Quadratic optimal control for discrete-time infinite-dimensional stochastic bilinear systems

Abstract

In this paper, we consider the class of infinite-dimensional discrete-time linear systems with multiplicative random disturbances (i.e. with the state multiplied by a random sequence), also known as stochastic bilinear systems. We formulate and solve the quadratic optimal-control problem for this class of systems subject to an arbitrary additive stochastic £ 2 input disturbance. Under assumptions that guarantee the existence of a solution to an algebraic Riccati-like operator equation (derived previously by the authors), we characterize a bounded linear operator that takes the additive stochastic (.2 input disturbance and the initial condition into the optimal control law. Such a result generalizes, to the infinite-dimensional bilinear stochastic case, some known results for the deterministic linear case.

Application of the difference lmis method to robust stochastic H_∞ control and filtering of distinct plants

“…Systems whose parameter uncertainties are modelled as white noise processes in a linear setting have been treated in [3] - [5], for the continuous-time case, and in [2], [6] - [8], for the discrete-time case (see [9] and the references therein). Such models of uncertainties are encountered in many areas of applications (see [2] and the references therein) such as: nuclear fission and heat transfer, population models and immunology.…”

“…Such models of uncertainties are encountered in many areas of applications (see [2] and the references therein) such as: nuclear fission and heat transfer, population models and immunology. In control theory such models are encountered in gain scheduling when the scheduling parameters are corrupted with white measurement noise.…”

Static output-feedback of state-multiplicative systems with application to altitude control

“…Recently, a renewed interest in this problem has been encountered and solutions to the stochastic control problem have been derived that ensure a worst case performance bound in the H 1 norm (Costa andKubrusly 1996, Dragan andMorozan 1997).…”

“…Systems with parameter uncertainties that are modelled as white noise processes in a linear setting have been treated in Gershon et al (2001 a) and Hinrischsen and Pritchard (1998) for the continuoustime case and in Costa and Kubrusly (1996), Dragan and Stoica (1998) and Gershon et al (2001Gershon et al ( b, 2002, for the discrete-time case. Models of uncertainties are encountered in many areas of application (see Costa and Kubrusly 1996, and the references therein) such as: nuclear fission and heat transfer, population models and immunology.…”

“…Models of uncertainties are encountered in many areas of application (see Costa and Kubrusly 1996, and the references therein) such as: nuclear fission and heat transfer, population models and immunology. In control theory such models are used in gain scheduling (Boyd et al 1994) where the scheduling parameters are corrupted with noise.…”