Abstract:

Receding horizon H∞ control scheme which can deal
with both the H∞ disturbance attenuation and mean square stability
is proposed for a class of discrete-time Markovian jump linear
systems when minimizing a given quadratic performance criteria.
First, a control law is established for jump systems based on
pontryagin’s minimum principle and it can be constructed through
numerical solution of iterative equations. The aim of this control
strategy is to obtain an optimal control which can minimize the
cost function under the worst disturbance at every sampling time.
Due to the difficulty of the assurance of stability, then the above
mentioned approach is improved by determining terminal weighting
matrix which satisfies cost monotonicity condition. The control
move which is calculated by using this type of terminal weighting
matrix as boundary condition naturally guarantees the mean
square stability of the closed-loop system. A sufficient condition for
the existence of the terminal weighting matrix is presented in linear
matrix inequality (LMI) form which can be solved efficiently by
available software toolbox. Finally, a numerical example is given to
illustrate the feasibility and effectiveness of the proposed method.