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It is shown for any rigidity-based, undirected triangular formation of the type studied in [1], that if neighboring agents in the formation have slightly different understandings of what the desired distance between them is suppose to be, then almost for certain, the trajectory of the resulting distorted but rigid formation will converge exponentially fast to a closed orbit in ℝ2 which is traversed...
We propose an integral sliding surface for linear time-invariant implicit descriptions (descriptor systems). We show that, under reasonable assumptions (regularity, stabilizability and a corresponding matching condition), it is possible to design a controller that drives the descriptor variables to zero, even in the presence of disturbances. Higher-order sliding motions are required since, for the...
The ubiquity of PID controllers in the industry has remained mysterious until now. We provide here a mathematical explanation of this strange phenomenon by comparing their sampling with the the one of “intelligent” PID controllers, which were recently introduced. Some computer simulations nevertheless confirm the superiority of the new intelligent feedback design.
In this paper the problem of the time inconsistency of the leader strategy in a Multi-Model Game is studied. Initially the game dynamic is given by a family of N different possible differential equations (Multi-Model representation) with no information about the trajectory which is realized. In a previous result the robust Leader-Follower strategy design the min-max strategies for each player which...
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