Abstract: Recently, feedback control systems using random dither
quantizers have been proposed for linear discrete-time systems.
However, the constraints imposed on state and control variables
have not yet been taken into account for the design of feedback
control systems with random dither quantization. Model predictive
control is a kind of optimal feedback control in which control
performance over a finite future is optimized with a performance
index that has a moving initial and terminal time. An important
advantage of model predictive control is its ability to handle
constraints imposed on state and control variables. Based on the
model predictive control approach, the objective of this paper is to
present a control method that satisfies probabilistic state constraints
for linear discrete-time feedback control systems with random dither
quantization. In other words, this paper provides a method for
solving the optimal control problems subject to probabilistic state
constraints for linear discrete-time feedback control systems with
random dither quantization.
Abstract: Model predictive control is a kind of optimal feedback
control in which control performance over a finite future is optimized
with a performance index that has a moving initial time and a moving
terminal time. This paper examines the stability of model predictive
control for linear discrete-time systems with additive stochastic
disturbances. A sufficient condition for the stability of the closed-loop
system with model predictive control is derived by means of a linear
matrix inequality. The objective of this paper is to show the results
of computational simulations in order to verify the effectiveness of
the obtained stability condition.