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Equivalence of control systems with linear systems on Lie groups and homogeneous spaces

Philippe Jouan (2010)

ESAIM: Control, Optimisation and Calculus of Variations

The aim of this paper is to prove that a control affine system on a manifold is equivalent by diffeomorphism to a linear system on a Lie group or a homogeneous space if and only if the vector fields of the system are complete and generate a finite dimensional Lie algebra. A vector field on a connected Lie group is linear if its flow is a one parameter group of automorphisms. An affine vector field is obtained by adding a left invariant one. Its projection on a homogeneous space, whenever it exists,...

Equivalent cost functionals and stochastic linear quadratic optimal control problems

Zhiyong Yu (2013)

ESAIM: Control, Optimisation and Calculus of Variations

This paper is concerned with the stochastic linear quadratic optimal control problems (LQ problems, for short) for which the coefficients are allowed to be random and the cost functionals are allowed to have negative weights on the square of control variables. We propose a new method, the equivalent cost functional method, to deal with the LQ problems. Comparing to the classical methods, the new method is simple, flexible and non-abstract. The new method can also be applied to deal with nonlinear...

Equivalent descriptions of a discrete-time fractional-order linear system and its stability domains

Piotr Ostalczyk (2012)

International Journal of Applied Mathematics and Computer Science

Two description forms of a linear fractional-order discrete system are considered. The first one is by a fractional-order difference equation, whereas the second by a fractional-order state-space equation. In relation to the two above-mentioned description forms, stability domains are evaluated. Several simulations of stable, marginally stable and unstable unit step responses of fractional-order systems due to different values of system parameters are presented.

Equivalent formulation and numerical analysis of a fire confinement problem

Alberto Bressan, Tao Wang (2010)

ESAIM: Control, Optimisation and Calculus of Variations

We consider a class of variational problems for differential inclusions, related to the control of wild fires. The area burned by the fire at time t> 0 is modelled as the reachable set for a differential inclusion x ˙ ∈F(x), starting from an initial set R0. To block the fire, a barrier can be constructed progressively in time. For each t> 0, the portion of the wall constructed within time t is described by a rectifiable set γ(t) ⊂ ℝ 2 . In this paper we show that the search for blocking strategies...

Ergodic control of linear stochastic equations in a Hilbert space with fractional Brownian motion

Tyrone E. Duncan, B. Maslowski, B. Pasik-Duncan (2015)

Banach Center Publications

A linear-quadratic control problem with an infinite time horizon for some infinite dimensional controlled stochastic differential equations driven by a fractional Brownian motion is formulated and solved. The feedback form of the optimal control and the optimal cost are given explicitly. The optimal control is the sum of the well known linear feedback control for the associated infinite dimensional deterministic linear-quadratic control problem and a suitable prediction of the adjoint optimal system...

Estimació del pol i de la variància del soroll d'un model AR (1) mitjançant filtratge no lineal.

M.ª Pilar Muñoz Gracia, Juan José Egozcue Rubí, Manuel Martí Recobert (1988)

Qüestiió

La estimación de los parámetros asociados a un proceso ARMA puede plantearse como un problema de filtrado no lineal. Para determinar un estimador recursivo de estos parámetros se define un vector de estado ampliado que incluye las variables de estado y los parámetros a estimar. Con un enfoque bayesiano se determina la distribución a posteriori del vector de estado ampliado. La síntesis del filtro no lineal permite: i) estimar los parámetros y determinar su precisión para un tamaño de muestra dado,...

Estimación adaptativa en tiempo real de funciones de transferencia. Revisión de las técnicas disponibles y presentación de nuevos algoritmos.

Daniel F. García Martínez, David de la Fuente García (1990)

Qüestiió

En este artículo se analizan los problemas planteados en la estimación en tiempo real de los parámetros de sistemas variantes con el tiempo, con el objeto de definir los requisitos que debe verificar un estimador de este tipo. Seguidamente se realiza un análisis crítico de las técnicas de estimación adaptativa más usuales, incidiendo en los aspectos fundamentales: la seguridad de funcionamiento del método, su capacidad de adaptación, la facilidad de uso del mismo y su coste computacional. Por último,...

Estimates for perturbations of average Markov decision processes with a minimal state and upper bounded by stochastically ordered Markov chains

Raúl Montes-de-Oca, Francisco Salem-Silva (2005)

Kybernetika

This paper deals with Markov decision processes (MDPs) with real state space for which its minimum is attained, and that are upper bounded by (uncontrolled) stochastically ordered (SO) Markov chains. We consider MDPs with (possibly) unbounded costs, and to evaluate the quality of each policy, we use the objective function known as the average cost. For this objective function we consider two Markov control models ℙ and ℙ 1 . ℙ and ℙ 1 have the same components except for the transition laws. The transition...

Estimates for perturbations of discounted Markov chains on general spaces

Raúl Montes-de-Oca, Alexander Sakhanenko, Francisco Salem-Silva (2003)

Applicationes Mathematicae

We analyse a Markov chain and perturbations of the transition probability and the one-step cost function (possibly unbounded) defined on it. Under certain conditions, of Lyapunov and Harris type, we obtain new estimates of the effects of such perturbations via an index of perturbations, defined as the difference of the total expected discounted costs between the original Markov chain and the perturbed one. We provide an example which illustrates our analysis.

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