Where is stochastic control used?
The field of stochastic control has developed greatly since the 1970s, particularly in its applications to finance. Robert Merton used stochastic control to study optimal portfolios of safe and risky assets. His work and that of Black–Scholes changed the nature of the finance literature.
What is stochastic control process?
Stochastic control refers to the general area in which some random variable distributions depend on the choice of certain controls, and one looks for an optimal strategy to choose those controls in order to maximize or minimize the expected value of the random variable.
What is stochastic system?
A stochastic system is a system whose future states, due to its components’ possible interactions, are not known precisely. This is the case in non-deterministic systems formed through the collective dynamics of participating components.
What is an optimal control problem?
Optimal control deals with the problem of finding a control law for a given system such that a certain optimality criterion is achieved. An optimal control is a set of differential equations describing the paths of the control variables that minimize the cost function.
What is a stochastic control problem?
A stochastic optimal control problem deals with uncertainties when making decisions to maximize or minimize an objective function. With a given objective function, decision makers need to determine a strategy, which is the stochastic control, to optimize the objective function in a random environment.
What are stochastic processes used for?
Stochastic processes are widely used as mathematical models of systems and phenomena that appear to vary in a random manner. Examples include the growth of a bacterial population, an electrical current fluctuating due to thermal noise, or the movement of a gas molecule.
What is optimal control used for?
Optimal control is the process of determining control and state trajectories for a dynamic system over a period of time to minimise a performance index.
What is robust control system?
Robust control is a controller design method that focuses on the reliability (robustness) of the control algorithm. Robustness is usually defined as the minimum requirement a control system has to satisfy in order to be useful in a practical environment.
What is deterministic control system?
Deterministic control systems are control systems that are designed for external deterministic disturbances or deterministic initial values. If the controlled variable is a position, velocity or acceleration, this is also called a servo control system. If the reference variable is constant, this is called a regulator.
Why do we need stochastic process?
In medical statistics, you need stochastic processes to calculate how to adjust significance levels when stopping a clinical trial early. In fact, the whole area of monitoring clinical trials as emerging evidence points to one hypothesis or another, is based on the theory of stochastic processes.
Which is an example of a stochastic control?
Introduction to stochastic control, with applications taken from a variety of areas including supply-chain optimization, advertising, finance, dynamic resource allocation, caching, and traditional automatic control.
What are the different types of MPCs for stochastic systems?
In the literature, there are two types of MPCs for stochastic systems; Robust model predictive control and Stochastic Model Predictive Control (SMPC). Robust model predictive control is a more conservative method which considers the worst scenario in the optimization procedure.
What is the result of stochastic control with only additive uncertainty?
A basic result for discrete-time centralized systems with only additive uncertainty is the certainty equivalence property: that the optimal control solution in this case is the same as would be obtained in the absence of the additive disturbances.
Which is the state variable in a stochastic differential equation?
In a continuous time approach in a finance context, the state variable in the stochastic differential equation is usually wealth or net worth, and the controls are the shares placed at each time in the various assets.