Optimal spiral-like solutions near a singular extremal in a two-input control problem

DOI10.3934/dcdsb.2021187OpenAlexW3185700508MaRDI QIDQ2671200

M. I. Ronzhina, L. A. Manita

Publication date: 3 June 2022

Published in: Discrete and Continuous Dynamical Systems. Series B (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/dcdsb.2021187

zbMATH Keywords

Hamiltonian systeminverted spherical pendulumsingular extremalblow-up singularitytwo-dimensional bounded control

Mathematics Subject Classification ID

Linear systems in control theory (93C05) Regularity of solutions in optimal control (49N60) Existence theories for free problems in two or more independent variables (49J10)

Related Items (1)

Spiral-like extremals near a singular surface in a rocket control problem

Cites Work

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• Planar tilting maneuver of a spacecraft: singular arcs in the minimum time problem and chattering
• Geometric optimal control. Theory, methods and examples
• Multi-input optimal control problems for combined tumor anti-angiogenic and radiotherapy treatments
• Singular optimal regimes in problems of mathematical economics
• Time-optimal swing-up feedback control of a pendulum
• Optimal control for a Timoshenko beam
• A family of smooth controllers for swinging up a pendulum
• Qualitative study of singularities for extremals of quadratic optimal control problem
• Theory of chattering control with applications to astronautics, robotics, economics, and engineering
• Periodic motions
• Swinging up the spherical pendulum via stabilization of its first integrals.
• Optimal control of a spherical inverted pendulum
• Typicality of chaotic fractal behavior of integral vortices in Hamiltonian systems with discontinuous right hand side
• Optimal synthesis in the control problem of an \(n\)-link inverted pendulum with a moving base
• Time-optimal trajectories of generic control-affine systems have at worst iterated Fuller singularities
• Singular trajectories and their role in control theory
• Singular trajectories in multi-input time-optimal problems: Application to controlled mechanical systems
• Optimal control--4. Transl. from the Russian
• Control theory from the geometric viewpoint.
• Swinging up a pendulum by energy control
• Optimal synthesis in a model problem with two-dimensional control lying in an arbitrary convex set
• Kelley condition and structure of Lagrange manifold in a neighborhood of a first-order singular extremal
• Controlled Lagrangians and the stabilization of mechanical systems. I. The first matching theorem
• Minimum Time Control of the Rocket Attitude Reorientation Associated with Orbit Dynamics
• Optimal feedback strategies for bacterial growth with degradation, recycling, and effect of temperature
• Non-local stabilization of a spherical inverted pendulum
• Regularization of Chattering Phenomena via Bounded Variation Controls
• Asymptotic Smooth Stabilization of the Inverted 3-D Pendulum
• Fuller Singularities for Generic Control-Affine Systems with an Even Number of Controls
• Optimality of intermediate-thrust arcs of rocket trajectories
• Almost global stabilization of the inverted pendulum via continuous state feedback

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