2,414 research outputs found
The extended symplectic pencil and the finite-horizon LQ problem with two-sided boundary conditions
This note introduces a new analytic approach to the solution of a very
general class of finite-horizon optimal control problems formulated for
discrete-time systems. This approach provides a parametric expression for the
optimal control sequences, as well as the corresponding optimal state
trajectories, by exploiting a new decomposition of the so-called extended
symplectic pencil. Importantly, the results established in this paper hold
under assumptions that are weaker than the ones considered in the literature so
far. Indeed, this approach does not require neither the regularity of the
symplectic pencil, nor the modulus controllability of the underlying system. In
the development of the approach presented in this paper, several ancillary
results of independent interest on generalised Riccati equations and on the
eigenstructure of the extended symplectic pencil will also be presented
Algorithms for Computing Nash Equilibria in Deterministic LQ Games
In this paper we review a number of algorithms to compute Nash equilibria in deterministic linear quadratic differential games.We will review the open-loop and feedback information case.In both cases we address both the finite and the infinite-planning horizon.Algebraic Riccati equations;linear quadratic differential games;Nash equilibria
Unconditionnally stable scheme for Riccati equation
We present a numerical scheme for the resolution of matrix Riccati equation
used in control problems. The scheme is unconditionnally stable and the
solution is definite positive at each time step of the resolution. We prove the
convergence in the scalar case and present several numerical experiments for
classical test cases.Comment: 11 page
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