Global Structure of Determining Matrices for a Class of Differential Control Systems

This paper developed and established unprecedented global results on the structure of determining matrices of generic double time-delay linear autonomous functional differential control systems, with a view to obtaining the controllability matrix associated with the rank condition for the Euclidean controllability of the system. The computational process and implementation of the controllability matrix were demonstrated on the MATLAB platform to determine the controllability disposition of a small-problem instance. Finally, the work examined the computing complexity of the determining matrices.

Dynamic Modeling and Optimal Control of a Novel Microswimmer with Gimbal Based Disks

SUMMARY We have introduced a new low-Reynolds-number microrobot with high 3D maneuverability. Our novel proposed microrobot has a higher rank of the controllability matrix with respect to the previous microswimmers which makes it capable of performing complex motions in space. In this study, governing equations of the microswimmer’s motion have been derived and simulated. Subsequently, we have proposed a cascade optimal control technique to control the swimmer trajectory. In the proposed control scheme, the actuation is provided in a way that an exponential stability on the system trajectory error as well as minimum fluctuations of control signals are achieved.

Output controllability and observability of mix-valued logic control networks

<abstract><p>This paper focuses on output controllability and observability of mix-valued logic control networks (MLCNs), of which the updating of outputs is determined by both inputs and states via logical rules. First, as for output controllability, the number of different control sequences are derived to steer a MLCN from a given initial state to a destination output in a given number of time steps via semi-tensor product method. By construsting the output controllability matrix, criteria for the output controllability are obtained. Second, to solve the problem of observability, we construct an augmented MLCN with the same transition matrix, and use the set controllability approach to determine the observability of MLCNs. Finally, a hydrogeological example is presented to verify the obtained results.</p></abstract>

Semitensor Product Approach to Controllability, Reachability, and Stabilizability of Probabilistic Finite Automata

This paper proposes a matrix-based approach to investigate the controllability, reachability, and stabilizability of probabilistic finite automata (PFA). Firstly, the state transition probabilistic structure matrix is constructed for PFA, based on which a kind of controllability matrix is defined for PFA. Secondly, some necessary and sufficient conditions are presented for the controllability, reachability, and stabilizability of PFA with positive probability by using the controllability matrix. Finally, an illustrate example is given to validate the obtained new results.

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.

Procedure of System Control Using Distributed Parameters through Discrete Finitisation

This paper presents an original method for the synthesis command involving a controllability matrix, which is used for systems with distributed parameters, and further more for systems reduced to a finite dimensional space.