Sliding-Mode Control for 2-D Hidden Markov Jump Roesser Systems With Partial Information and Its Application in Metal Rolling Process

2-D systems which can model many practical engineering systems, have attractive research in the control topic in both practice and theoretical aspects. Due to the complex engineering environment, systems may encounter sudden structural changes and be unable to work properly. Fortunately, the Markov jump process can model this situation. Meanwhile, the information of systems may not be accessed timely or only partial information can be accessed. This work focuses on the hidden Markov model-based sliding mode control for 2-D Markov jump systems with partially unknown information and its application in the metal rolling process. By utilizing the Lyapunov function approach, some criteria are obtained to guarantee that the dynamics state reaches the designed sliding surface within a finite time, and the system is passive. Finally, the practicability of asynchronous sliding mode control law is verified by providing a metal rolling process. Note to Practitioners—In some practical systems, their state depends on two independent variables, and the internal structure or parameters of the system are changed due to sudden environmental interference and device failure, which can be described as 2-D Markov jump systems. Meanwhile, in practical engineering applications, obtaining all statistical probability information of systems requires a great cost or is impossible to accomplish. This paper proposes the sliding mode control method for 2-D Markov jump Roesser systems with partial information, in which the partial information problems include the partially known system operation mode information and the partially known probabilities information. A hidden Markov model is used to address the above two partial information problems. The design approach of a hidden Markov model-based sliding mode controller with partially unknown statistical probability information is proposed. The engineering applicability of the method is verified by the metal rolling technology. This study provides a new sliding mode control method to address the control problem for 2-D systems where the system information is partially obtained or accessed.