DECENTRALIZED AND HIERARCHICAL CONTROL OF INTERCONNECTED UNCERTAIN SYSTEMS

The paper develops new decentralised and hierarchical control techniques for linear interconnected, uncertain dynamical systems with additive-type bounded uncertainties. The overall system is decomposed into N lower order subsystems, each containing uncertain elements and is corrupted by uncertain bounded disturbances. The uncertainties of the systems' parameters are known to belong to prescribed compact bounding intervals. It has been shown that, if uncertainty of the system is within a certain structure (i.e. the matching conditions hold), stabilising control always exists, no matter how large the uncertainty is. Based on this and on the theory of ultimate boundedness, the proposed decentralised and hierarchical control structures guarantee global uniform ultimate boundedness behaviour for the decomposed subsystems. Sufficient conditions are given for the stability of the global system, when driven with proposed control schemes and in the presence of interconnections with bounded uncertainties. It has been established that, with the satisfaction of these conditions and/or validity of the uncertainty matching structure, the developed decentralised and hierarchical control strategies provide robust design schemes, i.e. they are insensitive to the structural perturbations, either between the subsystems and/or in the communication network between the two-level hierarchical structure. Futhermore, the design algorithms are insensitive to parameter perturbations in their bounded ranges.