A dynamical system approach to continuous speech recognition

This paper derives conditions under which co-diagonalization of the controllability and observability Gramians can be performed in a physically consistent manner for the class of linear quantum stochastic systems that are common in the fields of quantum optics and related areas like quantum nano- and optomechanical systems. Such a class is essentially a quantum analogue of classical (non-quantum) linear stochastic systems. However, unlike their classical counterparts, the laws of quantum mechanics impose nonlinear equality constraints on the system matrices of linear quantum stochastic systems, the so-called physical realizability constraints. Therefore, a meaningful model reduction procedure must yield a physically realizable reduced model satisfying these constraints. Previous work has shown that model reduction by subsystem truncation preserves physical realizability, but did not propose a method for truncating a subsystem. One candidate approach for this truncation is a quantum adaptation of the well-known balanced truncation method for classical linear time-invariant systems. It is shown in this paper that balanced realization for linear quantum stochastic systems is only possible under a strongly restrictive necessary and sufficient condition. However, the paper also derives less restrictive necessary and sufficient conditions for other realizations with simultaneously diagonal controllability and observability Gramians, and introduces the notion of a quasi-balanced realization. An example of the application of the results is provided to demonstrate quasi-balanced truncation in the linear quantum stochastic setting.

Approximation identification for the stochastic time-delayed dynamical system

Identification of stochastic linear dynamic systems using Kalman filter representation

In order to accelerate computations and improve long time accuracy of numerical simulations, this thesis develops multiscale geometric integrators. For general multiscale stiff ODEs, SDEs, and PDEs, FLow AVeraging integratORs (FLAVORs) have been proposed for the coarse time-stepping without any identification of the slow or the fast variables. In the special case of deterministic and stochastic mechanical systems, symplectic, multisymplectic, and quasi-symplectic multiscale integrators are easily obtained using this strategy. For highly oscillatory mechanical systems (with quasi-quadratic stiff potentials and possibly high-dimensional), a specialized symplectic method has been devised to provide improved efficiency and accuracy. This method is based on the introduction of two highly nontrivial matrix exponentiation algorithms, which are generic, efficient, and symplectic (if the exact exponential is symplectic). For multiscale systems with Dirac-distributed fast processes, a family of symplectic, linearly-implicit and stable integrators has been designed for coarse step simulations. An application is the fast and accurate integration of constrained dynamics. In addition, if one cares about statistical properties of an ensemble of trajectories, but not the numerical accuracy of a single trajectory, we suggest tuning friction and annealing temperature in a Langevin process to accelerate its convergence. Other works include variational integration of circuits, efficient simulation of a nonlinear wave, and finding optimal transition pathways in stochastic dynamical systems (with a demonstration of mass effects in molecular dynamics).

This Paper deals with the recursive identification problem of stochastic linear dynamical systems , Important Algorithms are explained in the identification system domains that are time-varying, and using a recursive Least Square method with a famous approach to estimate the model parameter, that a forgetting factor, and a Kalman filter approach with different values for a best linear dynamic models, that are identified from the two type of stochastic linear dynamic systems: that the equation error models which contain ARX models and ARMAX models. Output error models which consist of OE and Box-Jenkins models, that are reached by using the suggested instrument in Off-Line Identification, where the exact Linear models reached their parameter stable with Time, Moreover, the Statistic terms are verified from a point of random errors and insignificant cross-correlation between inputs and outputs residual.

Control systems have several applications in real-world problems.One frequently wants to implement a system that works well even under abrupt changes or failures.Markov Jump Linear Systems (MJLS) is a fruitful model in this context.Even though there are numerous theories on MJLS, it is common to find them separately in continuous-time (C-MJLS) or discrete-time (D-MJLS) domains.In the present work, we present a model for a stochastic linear dynamic system that operates in continuous-time domain and in discrete-time domain, alternately, during random times in each domain, and we call it a Mixed-Time MJLS (M-MJLS).We succeed in modeling both C-MJLS and D-MJLS as particular cases of our model, such that the M-MJLS generalizes results of the classical theory.We define a notion of Mean Square Stability (MSS) for the M-MJLS and derive a necessary and sufficient condition for it in terms of the spectrum of two matrices.We also define an H 2 index for the new model, and develop a formula for computing it.A numerical example of an inverted pendulum illustrates the theory.

Almost sure asymptotic stabilization problem of continuous-time switched linear stochastic dynamical systems is considered. The mode signal, which manages the transition between subsystems, is modeled as a Markov chain. Mode information is assumed to be only available at certain time instances. We propose a control law that depends on the sampled information of the mode signal, which is constructed from the available mode samples. Based on our stability analysis for switched linear stochastic systems, we obtain sufficient conditions under which the proposed control law guarantees stability of the zero solution. Finally, we present an illustrative numerical example to demonstrate the efficacy of our results.

