In the mathematical treatment of many problems which arise in physics, economics, engineering, management, etc., the researcher frequently faces two major difficulties: infinite dimensionality and randomness of the evolution process. Infinite dimensionality occurs when the evolution in time of a process is accompanied by a space-like dependence; for example, spatial distribution of the temperature for a heat-conductor, spatial dependence of the time-varying displacement of a membrane subject to external forces, etc. Randomness is intrinsic to the mathematical formulation of many phenomena, such as fluctuation in the stock market, or noise in communication networks. Control theory of distributed parameter systems and stochastic systems focuses on physical phenomena which are governed by partial differential equations, delay-differential equations, integral differential equations, etc., and stochastic differential equations of various types. This has been a fertile field of research with over 40 years of history, which continues to be very active under the thrust of new emerging applications.
Among the subjects covered are:
- Control of distributed parameter systems;
- Stochastic control;
- Applications in finance/insurance/manufacturing;
- Adapted control;
- Numerical approximation
.
It is essential reading for applied mathematicians, control theorists, economic/financial analysts and engineers.
Reihe
Sprache
Verlagsort
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Dateigröße
ISBN-13
978-0-387-35359-3 (9780387353593)
DOI
10.1007/978-0-387-35359-3
Schweitzer Klassifikation
I. Distributed Parameter Systems.- Exact-Approximate Boundary Controllability of Thermoelastic Systems under Free Boundary Conditions.- A Linear Parabolic Boundary Control Problem with Mixed Control-State Constraint.- Membrane Shell Equation: Characterization of the Space of Solutions.- Renorming for Elastic Systems with Structural Damping.- Stability and Approximation of an Acoustic-Structure Model.- Analyticity of Semigroup Associated with a Laminated Composite Beam.- A Practical Estimation Technique for Spatial Distribution of Groundwater Contaminant.- Domain Decomposition in Optimal Control of Elliptic Systems on 2-d Networks.- An Observability Estimate in L2(?) × H?1(?) for Second-Order Hyperbolic Equations with Variable Coefficients.- Identification Problem for a Wave Equation via Optimal Control.- Optimal Control Theory: from Finite Dimensions to Infinite Dimensions.- Boundary Stabilization of a Hybrid System.- New Meaning of Exact Controllability of Linear Systems in Hilbert Spaces.- Minimax Design of Constrained Parabolic Systems.- Stabilization of Linear Boundary Control Systems of Parabolic Type: An Algebraic Approach.- A Distributed Bioremediation Problem with Modal Switching.- Optimal Control Problems Governed by an Elliptic Differential Equation with Critical Exponent.- Reconstruction of Source Terms in Evolution Equations by Exact Controllability.- Necessary Optimality Conditions for Control of Strongly Monotone Variational Inequalities.- Optimal Controls of a Class of Strongly Nonlinear Evolution Systems.- II. Stochastic Systems.- Robust Stabilization of Nonlinear Systems with Markovian Jumping Parameters.- Linear Quadratic Optimal Control: from Deterministic to Stochastic Cases.- Optimal Portfolio Selection with Transaction Costs.- Some Approachesto Ergodic and Adaptive Control of Stochastic Semilinear Systems.- A One-Dimensional Ratio Ergodic Control Problem.- Nonlinear H? Control: A Stochastic Perspective.- Reflected Forward Backward Stochastic Differential Equations and Contingent Claims.- Short Time Asymptotics of Random Heat Kernels.- Rough Asymptotics of Forward-Backward Stochastic Differential Equations.- On LQG Control of Linear Stochastic Systems with Control Dependent Noise.- Radial Symmetry of Classical Solutions for Bellman Equations in Ergodic Control.- Open Problems on Backward Stochastic Differential Equations.- Comparison Theorem of Solutions to BSDE with Jumps, and Viscosity Solution to a Generalized HJB Equation.- Multivariate Constrained Portfolio Rules: Derivation of Monge-Ampère Equations.- Limitations and Capabilities of Feedback for Controlling Uncertain Systems.- Time-scale Separation and State Aggregation in Singularly Perturbed Switching Diffusions.- Stochastic Controls and FBSDEs.- Asymptotically Optimal Controls of Hybrid LQG Problems: Summary of Results.- Explicit Efficient Frontier of a Continuous-Time Mean-Variance Portfolio Selection Problem.
