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Stochastic hybrid systems have several applications such as biological systems and communication networks, but it is difficult to consider analysis and control of general stochastic hybrid systems. In this paper, discrete-time hybrid systems with stochastic mode transitions (called here discrete-stochastic hybrid systems) are considered as a class of stochastic hybrid systems. For this system, a modeling...
This paper discusses the stabilization problem of hybrid systems using control Lyapunov functions (CLFs). A CLF approach is one of the powerful methods in the stabilization of nonlinear systems. However, there are a few results for the stabilization of hybrid systems. In this paper, to develop stability theory of hybrid systems with discrete dynamics, a construction method of a CLF is proposed. Furthermore,...
The model predictive/optimal control problem of hybrid systems is reduced to a mixed integer quadratic programming (MIQP) problem. However, the MIQP problem has one serious weakness, i.e., the computation time to solve the MIQP problem is too long for practical plants. For overcoming this technical issue, there are several approaches. In this paper, a modeling of mode transition constraints, which...
This paper addresses the model predictive control (MPC) problem of a hybrid system that consists of a continuous-time linear system and a directed graph, called here directed-graph type hybrid systems (DGHS). One of the keys to such a problem is to represent a directed graph in an effective form in order to reduce the original problem into the mixed integer problem. This paper gives a solution to...
In the model predictive control (MPC) of hybrid systems, the problem of reducing the online computational complexity for generating a control input is one of the main issues. Thus focussing on how concisely a model of discrete dynamics is expressed, the authors have recently proposed a minimal representation of a finite automaton, which is given as a linear state equation with the smallest number...
This paper discusses a new approach to representing a finite automaton as a linear state equation with the smallest number of binary input variables to reduce the computational time for solving the model predictive control problem of a class of hybrid systems. Our method for modeling a finite automaton, which has been proposed in our previous paper, is explained at first. Then an open question on...
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