LMIs in Control/pages/LMI for Decentralized Feedback Control

LMI for Decentralized Feedback Control In large-scale systems like a multi-agent robotic system, national economies, or chemical refineries, an actuator should act based on local information, which necessitates a decentralized or distributed control strategy. In a decentralized control framework, the controllers are distributed and each controller has only access to a subset of local measurements. We describe LMI formulations for a general decentralized control framework and then provide an illustrative example of a decentralized control design. The System In a decentralized controller design, the state feedback controller can be divided into sub-controllers . The Data A general state space representation of a linear time-invariant system is as follows: where is a vector of state variables, is the input matrix, is the output matrix, and is called the feedforward matrix. We assume that all the four matrices, , , , and are given. The Optimization Problem We aim to solve the -optimal full-state feedback control problem using a controller . In a decentralized fashion, the control input can be divided into sub-controllers and can be written as . For instance, let and . Thus, there are three control inputs , , and . We also assume that u_{1} only depends on the first and the second states, while and only depend on thrid to sixth states. For this example, the controller gain matrix can be described by: Thus, the decentralized controller gain consists of sub-matrices of gains. The LMI: LMI for decentralized feedback controller The mathematical description of the LMI formulation for a decentralised optimal full-state feedback controller can be described by: where is a positive definite matrix and such that the aforemtntioned constraints in LMIs are satisfied. Conclusion: The controller gain matrix is defined as: where can be found after solving the LMIs and obtaining the variables matrices and . Thus, . Implementation A link to Matlab codes for this problem in the Github repository: https://github.com/asalimil/LMI_for_decentralized_feedback_controller/tree/master Related LMIs External Links A list of references documenting and validating the LMI. - LMI in Control Systems Analysis, Design and Applications Return to Main Page LMIs in Control/Tools