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An Application of Nash Game to Distributed Multi-Rate Predictive Control
Abstract
In this paper we propose to study the underlying properties
of our formerly proposed distributed multi-rate predictive
control scheme in which a set of multi-rate constrained
agents communicate to accomplish their goals. The problems
of how to decide the multi-rate communication strategy,
share the inputs, estimated states and observers gains
are solved using tools from game theory. The proposed
scheme is demonstrated through a simulation example.
... In the distributed control structure, input coupling among subsystems is considered as given by (9). These subsystems communicate with one another to accomplish a global objective (see Fig. 1). ...
... These subsystems communicate with one another to accomplish a global objective (see Fig. 1). One type of distributed MPC based on Nash optimality has been investigated by [1], [9]. The main advantage of this scheme is that the on-line optimization of a large-scale problem can be converted into several small-scale sub-problems, thus reducing the computational complexity significantly while keeping satisfactory performance. ...
... The game theory-based MPC algorithm proceeds by allowing each subsystem/agent to optimize its objective function using its own control decision ϑ ϑ ϑ i (t) assuming that other subsystem's solutions ϑ ϑ ϑ j (t) are known, [1], [9]. ...
In this paper we propose to study the underlying properties of our formerly proposed distributed multi-rate predictive control strategy based on Nash game [1]. In this proposed method a set of multi-rate constrained agents communicate to accomplish their goals. The problems of how to decide the multirate communication strategy, share the inputs, estimated states and observers gains are solved using tools from game theory. The proposed scheme is demonstrated through a simulation example. Eventually different multi-rate scenarios have been simulated to present the performance of the method under all possible scenarios and also comparison of these scenarios together.
... By analysing the simulation results, it can be observed that the proposed scheme offers efficient tracking for constrained problems including both process and measurement noise. For further theoretical properties, such as convergence, computation cost comparison and optimality see [15] and [17,18]. In the presented method, each agent has knowledge of its own dynamics and also is aware of the neighboring agents' computed inputs. ...
In this chapter, a new Nash-based distributed MPC method is proposed to control large-scale multi-rate systems with linear dynamics that are coupled via inputs. These systems are multi-rate systems in the sense that either output measurements or input updates are not available at certain sampling times. Such systems can arise when the number of sensors is less than the number of variables to be controlled or when measurements of outputs cannot be completed simultaneously because of applicational limitations. The multi-rate nature gives rise to a lack of information which will cause uncertainty in the system's performance. To compensate for the information loss due to the multi-rate nature of the systems under study, a distributed Kalman filter is proposed to provide an optimal estimate of the missing information.
A model predictive control (MPC) technique is developed for systems with measurements available at different sampling rates. The method uses general state-space system representations that incorporate secondary measurements as well as primary measurements. The optimal multi-rate (MR) filtering method is used to develop prediction equations for MPC. A simple suboptimal cascade filter is also proposed for dual-rate (DR) systems where the primary measurements are available at a 'slow’ rate and the secondary measurements are available at a 'fast’ rate. In addition to significant reduction in filter-gain computation requirements, the suboptimal filtering strategy offers superior primary-measurement-failure tolerance. The applicability of the proposed methods to realistic systems is demonstrated through an example application to a high-purity distillation column.
This study presents closed-loop results regarding the production of high-density polyethylene with Ziegler–Natta and Phillips catalysis. The multivariable control algorithm based on the generalized predictive control approach is adopted. Additional features are employed to consider multiple sampling rates and desired trajectory for the output constraints in the cases of grade transition. Results show a significant improvement in the output profiles such as melt index and density. This work provides an extension in the predictive control practice applied to polymerization reactors and presents a new approach for the generalized predictive control algorithm capable to control outputs measured at different rates.
This paper presents a new methodology for selecting control structure in the context of distributed model predictive control. An index was developed to quantify the performance of distributed MPC strategies in the presence of model errors. This index was used for two purposes: to solve the decomposition problem whereby the process is decomposed into parts and to compare distributed MPC strategies with different degrees of coordination. Then, a multi-objective Mixed Integer Nonlinear Programming MINLP formulation is proposed to achieve an optimal trade-off between performance and structure simplicity.Four examples are considered to illustrate the methodology. The simulation results are consistent with the conclusions obtained from the analysis. The proposed methodology can be applied at the design stage to select the best control configuration in the presence of model errors.
Model based predictive control (MBPC) is an emerging design tool
in process control, thanks to its capability to incorporate several
attributes fundamental in practical applications. On the other hand,
multirate control systems are able to describe various practical
situations, where technological constraints require that sensor
measurements and control calculations are performed at different times
and rates. For these reasons, it seems appropriate to extend MBPC to the
multirate case. Then, a design procedure is developed in this paper,
leading to a multirate controller which guarantees stability and zero
error asymptotic regulation to the overall control system, even in the
presence of small plant parameter variations