(359h) Dual Offset Blocking Strategy for Computationally-Efficient Model Predictive Control

One of the most outstanding
issues with model predictive control (MPC) is the on-line computational load
required to solve the optimization problem within a sampling period, and move
blocking is one of the most commonly used input parameterization methods to
reduce the computational load by fixing the control inputs over arbitrary time
intervals denoted as blocks [1,2]. However, it is difficult to guarantee the recursive
feasibility of move blocked MPC because of the extra constraints imposed by move
blocking. An offset blocking based on LQR solution with a time-varying blocking
structure, denoted as moving window blocking (MWB), is suggested. This scheme
has the advantage of stabilizing a system a priori [3]. Another offset
blocking scheme retains previous control inputs as the base sequence. This
scheme can handle a relatively large domain and is flexible in choosing the blocking
structure without additional constraints [4,5].

However, the offset blocking schemes
can leave room for optimality because they are only focused on the recursive
feasibility. In particular, if the base sequence deviates from the feasible solution
set or the optimal solution set, the closed-loop performance can be degraded. For
example, the offset blocking with LQR solution using MWB may suffer from
performance degradation if the LQR solution deviates from the feasible solution
set. In addition, since the terminal constraint sets of these schemes are much
more restrictive than that of regular MPC, the reduction in domain would be
considerable.

In this study, we present a
geometric interpretation of move blocking, and analyze the existing offset
blocking schemes in terms of cost optimality based on the interpretation. Then,
we present the dual offset blocking scheme that inherits only the advantages
and overcome the disadvantages of the existing schemes. The proposed scheme
parameterizes the input sequence in terms of deviations from linear interpolation
between unconstrained infinite-horizon LQR solution and the retained solution
from the previous sampling instant as described in Figure 1. By this, we can improve
the cost optimality of the controller by adding a degree of freedom to the
selection of the base sequence, allowing the controller to select a more
desirable base sequence. Additionally, this scheme always guarantees the
recursive feasibility by utilizing the feasibility of the previous solution
only with the same terminal constraint of regular MPC, and improve stabilizing
performance by utilizing the pre-stabilizing property of the LQR solution. Moreover,
we apply the dual mode prediction paradigm [6] to this scheme by fixing the
input solution as the unconstrained infinite horizon LQR solution when the state
reaches the maximal positively invariant set subject to the LQR gain. We could
further improve the optimality of the controller with this. A LQR example of a
ball-plate system and other chemical process control examples are illustrated
to show the efficacy of the suggested approach.

Figure 1. A schematic
illustration of the dual offset blocking strategy.

REFERENCES

[1]
Hara, N., & Kojima, A. (2012). Reduced order model predictive control for
constrained discrete‐time linear systems. International
Journal of Robust and Nonlinear Control, 22(2), 144-169.

[2]
Li, S. E., Jia, Z., Li, K., & Cheng, B. (2015). Fast online computation of
a model predictive controller and its application to fuel economy–oriented
adaptive cruise control. IEEE Transactions on Intelligent
Transportation Systems, 16(3), 1199-1209.

[3]
Cagienard, R., Grieder, P., Kerrigan, E. C., & Morari, M.
(2007). Move blocking strategies in receding horizon control. Journal of
Process Control, 17(6), 563-570.

[4]
Ong, C. J., & Wang, Z. (2014). Reducing variables in Model Predictive
Control of linear system with disturbances using singular value
decomposition. Systems & Control Letters, 71, 62-68.

[5]
Shekhar, R. C., & Manzie, C. (2015). Optimal move blocking strategies for
model predictive control. Automatica, 61, 27-34.

[6]
Kouvaritakis, B., & Cannon, M. (2016). Model predictive control.
Springer, Switzerland.