Abstract: The random dither quantization method enables us
to achieve much better performance than the simple uniform
quantization method for the design of quantized control systems.
Motivated by this fact, the stochastic model predictive control
method in which a performance index is minimized subject to
probabilistic constraints imposed on the state variables of systems
has been proposed for linear feedback control systems with random
dither quantization. In other words, a method for solving optimal
control problems subject to probabilistic state constraints for linear
discrete-time control systems with random dither quantization has
been already established. To our best knowledge, however, the
feasibility of such a kind of optimal control problems has not
yet been studied. Our objective in this paper is to investigate the
feasibility of stochastic model predictive control problems for linear
discrete-time control systems with random dither quantization. To
this end, we provide the results of numerical simulations that verify
the feasibility of stochastic model predictive control problems for
linear discrete-time control systems with random dither quantization.
Abstract: Recently, feedback control systems using random dither
quantizers have been proposed for linear discrete-time systems.
However, the constraints imposed on state and control variables
have not yet been taken into account for the design of feedback
control systems with random dither quantization. Model predictive
control is a kind of optimal feedback control in which control
performance over a finite future is optimized with a performance
index that has a moving initial and terminal time. An important
advantage of model predictive control is its ability to handle
constraints imposed on state and control variables. Based on the
model predictive control approach, the objective of this paper is to
present a control method that satisfies probabilistic state constraints
for linear discrete-time feedback control systems with random dither
quantization. In other words, this paper provides a method for
solving the optimal control problems subject to probabilistic state
constraints for linear discrete-time feedback control systems with
random dither quantization.
Abstract: Recent technological advance has prompted significant
interest in developing the control theory of quantum systems.
Following the increasing interest in the control of quantum
dynamics, this paper examines the control problem of Schrödinger
equation because quantum dynamics is basically governed by
Schrödinger equation. From the practical point of view, stochastic
disturbances cannot be avoided in the implementation of control
method for quantum systems. Thus, we consider here the robust
stabilization problem of Schrödinger equation against stochastic
disturbances. In this paper, we adopt model predictive control method
in which control performance over a finite future is optimized with
a performance index that has a moving initial and terminal time.
The objective of this study is to derive the stability criterion for
model predictive control of Schrödinger equation under stochastic
disturbances.
Abstract: Recently, optimal control problems subject to probabilistic
constraints have attracted much attention in many research field. Although
probabilistic constraints are generally intractable in optimization problems,
several methods haven been proposed to deal with probabilistic constraints.
In most methods, probabilistic constraints are transformed to deterministic
constraints that are tractable in optimization problems. This paper examines
a method for transforming probabilistic constraints into deterministic
constraints for a class of probabilistic constrained optimal control problems.
Abstract: In recent decades, probabilistic constrained optimal
control problems have attracted much attention in many research
fields. Although probabilistic constraints are generally intractable
in an optimization problem, several tractable methods haven been
proposed to handle probabilistic constraints. In most methods,
probabilistic constraints are reduced to deterministic constraints
that are tractable in an optimization problem. However, there is a
gap between the transformed deterministic constraints in case of
known and unknown probability distribution. This paper examines
the conservativeness of probabilistic constrained optimization method
for unknown probability distribution. The objective of this paper is
to provide a quantitative assessment of the conservatism for tractable
constraints in probabilistic constrained optimization with unknown
probability distribution.
Abstract: Model predictive control is a kind of optimal feedback
control in which control performance over a finite future is optimized
with a performance index that has a moving initial time and a moving
terminal time. This paper examines the stability of model predictive
control for linear discrete-time systems with additive stochastic
disturbances. A sufficient condition for the stability of the closed-loop
system with model predictive control is derived by means of a linear
matrix inequality. The objective of this paper is to show the results
of computational simulations in order to verify the effectiveness of
the obtained stability condition.
Abstract: We have conducted the optimal synthesis of rootmean-
squared objective filter to estimate the state vector in the case if
within the observation channel with memory the anomalous noises
with unknown mathematical expectation are complement in the
function of the regular noises. The synthesis has been carried out for
linear stochastic systems of continuous - time.
Abstract: For optimal unbiased filter as mean-square and in the
case of functioning anomalous noises in the observation memory
channel, we have proved insensitivity of filter to inaccurate
knowledge of the anomalous noise intensity matrix and its
equivalence to truncated filter plotted only by non anomalous
components of an observation vector.
Abstract: A scheme integrated with deterministic–stochastic subspace system identification and the method of damage localization vector is proposed in this study for damage detection of structures based on seismic response data. A series of shaking table tests using a five-storey steel frame has been conducted in National Center for Research on Earthquake Engineering (NCREE), Taiwan. Damage condition is simulated by reducing the cross-sectional area of some of the columns at the bottom. Both single and combinations of multiple damage conditions at various locations have been considered. In the system identification analysis, either full or partial observation conditions have been taken into account. It has been shown that the damaged stories can be identified from global responses of the structure to earthquakes if sufficiently observed. In addition to detecting damage(s) with respect to the intact structure, identification of new or extended damages of the as-damaged (ill-conditioned) counterpart has also been studied. The proposed scheme proves to be effective.
Abstract: This paper proposes the analysis and design of robust
fuzzy control to Stochastic Parametrics Uncertaint Linear systems.
This system type to be controlled is partitioned into several linear
sub-models, in terms of transfer function, forming a convex polytope,
similar to LPV (Linear Parameters Varying) system. Once defined the
linear sub-models of the plant, these are organized into fuzzy Takagi-
Sugeno (TS) structure. From the Parallel Distributed Compensation
(PDC) strategy, a mathematical formulation is defined in the frequency
domain, based on the gain and phase margins specifications,
to obtain robust PI sub-controllers in accordance to the Takagi-
Sugeno fuzzy model of the plant. The main results of the paper are
based on the robust stability conditions with the proposal of one
Axiom and two Theorems.
Abstract: This paper considers H∞ performance for Markovian jump systems with Time-varying delays. The systems under consideration involve disturbance signal, Markovian switching and timevarying delays. By using a new Lyapunov-Krasovskii functional and a convex optimization approach, a delay-dependent stability condition in terms of linear matrix inequality (LMI) is addressed, which guarantee asymptotical stability in mean square and a prescribed H∞ performance index for the considered systems. Two numerical examples are given to illustrate the effectiveness and the less conservatism of the proposed main results. All these results are expected to be of use in the study of stochastic systems with time-varying delays.
Abstract: This work proposes a recursive weighted ELS
algorithm for system identification by applying numerically robust
orthogonal Householder transformations. The properties of the
proposed algorithm show it obtains acceptable results in a noisy
environment: fast convergence and asymptotically unbiased
estimates. Comparative analysis with others robust methods well
known from literature are also presented.