the LQR controller as the benchmark for best performance and the LQG as the worst. This study shows an application option that demonstrates optimal control system design in MATLAB/Simulink® and the approach put forward here proves to be very effective. 25indroduced here with a design for a novel variant of it. Results were discussed in section five before the conclusion section.

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Section: Discussion Of Resultssupporting

confidence: 79%

Pitch Control of a Rocket with a Novel LQG/LTR Control Algorithm

Kisabo¹,

Adebimpe²,

Sholiyi³

2019

Journal of Aircraft and Spacecraft Technology

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“…Not least, Example 2 reconsiders Hilbert's isoperimetric problem in this newly provided setting, while Example 3 provides an additional argument for the utility of this geometric approach. We point out the idea that our Riemannian optimal control is completely distinct from the geometric optimal control described in [6][7][8], where the role of the evolution variable was the classical one (time variable), while the state and control variables were assumed to be lying on differentiable manifolds.…”

Section: Introductionmentioning

confidence: 99%

Multivariate Optimal Control with Payoffs Defined by Submanifold Integrals

Bejenaru

Udrişte

2019

Symmetry

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This paper adapts the multivariate optimal control theory to a Riemannian setting. In this sense, a coherent correspondence between the key elements of a standard optimal control problem and several basic geometric ingredients is created, with the purpose of generating a geometric version of Pontryagin’s maximum principle. More precisely, the local coordinates on a Riemannian manifold play the role of evolution variables (“multitime”), the Riemannian structure, and the corresponding Levi–Civita linear connection become state variables, while the control variables are represented by some objects with the properties of the Riemann curvature tensor field. Moreover, the constraints are provided by the second order partial differential equations describing the dynamics of the Riemannian structure. The shift from formal analysis to optimal Riemannian control takes deeply into account the symmetries (or anti-symmetries) these geometric elements or equations rely on. In addition, various submanifold integral cost functionals are considered as controlled payoffs.

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“…e subject of optimal control problem (OCP) plays a basic role in many real life problems in different branches of sciences; for example, in, medicine [1], engineering and social sciences [2], biology [3], ecology [4], electric power [5], aerospace [6], and many other branches.…”

Section: Introductionmentioning

confidence: 99%

Constraints Optimal Control Governing by Triple Nonlinear Hyperbolic Boundary Value Problem

Al-Hawasy

Ali

2020

Journal of Applied Mathematics

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The focus of this work lies on proving the existence theorem of a unique state vector solution (Stvs) of the triple nonlinear hyperbolic boundary value problem (TNHBVP) when the classical continuous control vector (CCCVE) is fixed by using the Galerkin method (Galm), proving the existence theorem of a unique constraints classical continuous optimal control vector (CCCOCVE) with vector state constraints (equality EQVC and inequality INEQVC). Also, it consists of studying for the existence and uniqueness adjoint vector solution (Advs) of the triple adjoint vector equations (TAEqs) associated with the considered triple state equations (Tsteqs). The Fréchet Derivative (Frde.) of the Hamiltonian (HAM) is found. At the end, the theorems for the necessary conditions and the sufficient conditions of optimality (Necoop and Sucoop) are achieved.

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Geometric optimal control and applications to aerospace

Cited by 23 publications

References 78 publications

Pitch Control of a Rocket with a Novel LQG/LTR Control Algorithm

Pitch Control of a Rocket with a Novel LQG/LTR Control Algorithm

Multivariate Optimal Control with Payoffs Defined by Submanifold Integrals

Constraints Optimal Control Governing by Triple Nonlinear Hyperbolic Boundary Value Problem

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