Decentralised control of nonlinear dynamical systems

In this paper, we provide a simple novel approach to decentralised control design. Each subsystem of an interconnected interacting system is controlled in a decentralised manner using locally available information related only to the state of that particular subsystem. The method is developed in two steps. In the first step, we define what we call a 'nominal system', which consists of 'nominal subsystems'. The nominal subsystems are assumed to be acted upon by forces that can be computed using only locally available information. We obtain an asymptotically stable control for each nominal subsystem which minimises a suitable, desired norm of the control effort at each instant of time. In the second step, we determine the control force that needs to be applied to the actual (interconnected) subsystem in addition to the control force calculated for the nominal subsystem, so each actual subsystem tracks the state of the controlled nominal subsystem as closely as desired. This additional compensating controller is obtained using the concept of a generalised sliding surface control. The design of this additional controller needs as its input an estimate of the bound on the mismatch between the nominal and the actual subsystems. Examples of non-autonomous, nonlinear, distributed systems are provided that demonstrate the efficacy and ease of implementation of the control method.