Controllability, Reachability, and Stabilizability of Finite Automata: A Controllability Matrix Method

This paper investigates the controllability, reachability, and stabilizability of finite automata by using the semitensor product of matrices. Firstly, by expressing the states, inputs, and outputs as vector forms, an algebraic form is obtained for finite automata. Secondly, based on the algebraic form, a controllability matrix is constructed for finite automata. Thirdly, some necessary and sufficient conditions are presented for the controllability, reachability, and stabilizability of finite automata by using the controllability matrix. Finally, an illustrative example is given to support the obtained new results

On Finite Potential Games

Abstract A linear system, called the potential equation (PE), is presented. It is proved that a finite game is potential if and only if its potential equation has solution. Some properties of the potential equation are obtained. Based on these properties, a closed form solution of the PE is obtained. Moreover, a formula based on the solution of the PE is obtained to calculate the potential function. Finally, it is proved that a networked evolutionary game is potential if and only if its fundamental network game is potential. Some interesting examples are presented to illustrate the theoretical results

Multivariable Fuzzy Control Based Mobile Robot Odor Source Localization via Semitensor Product

In order to take full advantage of the multisensor information, a MIMO fuzzy control system based on semitensor product (STP) is set up for mobile robot odor source localization (OSL). Multisensor information, such as vision, olfaction, laser, wind speed, and direction, is the input of the fuzzy control system and the relative searching strategies, such as random searching (RS), nearest distance-based vision searching (NDVS), and odor source declaration (OSD), are the outputs. Fuzzy control rules with algebraic equations are given according to the multisensor information via STP. Any output can be updated in the proposed fuzzy control system and has no influence on the other searching strategies. The proposed MIMO fuzzy control scheme based on STP can reach the theoretical system of the mobile robot OSL. Experimental results show the efficiency of the proposed method