Linear-exponential-quadratic Gaussian Control for Stochastic Partial Differential Equations
نویسنده
چکیده
In this paper a control problem for a controlled linear stochastic equation in a Hilbert space and an exponential quadratic cost functional of the state and the control is formulated and solved. The stochastic equation can model a variety of stochastic partial differential equations with the control restricted to the boundary or to discrete points in the domain. The solution method does not require solving a Hamilton-Jacobi-Bellman equation and the method provides an explanation for an additional term in the Riccati equation as compared to the Riccati equation for a quadratic cost functional. The optimal cost is also given explicitly. Some examples of controlled stochastic partial differential equations are given.
منابع مشابه
Numerical solution of second-order stochastic differential equations with Gaussian random parameters
In this paper, we present the numerical solution of ordinary differential equations (or SDEs), from each order especially second-order with time-varying and Gaussian random coefficients. We indicate a complete analysis for second-order equations in special case of scalar linear second-order equations (damped harmonic oscillators with additive or multiplicative noises). Making stochastic differe...
متن کاملControl of Some Linear Equations in a Hilbert Space with Fractional Brownian Motions
A linear-quadratic control problem for some infinite-dimensional controlled stochastic differential equations driven by a fractional Gaussian noise is solved. The feedback form of the optimal control and the optimal cost are given. The optimal control is the sum of the well known linear feedback control for the associated deterministic linear-quadratic control problem and a suitable prediction ...
متن کاملSolving high-order partial differential equations in unbounded domains by means of double exponential second kind Chebyshev approximation
In this paper, a collocation method for solving high-order linear partial differential equations (PDEs) with variable coefficients under more general form of conditions is presented. This method is based on the approximation of the truncated double exponential second kind Chebyshev (ESC) series. The definition of the partial derivative is presented and derived as new operational matrices of der...
متن کاملMulti-point Gaussian states, quadratic-exponential cost functionals, and large deviations estimates for linear quantum stochastic systems
This paper is concerned with risk-sensitive performance analysis for linear quantum stochastic systems interacting with external bosonic fields. We consider a cost functional in the form of the exponential moment of the integral of a quadratic polynomial of the system variables over a bounded time interval. An integro-differential equation is obtained for the time evolution of this quadratic-ex...
متن کاملLinear-Quadratic N-person and Mean-Field Games with Ergodic Cost
We consider stochastic differential games with N players, linear-Gaussian dynamics in arbitrary state-space dimension, and long-time-average cost with quadratic running cost. Admissible controls are feedbacks for which the system is ergodic. We first study the existence of affine Nash equilibria by means of an associated system of N Hamilton-JacobiBellman and N Kolmogorov-Fokker-Planck partial ...
متن کامل