Robust Verification and Identification of Piecewise Affine Systems

Sammanfattning: iecewise affine systems constitute an important subclass of hybrid systems, and consist of several affine dynamic subsystems, between which switchings occur at different occasions. As for hybrid systems in general, there has been a growing interest for piecewise affine systems in recent years, and they occur in many application areas.In many cases, safety is an important issue, and there is a need for tools that prove that certain states are never reached, or that some states are reached in finite time. The process of proving these kinds of statements is called verification. Many verification tools for hybrid systems have emerged in the last ten years. They all depend on a model of the system, which will in practice be an approximation of the real system. Therefore it would be desirable to learn how large the model errors can be, before the verification is not valid anymore. In this thesis, a verification method for piecewise affine systems is presented, where bounds on the allowed model errors are given along with the verification.Apart from being necessary for verification, system models are needed for various control, stability analysis, and fault detection tools. Hence, identification of piecewise affine systems is an important area. Here, an overview of different approaches appearing in the literature is presented, and a new identification method based on mixed-integer programming is proposed. One notable property of the latter method is that the global optimum is guaranteed to be found within a finite number of steps. The complexity of the mixed-integer programming approach is discussed, and its relations to existing approaches are pointed out. The special case of identification of Wiener models is considered in detail, since that model structure makes it possible to reduce the computational complexity. A combination of the mixed-integer programming approach and a local minimisation approach is also investigated.