Approximate Explicit MPC and Closed-loop Stability: Analysis based on PWA Lyapunov Functions

Model Predictive Control (MPC) is the de facto standard in advanced industrial automation systems. There are two main formulations of the MPC algorithm: an implicit one and an explicit MPC one. The first requires an optimization problem to be solved on-line, which is the main limitation when dealing with hard real-time applications. As the implicit MPC algorithm cannot be guaran- teed in terms of execution time, in many applications the explicit MPC solution is preferable. In order to deal with systems integrating mixed logic and dynam- ics, the class of the hybrid and piecewise affine models (PWA) were introduced and tackled by the explicit MPC strategy. However, the resulting controller complexity leads to a requirement on the CPU/memory combination which is as strict as the number of states, inputs and outputs increases. To reduce drasti- cally the complexity of the explicit controller while preserving the controller’s performance, a strategy combining switched MPC with discontinuous simpli- cial PWA models is introduced in this thesis. The latter is proven to be circuit implementable, e.g., in FPGA. To ensure that closed-loop stability properties are guaranteed, a stability analysis tool is proposed which exploits suitable and possibly discontinuous PWA Lyapunov-like functions. The tool requires solving offline a linear programming problem. Moreover, the tool is able to compute an invariant set for the closed-loop system, as well as ultimate boundedness and input-to-state stability properties.

Grantor dc:publisher

Università degli studi di Trento

Year dc:date

2012

Author dc:creator

• Trimboli, Sergio

Contributors dc:contributor

• Bemporad, Alberto

• Settore ING-INF/04 - Automatica

Statement dc:rights

• info:eu-repo/semantics/openAccess
• license:Tutti i diritti riservati (All rights reserved)

Language dc:language

eng

Identifier

http://dx.doi.org/10.15168/11572_368455
10.15168/11572_368455

OAI identifier oai:identifier

oai:iris.unitn.it:11572/368455