Yoshifumi Sunahara

On stochastic controllability for nonlinear systems

Both the stochastic e-controllability and the stochastic controllability with probability one are first defined. Second, by using a stochastic Lyapunov-like approach, several theorems are developed which give sufficient conditions for the stochastic controllability defined for an important class of nonlinear stochastic systems. A theorem of stochastic uncontrollability is also presented, giving sufficient conditions for stochastic uncontrollability for a class of nonlinear systems. Finally, the relation between the deterministic controllability and the stochastic one is comparatively discussed.

On the stochastic observability and controllability for non-linear systems†

The purpose of this paper is to present sufficient conditions for the stochastic observability and controllability of non-linear systems. First, the stochastic observability is defined and several theorems which give sufficient conditions of the stochastic observability are developed for an important class of non-linear systems. Secondly, the definition of stochastic controllability is also presented. By using the Lyapunov-like approach, sufficient conditions of the stochastic controllability are also shown. Finally, the mutual relation between the stochastic observability and controllability is discussed via sufficient conditions obtained above. For the purpose of supporting the theoretical aspects developed here, results of simulation studies are also demonstrated.

An approximate method of state estimation for non-linear dynamical systems with state-dependent noise†

In this paper a method of stochastic linearization is demonstrated for the purpose of establishing an approximate approach to solve filtering problems of non-linear stochastic systems with state-dependent noise in a Markovian framework. The models of both the dynamical system and the observation process are described by non-linear stochastic differential equations of Ito type. The principal line of attack is to expand the non-linear drift term into a certain linear function with coefficients which are determined under the minimal squared error criterion. Two methods of linearization are developed for the non-linear diffusion term. The linearized models are thus characterized by expansion coefficients dependent on both the state estimate and the error covariance. A method is given for the simultaneous treatment of the approximate structure of state estimator dynamics and of the running evaluation of the error covariance, including quantitative aspects of sample path behaviours obtained by digital simulatio...

Paper: A method of parameter identification for linear distributed parameter systems

A method is presented for estimating unknown parameters in distributed parameter systems. The system considered is assumed to be modeled by a stochastic partial differential equation whose form is known to be linear and unknown parameters are contained in exciting terms. Unknown parameters are assumed to be a set of random constants whose a priori probabilities are known. First, the estimation process of unknown parameters is given by the Bayesian approach in the Markovian framework. The dynamics of the state estimation is also given, which is simultaneously required in the parameter identification scheme. Secondly, the computing procedure is presented, circumventing tedious calculations of the covariance function between the system state and unknown parameters. Finally, two numerical examples are shown, emphasizing that the dynamics of the observation mechanisms adopted plays an important role in both the state estimation and parameter identification.

Stochastic optimal control for non-linear dynamical systems under noisy observations

In this paper, an approximate technique based on stochastic linearization is developed which permits us to design sub-optimal state estimates and feedback controls for non-linear dynamical systems with state-independent noise. First, a method of establishing approximate filter dynamics is briefly outlined. Secondly, by using the filter dynamics obtained, an approximate technique for finding sub-optimal controls is presented for the quadratic cost functional. Finally, detailed discussions are given by a numerical example, including quantitative aspects of sample paths behavior of state estimate and sub-optimal control signals.

A method for parameter estimation of a class of non-linear distributed systems under noisy observations

Abstract A method is presented for estimating an unknown parameter of a distributed parameter system which depends on the system state. The system considered is modelled by a class of non-linear partial differential equations of a parabolic type. Noisy observations are assumed to be taken through an arbitrary number of sensors allocated on the spatial region. First, the explicit form of the stationary solution of the state equation is discussed. Second, use is made of the maximum likelihood approach to obtain the optimal estimate of the unknown parameter. Consistency properties w.p.1 of the optimal estimate obtained are also shown. Finally, results of digital simulation experiments are included to support the theoretical aspects.

A Method of Parameter Estimation for Stochastic Distributed Parameter Systems and its Applications to Seismic Profiles Identification

Abstract Bearing in mind an application to the identification of seismic profiles, e.g., the oil exploration survey, this taper gives a feasible method for estimating parameters of a class of distributed parameter systems modeled by the one-dimensional hyperbolic partial differential equation with stochastic boundary input. Fast, the theoretical aspect of existence and uniqueness conditions of the solution to the basic equation is discussed in a Kilbert space. Secondly, a method for estimating the system parameter is developed within the framework of the maximum likelihood ratio principle. An example of practical applications is finally shown, including estimation of the reflection coefficients in layered media by using reflected seismic wave data.

An approximate method of stochastic terminal control for nonlinear dynamical systems

Abstract The purpose of this paper is to establish an approximate method of stochastic terminal control for nonlinear dynamical systems with state-independent noise. Guided by the state variable representation concept in control theory, we describe approximately mathematical models for both the dynamical system and the observation mechanism by the nonlinear vector stochastic differential equations of Ito-type. First, for the purpose of overcoming difficulties caused by nonlinear characteristics, a method of stochastic linearization is introduced. By using the stochastic linearization technique presented here, an approximate method is described for solving state estimation problems of nonlinear dynamical systems in a Markovian framework. Secondly, by using the estimator dynamics obtained, an approximation to the optimal control is presented for a terminal cost functional. Finally, detailed discussions are given by an example, including quantitative aspects of sample paths behavior of state estimation and optimal control signal.

A Method for Spatial Domain Identification of Distributed Parameter Systems Under Noisy Observations

Abstract Motivated by oil reservoir problems, this paper is concerned with the theoretical and computation aspects of a method for identifying the spatial domain of distributed parameter systems under noisy observations. The system model is given by a partial differential equation of parabolic type derived by a known distributed input. A mathematical model with an additive noise term of the observation mecnanism is also given. Based on the concept of the maximum likelihood estimate, the estimation algorithm is presented in a form of the recursive computation. The main body of theoretical aspects in this paper is convergency properties of the estimation algorithm. Both the feasibility and the validity of the method presented here are discussed including results of digital simulation experiments.

Boundary Identification for a Two-Dimensional Diffusion System Under Noisy Observations

Abstract This paper is concerned with the boundary identification problem for a diffusion system under noisy observations. First, the system domain with a partially unknown boundary is given by the bounded set in R(2) . For the system governed by a two-dimensional diffusion equation, noisy observation data are acquired through sensors allocated on the part of known boundary. Secondly, with background knowledge of maximum likelihood estimate, the on-line parameter estimation method is proposed in a form of recursive computation. A method for computer implementation of the proposed estimator is discussed by applying the boundary clement method. Finally, results of digital simulation experiments are shown for the purpose of supporting the theoretical aspect.