Under the usual assumptions of normality, the recursive estimator known as the Kalman filter gives excellent results and has found an extremely broad field of application--not only for estimating the state of a stochastic dynamic system, but also for estimating model parameters as well as detecting abrupt changes in the states or the parameters. It is well known, however, that significantly nonnormal noise, and particularly the presence of outliers, severely degrades the performance of the Kalman filter. This results in poor state estimates, nonwhite residuals and invalid inference. A first-order approximation is derived for the conditional prior distribution of the state of a discrete-time stochastic linear dynamic system in the presence of $\varepsilon$-contaminated normal observation noise. This distribution is then used to derive a first-order approximation of the conditional mean (minimum-variance) estimator. If the observation noise distribution can be represented as a member of the $\varepsilon$-contaminated normal neighborhood, then the conditional prior is also, to first order, an analogous perturbation from a normal distribution whose first two moments are given by the Kalman filter. Moreover, the perturbation is itself of a special form, combining distributions whose parameters are given by banks of parallel Kalman filters and optimal smoothers.

The stability of stochastic dynamic systems have widespread application prospects and greater theoretical significance. Its theory are mainly applied to engineering control, communication equipment, military technology, biology, finance, etc. In this article, we consider the stability of a Class of nonlinear impulsive neutral stochastic differential dynamic systems. A new set of conditions proving the mean square stability of this nonlinear impulsive neutral stochastic dynamic systems are derived by means of the Banach fixed point theorem. Some well-known results are improved and generalized.

In this paper we consider a series of algorithms for calculating radicals of matrix polynomial equations. A particular aspect of this problem arise in author’s work, concerning parameter identification of linear dynamic stochastic system. Special attention is given to searching the solution of an equation in a neighbourhood of some initial approximation.

The robust exponential stability in mean square for a class of linear stochastic uncertain control systems is dealt with. For the uncertain stochastic systems, we have designed an optimal controller which guarantees the exponential stability of the system. Actually, we employed Lyapunov function approach and the stochastic algebraic Riccati equation (SARE) to have shown the robustness of the linear quadratic(LQ) optimal control law. And the algebraic criteria for the exponential stability on the linear stochastic uncertain closed-loop systems are given.

This paper discusses the optimal preview control problem for a class of linear continuous stochastic control systems in the infinite horizon, based on the augmented error system method. Firstly, an assistant system is designed and the state equation is translated to the assistant system. Then, an integrator is introduced to construct a stochastic augmented error system. As a result, the tracking problem is converted to a regulation problem. Secondly, the optimal regulator is solved based on dynamic programming principle for the stochastic system, and the optimal preview controller of the original system is obtained. Compared with the finite horizon, we simplify the performance index. We also study the stability of the stochastic augmented error system and design the observer for the original stochastic system. Finally, the simulation example shows the effectiveness of the conclusion in this paper.

Control of industrial plants is an important engineering field of study, where the optimization of such processes can lead to better product quality and higher profit. The present work deals with the optimization of an industrial gasifier, proposed as a benchmark challenge by ALSTOM Power Technologies in 2002. Researchers from around the globe proposed different methods for optimizing such system, using linear and nonlinear system identification techniques, different controller schemes, such as proportional-integral-derivative and model predictive controllers, and search methods for controller tuning. The authors care for the study of a methodology that can generalize the controller optimization process of real industrial systems, where linear system identification can lead to simpler systems, which are used to design more robust controllers. The proposed work deals with linear system identification and multiobjective optimization for the gasifier's controller design. To do so, the authors divide the problem in two steps, the linear system identification, where step functions are fed to the gasifier in order to detect the output response of the system, and the design of a proportional-integral-derivative controller, where spherical pruned multi-objective differential evolution algorithm is used in order to optimize the controller gains. The proposed method, unfortunately, does not provide an optimal controller, which can be explained by the complexity of the benchmark system. With such results, the authors believe a better multi-objective problem definition is necessary. Also, it is concluded that such benchmark presents a real challenge for future controller design methndologies.

For the identification and the adaptive control of a linear stochastic system it is assumed that there is an unknown ideal system or an unknown ideal set point for the system. A system is constructed based on a family of parameter estimates and an algorithm is given for it. For the adaptive control, this system is required to track a known function where an ergodic, quadratic cost functional is used. An algorithm is given for the identification of an unknown ideal semilinear system.

On Identifying Envelop Type Nonlinear Output Error Takagi-Sugeno Fuzzy Models for Dynamic Systems with Uncertainties