Reset law design based on robust model predictive strategy for uncertain systems

• In real time applications, a reset law is designed when the system states enter the reset set.
• A model predictive strategy is proposed to obtain the after reset value by minimizing a quadratic performance index.
• The reset law is determined by solving an LMI optimization problem at certain reset times.

In a continuous time control system, if some of the controller states are reset, certain limitations on the system response can be removed. Moreover, the stability and performance of such a reset control system may be improved. Resetting action has two main characteristics which should be determined: (a) when the controller states are reset and (b) how the after reset values of the controller states are determined. By defining a reset set, when the system states enter this set, the instants for the controller states reset, can be determined. This paper addresses the second question on how to determine the after reset values. In order to design a reset law for real time applications, a model predictive strategy is proposed that specifies the after reset values by minimizing a quadratic performance index. The quadratic minimization problem is converted to a LMI formulation and the reset law is determined by solving this LMI optimization problem at certain reset times. This approach is applied to a typical CSTR system to demonstrate the effectiveness of the proposed method for industrial process control application.