Bumpless Transfer MPC for Hidden Markovian Jump Nonlinear Systems With Saturated Inputs

This paper addresses the problem of the model predictive control (MPC) for a class of T–S fuzzy Markovian jump systems with bounded inputs and states. Two scenarios are considered, which are often overlooked in existing literature but common in practice: (
i
) asynchronous switching between the observed mode and the actual mode, and (
ii
) the excessive bump of system states. By virtue of the emission probability, the underlying systems are modeled as hidden Markovian jump systems to describe the asynchrony phenomenon. The time-varying emission probabilities are transformed into the ones in a more tractable form. Moreover, the bumpless transfer MPC (BT-MPC) is introduced to tackle the state bump phenomenon. An asynchronous fuzzy controller is obtained by the receding-horizon optimization, while ensuring recursive feasibility and stochastic stability. Besides, by a saturated state feedback scheme, the control law exploits the full control range with less conservatism compared with the case of directly dealing with control constraints. Two simulation examples are provided to demonstrate the effectiveness and advantages of the proposed control approach.
Note to Practitioners
—As a special hybrid system, Markovian jump systems can effectively describe the randomness of multi-modal systems. However, both the asynchrony phenomenon and hard constraints in the actual process reduce the range of existing control strategies. In addition, bumpless transfer performance is significant in many practical engineering systems. In this paper, a novel methodology is proposed to design bumpless transfer control for the fuzzy hidden Markovian jump system with time-varying emission probabilities. The proposed approach can handle both multiple control objectives and system constraints under the framework of BT-MPC. The proposed theoretical result is of a convex optimization characterization, which can be implemented algorithmically by means of the advanced and proven convex optimization toolbox. Finally, both a numerical example and a practical example of a robot arm are presented to demonstrate the effectiveness and great application prospect of the proposed approach.