Control as an Embedded Technology

Abstract

We envision the role of control to expand rapidly in two directions. It will impact novel application areas, which have yet to benefit from the power of feedback, and, as an embedded technology, control will extend its reach far beyond the traditional narrow concept to include higher level functions of operation. Our research program is built on this vision. Eventually, these ideas should also radically change what is taught in our class rooms, so that our students can transfer these techniques to industry effectively and reap its benefits.

In all control applications the actual control algorithm is just one tiny part of the overall system designed to ensure safe, reliable and economical operation. Success or failure of “operation” are attributable at least as much to “the rest” as to the control algorithm itself. At the lowest level the control algorithm is endowed with functionality to deal with operating constraints and to switch smoothly between different operating regimes. At the highest levels the control algorithm may be embedded in a scheduling system or even an Enterprise Resource Planning (ERP) system. At all levels this embedding creates a heterogeneous system comprised of many interacting subsystems, typically referred to as a hybrid system.

The integration should eventually lead to a safer, smoother, more responsive and more competitive functioning of the entire system or organization. About three years ago we embarked on a major research program toward this goal. Its objective is the development of new theoretical tools to model, analyze, simulate and control such large complex hybrid systems involving continuous and discrete states, whose behavior is governed by dynamics, logical statements and constraints. In this talk we will summarize the highlights and try to put them in perspective. Modeling and Simulation: The models should facilitate the analysis and, at the same time, capture the complex behavior, that hybrid systems are known to exhibit. Based on these considerations, we introduced a discrete time description, combining linear dynamics with Boolean variables. This mixed logical dynamical form (MLD) form is capable to model a broad class of systems arising in many applications from the automotive, aircraft, chemical and information technology fields. Supply chains used in business models can be conveniently modeled as MLD systems as well. We defined a new modelling language (HYSDEL) and wrote a compiler to assist the user in the formulation of MLD models.

Controller Synthesis: For controller synthesis we formulate a finite horizon optimal control problem and apply the result in a moving horizon fashion. For MLD models the optimization problem is a mixed-integer linear program (MILP) which must be solved in real time at each sampling time. We have proven that the resulting state feedback control law is piece-wise linear over a polyhedral partition of the state space. As an alternative to on-line optimization, we can determine this control law explicitly by solving a multi-parametric MILP.

State Estimation and Fault Detection: For application of the described control law the system states must be known. Estimation of the states of an MLD system is a complex nonlinear filtering problem. We have defined a moving horizon estimator, where at each time step a mixed integer quadratic program must be solved to arrive at the state estimates. We have proven the convergence of the estimator if certain observability properties are satisfied. Complex fault situations can be modeled accurately in the MLD framework. Fault detection is another application of the new estimator.