Analytical single-mode sliding predictive control of arbitrarily switched nonlinear systems incorporating dynamical variations. (November 2020) - Yaqubi, S.; Homaeinezhad, M.R.
Abstract: In this paper, a novel control scheme is proposed for model predictive control (MPC) of switched systems under arbitrarily generated undetectable switching signals. To this end, it is assigned that control scheme should simultaneously ensure reduction in optimization cost and maintain closed-loop stability. In other words, the control algorithm operates as single-mode in case corresponding conditions are satisfied, resulting in reduction of number of required calculations and ease of implementation. The proposed stabilization scheme is based on prediction of sliding hyperplane in various switched configurations, leading to reduced problem dimensions and ease of implementation of robustness analysis. To this end, an analytic gradient-descent expression of the optimization solution is obtained, shown to be robustly input-to-state stable (ISS) given the existence of a common Lyapunov function (CLF) corresponding to sliding mode controller (SMC). Furthermore, effects of dynamical variations over the prediction horizon are investigated, noting important effects on the stability criteria, which have been ignored in previous analytical studies. In case sufficient conditions are satisfied, the control scheme results in closed-loop stability and gradual convergence of sliding functions to origin in all potential modes of switched dynamics regardless of active switching state. However, the necessary conditions corresponding to sampling rate pertaining to this objective are potentially over-strict. To overcome this issue, it is proposed that control objectives and stability conditions can be relaxed such that boundedness of sliding functions in all switched modes is maintained according to the cost-reducing input update law rather than their strict convergence to the origin. The effects of state and input constraint violations are then incorporated as soft constraints. Experimental and numerical evaluations demonstrate the effectiveness of control method.