Myers C. (ed.) Stochastic Control

InTech, 2010. — 660 p.Uncertainty presents significant challenges in the reasoning about and controlling of complex dynamical systems. To address this challenge, numerous researchers are developing improved methods for stochastic analysis. This book presents a diverse collection of some of the latest research in this important area. In particular, this book gives an overview of some of the theoretical methods and tools for stochastic analysis, and it presents the applications of these methods to problems in systems theory, science, and economics.
The first section of the book presents theoretical methods and tools for the analysis of stochastic systems. The first two chapters by Sharma et al. present the Fokker-Planck equation and the Ito calculus. In Chapter 3, Charles presents the use of colored noise with stochastic differential equations. In Chapter 4, Lopez-Ruiz and Sanchez discuss coupled map lattices and cellular automata. In Chapter 5, Ohtsubo presents a game theoretic approach. In Chapter 6, Doria presents an approach that uses Hausdorff outer and inner measures. In Chapter 7, Warin and Vialle for analysis using distributed algorithms. Finally, in Chapter 8, Spiring explores the use of Mathematica 7.
The second section of the book presents the application of stochastic methods in systems theory. In Chapter 9, Yang et al. present a learning algorithm for the parity problem. In Chapter 10, Nechval and Pugailis present an improved technique for state estimation. In Chapter 11, Serra presents a fuzzy identification method. In Chapter 12, Ferreira and Serra present an application of fuzzy methods to dynamic systems. The next three chapters by Yan et al., Perez et al., and Courmontagne explore the problem of filtering for stochastic systems. In Chapter 16, Olama et al. look at wireless fading channel models. In Chapter 17, Liang considers information flow and causality quantification. The last two chapters of this section by Zhang and Zhang and Sokolov consider control systems.
The third section of the book presents the application of stochastic methods to problems in science. In Chapter 20, Marano and Sgobba present design criteria for vibration control. In Chapter 21, Kaminski and Lauke consider reinforced elastomers. In Chapter 22, Alessandro and Francesco discuss structural design. In Chapter 23, Lam et al. apply stochastic methods to the modeling of earthquake ground motion. In Chapter 24, Rastovic addresses laser-plasma interactions. Finally, in Chapter 25, Kuwahara et al. apply new, efficient stochastic simulation methods to biological systems.
The final section of the book presents the application of stochastic methods to problems in economics. In Chapter 26, Nechval and Purgailis consider the problem of determining a products lifetime. In Chapter 27, Gontis et al. applies a stochastic model to financial markets. In Chapter 28, Mania et al. take on the problem of hedging in the market. In Chapter 29, Simovic and Simovic apply stochastic control approaches to tactical and strategic operations in the market. Finally, in Chapter 30, Darya et al. consider optimal control problems in fractional bio-economic systems.The Fokker-Planck equation
The Itô calculus for a noisy dynamical system
Application of coloured noise as a driving force in the stochastic differential equations
Complexity and stochastic synchronization in coupled map lattices and cellular automata
Zero-sum stopping game associated with threshold probability
Stochastic independence with respect to upper and lower conditional probabilities defined by Hausdorff outer and inner measures
Design and experimentation of a large scale distributed stochastic control algorithm applied to energy management problems
Exploring Statistical Processes with Mathematica
A learning algorithm based on PSO and L-M for parity problem
Improved State Estimation of Stochastic Systems via a New Technique of Invariant Embedding
Fuzzy identification of discrete time nonlinear stochastic systems
Fuzzy frequency response for stochastic linear parameter varying dynamic systems
Delay-dependent exponential stability and filtering for time-delay stochastic systems with nonlinearities
Optimal filtering for linear states over polynomial observations
The stochastic matched filter and its applications to detection and de-noising
Wireless fading channel models: from classical to stochastic differential equations
Information flow and causality quantification in discrete and continuous stochastic systems
Reduced-Order LQG Controller Design by Minimizing Information Loss
The synthesis problem of the optimum control for nonlinear stochastic structures in the multistructural systems and methods of its solution
Optimal design criteria for isolation devices in vibration control
Sensitivity analysis and stochastic modeling of the effective properties for reinforced elastomers
Stochastic improvement of structural design
Modelling earthquake ground motions by stochastic method
Quasi-self-similarity for laser-plasma interactions modelled with fuzzy scaling and genetic algorithms
Efficient Stochastic Simulation to Analyze Targeted Properties of Biological Systems
Stochastic Decision Support Models and Optimal Stopping Rules in a New Product Lifetime Testing
A non-linear double stochastic model of return in financial markets
Mean-variance hedging under partial information
Pertinence and information needs of different subjects on markets and appropriate operative (tactical or strategic) stochastic control approaches
Fractional bioeconomic systems: optimal control problems, theory and applications