2012/08/31 by Augusto Ferrante, Ferrante, Augusto, Lorenzo Ntogramatzidis +1
Engineering · Mathematics · #Computational Fluid Dynamics and Aerodynamics #FOS: Mathematics #Frequency Control in Power Systems #Numerical methods for differential equations #Optimization and Control (math.OC) #Spacecraft Dynamics and Control #Stability and Controllability of Differential Equations
paper · pdf · doi:10.48550/arxiv.1208.6481
openalex publication_date 2012/08/31 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28
This note introduces a new analytic approach to the solution of a very\ngeneral class of finite-horizon optimal control problems formulated for\ndiscrete-time systems. This approach provides a parametric expression for the\noptimal control sequences, as well as the corresponding optimal state\ntrajectories, by exploiting a new decomposition of the so-called extended\nsymplectic pencil. Importantly, the results established in this paper hold\nunder assumptions that are weaker than the ones considered in the literature so\nfar. Indeed, this approach does not require neither the regularity of the\nsymplectic pencil, nor the modulus controllability of the underlying system. In\nthe development of the approach presented in this paper, several ancillary\nresults of independent interest on generalised Riccati equations and on the\neigenstructure of the extended symplectic pencil will also be presented.\n