Robust Controllability and Observability of Boolean Control Networks under Different Disturbances

This paper investigates robust controllability and observability of Boolean control networks under disturbances. Firstly, under unobservable disturbances, some sufficient conditions are obtained for robust controllability of BCNs. Then an algorithm is proposed to construct the least control sequences which drive the trajectory from a state to a given reachable state. If the disturbances are observable, by defining the order-preserving system, an efficient sufficient condition is obtained for robust controllability of BCNs. Finally, the robust observability problem is converted into an equivalent robust controllability via set controllability and is solved by using the results obtained for set controllability. Some numerical examples are presented to illustrate the obtained results.

Efficient control of mechatronic systems in dynamic motion tasks

Robots and powered exoskeletons have often complex and non-linear dynamics due to friction, elasticity, and changing load. The proposed study addresses various-type robots that have to perform dynamic point-to-point motion tasks (PTPMT). The performance demands are for faster motion, higher positioning accuracy, and lower energy consumption. With given motion task, it is of primary importance to study the structure and controllability of the corresponding controlled system. The following natural decentralized controllability condition is assumed: the signs of any control input and the corresponding output (the acceleration) are the same, at least when the control input is at its maximum absolute value. Then we find explicit necessary and sufficient conditions on the control transfer matrix that can guarantee robust controllability in the face of arbitrary, but bounded disturbances. Further on, we propose a generic optimisation approach for control learning synthesis of various type robotic systems in PTPMT. Our procedure for iterative learning control (LC) has the following main steps: (1) choose a set of appropriate test control functions; (2) define the most relevant input-output pairs; and (3) solve shooting equations and perform control parameter optimisation. We will give several examples to explain our controllability and optimisation concepts.