Multi-step smooth transition control synthesis for multi-equilibrium switched systems

This paper is devoted to the issue of smooth transition control synthesis of multi-equilibrium switched systems (MESS), which exhibits a pair of unique trim states and control inputs in each mode and treats conventional common-equilibrium switched systems as special cases. Unlike the existing mode-dependent Lyapunov function (MLF) with common-equilibrium assumption, a partly increasable equilibrium-related mode-dependent Lyapunov function (piEMLF) is proposed for stability analysis of MESS, where the increase allows flexible control design or complex dynamics, while the descending ensures states move toward a limited set, i.e. stability region. Considering the difference of switched controller in equilibria, trim control inputs, and gains, a multi-step smooth transition control (MS-STC) approach is proposed via piEMLF, where a series of variable interpolation parameters between them are utilised to gradually transfer the control inputs in adjacent modes, in contrast to the existing studies that only consider the gains-arising bump alleviation or utilise the one-step transition approach. By a numerical example and a flight control simulation of a multiple heavy payloads airdrop of a fixed-wing aircraft for forestry fire fighting with the parameter and equilibrium changes therein, the advantages and effectiveness of the proposed MESS modelling and MS-STC approach are demonstrated.