1 Department of Informatics and Mathematical Modeling, Technical University of Denmark2 Norwegian University of Science and Technology
Why Multiple Models?This book presents a variety of approaches which produce complex models or controllers by piecing together a number of simpler subsystems. Thisdivide-and-conquer strategy is a long-standing and general way of copingwith complexity in engineering systems, nature and human problem solving. More complex plants, advances in information technology, and tightened economical and environmental constraints in recent years have lead topractising engineers being faced with modelling and control problems of increasing complexity. When confronted with such problems, there is a strongintuitive appeal in building systems which operate robustly over a wide range of operating conditions by decomposing them into a number of simplerlinear modelling or control problems, even for nonlinear modelling or control problems. This appeal has been a factor in the development of increasinglypopular `local' and multiple-model approaches to coping with strongly nonlinear and time-varying systems.Such local approaches are directly based on the divide-and-conquer strategy, in the sense that the core of the representation of the model or controlleris a partitioning of the system's full range of operation into multiple smaller operating regimes each of which is associated a locally valid model orcontroller. This can often give a simplified and transparent nonlinear model or control representation. In addition, the local approach has computationaladvantages, it lends itself to adaptation and learning algorithms, and allows direct incorporation of high-level and qualitative plant knowledge into themodel. These advantages have proven to be very appealing for industrial applications, and the practical, intuitively appealing nature of the framework isdemonstrated in chapters describing applications of local methods to problems in the process industries, biomedical applications and autonomoussystems. The successful application of the ideas to demanding problems is already encouraging, but creative development of the basic framework isneeded to better allow the integration of human knowledge with automated learning. The underlying question is `How should we partition the system - what is `local'?'. This book presents alternative ways of bringing submodels together,which lead to varying levels of performance and insight. Some are further developed for autonomous learning of parameters from data, while others havefocused on the ease with which prior knowledge can be incorporated. It is interesting to note that researchers in Control Theory, Neural Networks,Statistics, Artificial Intelligence and Fuzzy Logic have more or less independently developed very similar modelling methods, calling them Local ModelNetworks, Operating Regime based Models, Multiple Model Estimation and Adaptive Control, Gain Scheduled Controllers Heterogeneous Control,Mixtures of Experts, Piecewise Models, Local Regression techniques, or Tagaki-Sugeno Fuzzy Models}, among other names. Each of these approacheshas different merits, varying in the ease of introduction of existing knowledge, as well as the ease of model interpretation. This book attempts to outlinemuch of the common ground between the various approaches, encouraging the transfer of ideas.Recent progress in algorithms and analysis is presented, with constructive algorithms for automated model development and control design, as well astechniques for stability analysis, model interpretation and model validation.