MUSMAR
An Adaptive Model Predictive
Controller
based
on Redundancy
What is MUSMAR?
MUSMAR is an adaptive Model Predictive Controller for ARMAX models with special features:
- The predictive models over the prediction horizon are separately estimated (but sharing a common regressor). This redundancy allows for interesting properties with respect to the performance in the presence of smooth nonlinearities and un-modelled dynamics.
- A constant feedback is assumed over the control horizon. This yields a special type of structure for the predictive models and turns the optimization problem underlying MUSMAR into an approximation to an iterative method to solve the Riccati equation in an equivalent LQ problem.
The acronym “MUSMAR” stands for “Multistep, Multivariable Adaptive Regulator”.
What are the landmarks in the
development of MUSMAR?
MUSMAR was developed in 1980 by Menga and Mosca, who conceived it as adaptive regulator that approximates the LQ controller and published it as a conference paper.
This initial version was published in journal form (in Automatica), in 1984, together with an analysis of the underlying approximation to the LQ controller. It was shown that the “basic MUSMAR optimization algorithm” corresponds to a truncated form of Kleinman’s iterations to solve the Riccati equation. These iteration have the nice feature that it converges to the optimal feedback even if the initial guess is non-stabilizing.
In 1989 it was established (in a
paper in Automatica)
that the only possible convergence gains of MUSMAR are approximations to the
local minima of the underlying LQ stochastic cost, constrained to the a priori chosen controller structure.
What are the main extensions
of the basic MUSMAR algorithm?
MUSMAR was initially conceived as an adaptive regulator. Since then, a number of extensions have been made, including:
- The servo problem
- Inclusion of integral effect
- Equivalent observer polynomial in order to improve robustness features
- Input and output “soft” (in average power) constraints
- Dual control modification in order to improve adaptation transients
- Cascade control
- Feedforward control
- Detection of abrupt plant changes in order to embed fault tolerant control features
- Solution of the exact
infinite horizon underlying control problem in the presence of coloured
noise
What are the main
applications of MUSMAR?
Due to its data-driven features,
MUSMAR may be used in a wide variety of control problems, whenever a solution
derived from LQ control is appropriate. A rich set of examples concerning
industrial applications and case studies on large scale pilot processes are
reported in the literature, including:
- Temperature control in distributed collector solar
fields;
- Rate of cooling in arc-welding
- Level control in water delivery canals
- Drug administration for anaesthesia control
Paper repository
A concise guide to the literature
on MUSMAR is provided by the paper:
http://ramses.inesc.pt/MUSMAR/ECC2007-1245MUSMAR.pdf
You can find a number of papers
related with MUSMAR theory and applications by following the link (about 6 M):
http://ramses.inesc.pt/MUSMAR/MUSMAR-papers.zip
Page maintenance
This page is maintained by:
J. M. Lemos, jlml@inesc.pt
Research Group on Control of
Dynamic Systems, http://ramses.inesc.pt
INESC-ID, http://www.inesc-id.pt