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

A reduction technique for generalised Riccati difference equations arising in linear-quadratic optimal control

In this paper we develop a reduction technique for the generalised Riccati difference equation arising in optimal control and optimal filtering. This technique relies on a decomposition method for the generalised Riccati difference equation that isolates its nilpotent part, which becomes constant in a number of iteration steps equal to the nilpotency index of the closed-loop, from another part that can be computed by iterating a reduced-order Riccati difference equation

A reduction technique for discrete generalized algebraic and difference Riccati equations

This paper proposes a reduction technique for the generalized Riccati difference equation arising in optimal control and optimal filtering. This technique relies on a study on the generalized discrete algebraic Riccati equation. In particular, an analysis on the eigenstructure of the corresponding extended symplectic pencil enables to identify a subspace in which all the solutions of the generalized discrete algebraic Riccati equation are coincident. This subspace is the key to derive a decomposition technique for the generalized Riccati difference equation. This decomposition isolates a “nilpotent” part, which converges to a steady-state solution in a finite number of steps, from another part that can be computed by iterating a reduced-order generalized Riccati difference equation

The non-symmetric discrete algebraic Riccati equation and canonical factorization of rational matrix functions on the unit circle.

Canonical factorization of a rational matrix function on the unit circle is described explicitly in terms of a stabilizing solution of a discrete algebraic Riccati equation using a special state space representation of the symbol. The corresponding Riccati difference equation is also discussed. © The Author(s)

Almost optimal adaptive LQ control: observed state case

In this paper we propose an almost optimal indirect adaptive controller for input/state dynamical systems. The control part of the adaptive scheme is based on a modified LQ control law: by adding a time varying gain to the certainty equivalent control law we avoid the conflict between identification and contro

Asymptotic properties for half-linear difference equations

summary:Asymptotic properties of the half-linear difference equation $$\Delta (a_{n}|\Delta x_{n}|^{\alpha }\mathop {\mathrm sgn}\Delta x_{n} )=b_{n}|x_{n+1}|^{\alpha }\mathop {\mathrm sgn}x_{n+1} \qquad \mathrm{(*)}$$ are investigated by means of some summation criteria. Recessive solutions and the Riccati difference equation associated to $(*)$ are considered too. Our approach is based on a classification of solutions of $(*)$ and on some summation inequalities for double series, which can be used also in other different contexts

LQ-optimal Sample-data Control under Stochastic Delays: Gridding Approach for Stabilizability and Detectability

We solve a linear quadratic optimal control problem for sampled-data systems with stochastic delays. The delays are stochastically determined by the last few delays. The proposed optimal controller can be efficiently computed by iteratively solving a Riccati difference equation, provided that a discrete-time Markov jump system equivalent to the sampled-data system is stochastic stabilizable and detectable. Sufficient conditions for these notions are provided in the form of linear matrix inequalities, from which stabilizing controllers and state observers can be constructed.Comment: 28 pages, 3 figure