Stochastic Control System:
A control system that operates under unknown random actions is called a stochastic control system. In this type of control system, the actions or inputs to the system are not completely known or predictable. The random nature of the actions makes it challenging to design an optimal control strategy.

Explanation:
Stochastic control systems are used in various fields including engineering, economics, finance, and biology, where uncertainties and random events are present. These systems are designed to handle and adapt to random disturbances or actions in order to achieve a desired control objective.

Characteristics of Stochastic Control System:
1. Random Actions: In a stochastic control system, the actions or inputs to the system are random and unpredictable. These actions can be modeled as stochastic processes or random variables.

2. Uncertainty: Due to the random nature of the actions, there is inherent uncertainty in the system. The controller needs to account for this uncertainty and make decisions based on probabilistic information.

3. Adaptability: Stochastic control systems are designed to adapt and adjust the control strategy based on the observed actions and system states. The controller may update its decision-making process in real-time to optimize the control objective.

4. Optimization: The goal of a stochastic control system is to optimize a certain performance criterion or objective. This objective could be minimizing costs, maximizing efficiency, or achieving a desired output under uncertain conditions.

5. Feedback: Stochastic control systems often incorporate feedback mechanisms to continuously monitor the system's performance and adjust the control actions accordingly. Feedback helps in reducing the effects of uncertainties and improves the overall performance of the system.

6. Modeling and Analysis: Stochastic control systems require modeling and analysis techniques that can handle random processes and uncertainties. Tools such as probability theory, stochastic calculus, and optimization methods are commonly used in the design and analysis of these systems.

Applications of Stochastic Control Systems:
1. Robotics: Stochastic control systems are used in robotics to handle uncertainties in the environment and adapt the robot's actions accordingly.

2. Finance: Stochastic control systems are used in financial modeling and investment strategies to optimize portfolio management under uncertain market conditions.

3. Power Systems: Stochastic control systems are used in power systems to optimize generation and distribution under varying load and renewable energy sources.

4. Manufacturing: Stochastic control systems are used in manufacturing processes to optimize production and resource allocation under uncertain demand and supply conditions.

In conclusion, a stochastic control system is a control system that operates under unknown random actions. It is designed to adapt and optimize control strategies in the presence of uncertainties. This type of control system finds applications in various fields where uncertainties and random events are present.