Jv
J.H. van Schuppen
58 records found
1
Improving the small-signal stability of a stochastic power system
Algorithms and mathematical analysis
Tools and analysis for improving the small-signal stability of a stochastic power system by optimal power dispatch in each short time horizon, such as five-minute intervals, are provided in this paper. An objective function which characterizes the maximal exit probability from th
...
Serious fluctuations caused by disturbances may lead to instability of power systems. With the disturbance modeled by a Brownian motion process, the fluctuations are often described by the asymptotic variance at the invariant probability distribution of an associated Gaussian sto
...
The synchronization of power generators is an important condition for the proper functioning of a power system, in which the fluctuations in frequency and the phase angle differences between the generators are sufficiently small when subjected to stochastic disturbances. Serious
...
We aim to increase the ability of coupled phase oscillators to maintain synchronization when the system is affected by stochastic disturbances. We model the disturbances by Gaussian noise and use the mean first hitting time when the state hits the boundary of a secure domain, tha
...
The synchronization stability of a complex network system of coupled phase oscillators is discussed. In case the network is affected by disturbances, a stochastic linearized system of the coupled phase oscillators may be used to determine the fluctuations of phase differences in
...
Appendix
Control and System Theory of Deterministic Systems
Concepts and theorems of the system theory of deterministic linear systems are summarized. Controllability, observability, and a realization are formulated. Realization theory includes necessary and sufficient conditions for the existence of a realization, a characterization of t
...
Optimal stochastic control problems with complete observations and on an infinite horizon are considered. Control theory for both the average cost and the discounted cost function is treated. The dynamic programming approach is formulated as a procedure to determine the value and
...
The concept of a stochastic control system is defined as a map from a tuple of the current state and the current input to the conditional probability distribution of the tuple of the next state and the current output. A Gaussian stochastic control system representation is defined
...
Appendix
Probability
Concepts and results of probability theory are presented in this chapter which complement those of Chapter 2. Concepts covered in detail include the canonical variable decomposition of a tuple of Gaussian random variables, a set of stable probability distribution functions, condi
...
Filter problems are formulated for stochastic systems which are not Gaussian systems. Both the estimation problem, the sequential estimation problem, and the filter problem are treated. A sufficient condition for the existence of a finite-dimensional filter system is formulated.
...
Appendix
Matrix Equations
The Lyapunov equation and the algebraic Riccati equation are treated in depth. The Lyapunov equation arises as the equation for the asymptotic covariance matrix of the state of a stationary Gaussian system. The algebraic Riccati equation arises in the Kalman filter, in stochastic
...
Appendix
Mathematics
The reader finds in this short appendix concepts and results of various topics of mathematics. These topics are used in the body of the book but are not part of control theory. Topics covered are: algebra of set theory; a canonical form; algebraic structures including monoids, gr
...
Appendix
Covariance Functions and Dissipative Systems
The concept of a dissipative system is defined for a deterministic linear system and is satisfied if there exists a storage function and a supply rate such that the dissipation inequality holds. It is proven that a deterministic linear system is dissipative if and only if a relat
...
Appendix
Positive Matrices
This chapter concerns positive matrices which are matrices with elements of the positive real numbers. The motivations for the inclusion of the algebraic structure of positive matrices are the problems (1) of stability of the system of probability measures of the Markov process o
...
Elementary concepts and results of the theory of stochastic processes are summarized in this chapter. Concepts presented include a stochastic process, equivalent processes, a Gaussian process, stationarity, time-reversibility, and a Markov process. It is shown how to go from the
...
Stochastic control issues of a general character are presented. Problems of control theory are mentioned which require research interest the coming years. A general method for sufficient and necessary conditions for the existence of an optimal control law is discussed. The framew
...
This book helps students, researchers, and practicing engineers to understand the theoretical framework of control and system theory for discrete-time stochastic systems so that they can then apply its principles to their own stochastic control systems and to the solution of cont
...
Stochastic realization problems are presented for a tuple of Gaussian random variables, for a tuple of σ -algebras, for a σ -algebra family, and for a finite stochastic system. The solution of the weak and of the strong stochastic realization of a tuple of Gaussian random variabl
...
A stochastic system (without input) is a mathematical model of a dynamic phenomenon exhibiting uncertain signals. Such a system is mathematically characterized by the transition map from the current state to the joint probability distribution of the next state and the current out
...