Sum of squares approaches for control of continuous-time recurrent fuzzy systems

In recent years, a concise theory of recurrent fuzzy systems has emerged and methods for utilizing these fuzzy systems with dynamics for modeling and fault detection were developed. At the same time, sum of squares decompositions in conjunction with semidefinite programming were successfully applied for the synthesis of controllers for polynomial systems. In this paper, we combine both approaches and present sum of squares based control strategies for continuous-time recurrent fuzzy systems. The system dynamics under consideration is defined by gradients at discrete points in the input-state space. An alternative description as piecewise polynomial system is possible. This motivates to utilize a controller switching between local polynomial control laws. We propose three different approaches for controller synthesis based on this idea and demonstrate this new synthesis method by means of an example. In addition, advantages and drawbacks of the approaches are discussed.