{"id":{"repo_id":"trento","oai_identifier":"oai:iris.unitn.it:11572/368455"},"canonical_url":"https://search.dev.ndltd.org/etd/trento/oai:iris.unitn.it:11572/368455","repository":{"repo_id":"trento","name":"Università degli Studi di Trento","base_url":"https://iris.unitn.it/oai/request"},"display":{"title":"Approximate Explicit MPC and Closed-loop Stability: Analysis based on PWA Lyapunov Functions","abstract":"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.","abstract_html":"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.","abstract_has_math":false,"creators":["Trimboli, Sergio"],"institution":"Università degli studi di Trento","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":["Bemporad, Alberto"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2012,"date_issued":"2012","date_published":"2012","updated_at":"2026-07-24T05:04:43Z","subjects":["Settore ING-INF/04 - Automatica"],"languages":["eng"],"rights":["info:eu-repo/semantics/openAccess","license:Tutti i diritti riservati (All rights reserved)"],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["http://dx.doi.org/10.15168/11572_368455","10.15168/11572_368455"],"render_values":[{"text":"http://dx.doi.org/10.15168/11572_368455","href":"http://dx.doi.org/10.15168/11572_368455","code":true},{"text":"10.15168/11572_368455","href":"https://doi.org/10.15168/11572_368455","code":true}]}]},"links":{"outbound_url":"https://hdl.handle.net/11572/368455","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Trimboli, Sergio","Bemporad, Alberto"]},{"key":"dc:creator","label":"Author","values":["Trimboli, Sergio"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2012"]},{"key":"dc:publisher","label":"Institution","values":["Università degli studi di Trento","place:TRENTO"]},{"key":"dc:relation","label":"Dc Relation","values":["firstpage:1","lastpage:86","numberofpages:86"]},{"key":"dc:type","label":"Dc Type","values":["info:eu-repo/semantics/doctoralThesis"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Settore ING-INF/04 - Automatica"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["eng"]},{"key":"dc:rights","label":"Dc Rights","values":["info:eu-repo/semantics/openAccess","license:Tutti i diritti riservati (All rights reserved)"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://hdl.handle.net/11572/368455","http://dx.doi.org/10.15168/11572_368455","10.15168/11572_368455"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["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."]},{"key":"dc:title","label":"Title","values":["Approximate Explicit MPC and Closed-loop Stability: Analysis based on PWA Lyapunov Functions"]}]}],"canonical_facts":{"dc:contributor":["Trimboli, Sergio","Bemporad, Alberto"],"dc:creator":["Trimboli, Sergio"],"dc:date":["2012"],"dc:description":["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."],"dc:identifier":["https://hdl.handle.net/11572/368455","http://dx.doi.org/10.15168/11572_368455","10.15168/11572_368455"],"dc:language":["eng"],"dc:publisher":["Università degli studi di Trento","place:TRENTO"],"dc:relation":["firstpage:1","lastpage:86","numberofpages:86"],"dc:rights":["info:eu-repo/semantics/openAccess","license:Tutti i diritti riservati (All rights reserved)"],"dc:subject":["Settore ING-INF/04 - Automatica"],"dc:title":["Approximate Explicit MPC and Closed-loop Stability: Analysis based on PWA Lyapunov Functions"],"dc:type":["info:eu-repo/semantics/doctoralThesis"]},"updated_at":"2026-07-24T05:04:43Z"}