136 research outputs found
A reduction technique for Generalised Riccati Difference Equations
This paper proposes a reduction technique for the generalised Riccati
difference equation arising in optimal control and optimal filtering. This
technique relies on a study on the generalised discrete algebraic Riccati
equation. In particular, an analysis on the eigen- structure of the
corresponding extended symplectic pencil enables to identify a subspace in
which all the solutions of the generalised discrete algebraic Riccati equation
are coin- cident. This subspace is the key to derive a decomposition technique
for the generalised Riccati difference equation that isolates its nilpotent
part, which becomes constant in a number of steps equal to the nilpotency index
of the closed-loop, from another part that can be computed by iterating a
reduced-order generalised Riccati difference equation
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
Structural invariants of two-dimensional systems
In this paper, some fundamental structural properties of two-dimensional (2-D) systems which remain invariant under feedback and output-injection transformation groups are identified and investigated for the first time. As is well known, structural invariants that follow from the definition of controlled and conditioned invariance, output-nulling, input-containing, self-bounded and self-hidden subspaces play pivotal roles in many theoretical studies of systems theory and in the solution of several control/estimation problems. These concepts are developed and studied within a 2-D context in this paper
Repeated eigenstructure assignment in the computation of friends of output-nulling subspaces
This paper is concerned with the parameterisation of basis matrices and the simultaneous computation of friends of the output nulling subspaces V*, V*g and R* with the assignment of the corresponding inner and outer closed-loop free eigenstructure. Differently from the classical techniques presented in the literature so far on this topic, which are based on the standard pole assignment algorithms and are therefore applicable only in the non-defective case, the method presented in this paper can be applied in the case of closed-loop eigenvalues with arbitrary multiplicity
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