2016/01/15 by Sergio Grillo, Grillo, Sergio, Leandro Salomone +3
Biochemistry, Genetics and Molecular Biology · Engineering · Mathematics · Physics and Astronomy · #ATP Synthase and ATPases Research #Control and Stability of Dynamical Systems #FOS: Mathematics #Numerical methods for differential equations #Optimization and Control (math.OC) #Quantum chaos and dynamical systems
paper · pdf · doi:10.48550/arxiv.1601.03975
openalex publication_date 2016/01/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we make a review of the controlled Hamiltonians (CH) method\nand its related matching conditions, focusing on an improved version recently\ndeveloped by D.E. Chang. Also, we review the general ideas around the Lyapunov\nconstraint based (LCB) method, whose related partial differential equations\n(PDEs) were originally studied for underactuated systems with only one\nactuator, and then we study its PDEs for an arbitrary number of actuators. We\nanalyze and compare these methods within the framework of Differential\nGeometry, and from a purely theoretical point of view. We show, in the context\nof underactuated systems defined by simple Hamiltonian functions, that the LCB\nmethod and the Chang's version of the CH method are equivalent stabilization\nmethods (i.e. they give rise to the same set of control laws). In other words,\nwe show that the Chang's improvement of the energy shaping method is precisely\nthe LCB method. As a by-product, coordinate-free and connection-free\nexpressions of Chang's matching conditions are obtained.\n