Max-Plus Linear Parameter Varying Systems: Solvability Framework for Implicit Systems and a Model Predictive Control Approach

This thesis is devoted to the class of Max-Plus Linear Parameter Varying (MP-LPV) systems. Recently, this class is introduced as an extension of the class of Max-Plus-Linear (MPL) systems in the field of max-plus algebra. The MPL framework is useful when modeling Discrete Event Systems (DES). Describing DES in conventional algebra results in...

Throughput and Stabilisability Analysis of Mode-Constrained Stochastic Switching Max-Plus Linear Systems

Switching max-plus linear (SMPL) systems written in max-plus algebra form a robust framework to model discrete-event systems governed by synchronisation whose behaviour may switch over time. Their evolution is described by a max-plus linear state-space representation that may change by switching modes. In their typical form, switching may depend...

Max-plus linear parameter varying systems

In this research, we introduce and discuss an extension of max-plus linear systems, called max-plus linear parameter varying systems. In this extension, uncertainty is modelled as a varying parameter, making it possible to leverage non-linearities and non-max-plus terms within the model. Issues arise when the varying parameter is dependent on...