Abstract-This paper deals with optimal control of switched piecewise affine autonomous systems, where the objective is to minimize a performance index over an infinite time horizon. We assume that the switching sequence has a finite length, and that the decision variables are the switching instants and the sequence of operating modes. We present two different approaches for solving such an optimal control problem. The first approach iterates between a procedure that finds an optimal switching sequence of modes, and a procedure that finds the optimal switching instants. The second approach is inspired by dynamic programming and identifies the regions of the state space where an optimal mode switch should occur, therefore providing a state feedback control law.

Abstract-The design of an adaptive cruise controller for a SMART car, a type of small car, is proposed as a benchmark setup for several model predictive control methods for nonlinear and piecewise affine systems. Each of these methods has been already applied to specific case studies, different from method to method. This paper has therefore the purpose of implementing and comparing them over a common benchmark, allowing us to assess the main properties, characteristics, and strong/weak points of each method. In the simulations, a realistic model of the SMART car, including gear box and engine nonlinearities, is considered. A description of the methods to be compared is presented, and the comparison results are collected in a table. In particular, the tradeoffs between complexity and accuracy of the solution, as well as computational aspects are highlighted.Index Terms-Adaptive cruise control, mixed integer optimization, model predictive control (MPC), piecewise affine systems, road vehicles.

In this paper we extend a technique developed to design a feedback stabilizing control law for autonomous switched systems all modes of which are unstable. More specifically, we extend the switching table procedure to the class of affine switched systems, the dynamics of which either do not have an equilibrium point or, if they do, it is not common. This method is then applied to the DC-DC buck-boost converter. The design of the control law is based on dynamic programming and it results in a partition of the state space into switching look-up tables. A comparison with a Lyapunov based technique is also discussed

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In this paper we deal with the problem of estimating the marking of a labeled Petri net with nondeterministic transitions. In particular, we consider the case in which nondeterminism is due to the presence of transitions that share the same label and that can be simultaneously enabled. Under the assumption that: the structure of the net is known, the initial marking is known, the transition labels can be observed, the nondeterministic transitions are contact-free, we present a technique for characterizing the set of markings that are consistent with the actual observation. More precisely, we show that the set of markings consistent with an observed word can be represented by a linear system with a fixed structure that does not depend on the length of the observed word.