In this paper, we propose a new modeling method to express discrete-time hybrid systems with parameter uncertainty as a mixed logical dynamical (MLD) model. In analysis and control of hybrid systems, there are problem formulations in which convex polyhedra are computed, but for high-dimensional systems, it is difficult to solve these problems within a practical computation time. The key idea of this paper is to use an interval method, which is one of the classical methods in verified numerical computation, and to regard an interval as an over-approximation of a convex polyhedron. By using the obtained MLD model, analysis and synthesis of robust control systems are formulated.

Based on hybrid system theory, we propose a modeling and control approach for a multi-contact planar manipulation system, whereby a dexterous manipulation task is formulated as a mixed logic dynamical (MLD) model. The MLD model provides the possibility of carrying out the selection of modes, the timing for mode switching, and the determination of the continuous control input simultaneously in a systematical way. Model predictive control (MPC) is adopted for the synthesis of the dexterous hand manipulation system. The solution of the MPC can be found by using mixed integer quadric programming (MIQP) algorithm, and corresponds to the optimal motion of the hand manipulation. The validation of the proposed approach is shown by some simulation results.

The control problem of hybrid systems have received considerable attention. However, because of the existence of constraints and the combinatorial nature of continuous time and discrete event dynamics, the understanding of hybrid systems is rather limited at present. Only optimal control approaches were proposed based on heuristic rules. Few theoretical properties of system can be predicted until now. In this paper, we consider the tracking control problem of hybrid plants represented by MLD model to follow a family of reference signals produced by an external generator. Some new results are presented. The internal model principle of continuous system is extended to hybrid systems so as to solve the problem.