This article studies the optimal control of probabilistic Boolean control networks (PBCNs) with the infinite horizon average cost criterion. By resorting to the semitensor product (STP) of matrices, a nested optimality equation for the optimal control problem of PBCNs is proposed. The Laurent series expression technique and the Jordan decomposition method derive a novel policy iteration-type algorithm, where finite iteration steps can provide the optimal state feedback law, which is presented. Finally, the intervention problem of the probabilistic Ara operon in E. coil, as a biological application, is solved to demonstrate the effectiveness and feasibility of the proposed theoretical approach and algorithms.

Stochastic Logical Networks (SLNs) are discrete-time stochastic dynamical systems with Boolean (or multi-valued) logical state variables. The discounted infinite horizon optimal control problem for stochastic logical networks is addressed in this paper. By resorting to the equivalent Markov decision process description, the infinite horizon optimization problem is presented in algebraic form. Then using the increasing-dimension technique, an improved finite convergence criterion, which can find the optimal stationary policy, is derived for value iteration approach.To demonstrate the theoretical value of this approach, it is applied to the optimization problems of the human-machine game and the p53-Mdm2 gene network.

We propose a new concept, stability in the distribution (SD) of a probabilistic Boolean network (PBN), which determines whether the probability distribution converges to the distribution of the target state (namely, a one-point distributed random variable). In a PBN, stability with probability one (SPO), stability in the stochastic sense (SSS), and SD are equivalent. The SD is easily generalized to subset stability; that is, to set stability in distribution (SSD). We prove that the transition probability from any state to an invariant subset (or to a fixed point) is nondecreasing in time. This monotonicity is an important property in establishing stability criteria and in calculating or estimating the transient period. We also obtain a verifiable necessary and sufficient condition for SD of PBNs with independently and identically distributed switching. We then show that SD problems of PBNs with Markovian switching and PBN synchronizations can be recast as SSD problems of Markov chains. After calculating the largest invariant subset of a Markov chain in a given set by the newly proposed algorithm, we propose a necessary and sufficient condition for SSDs of Markov chains. The propose

In this article, we investigate the asymptotical feedback set stabilization in distribution of probabilistic Boolean control networks (PBCNs). We prove that a PBCN is asymptotically feedback stabilizable to a given subset if and only if (iff) it constitutes asymptotically feedback stabilizable to the largest control-invariant subset (LCIS) contained in this subset. We proposed an algorithm to calculate the LCIS contained in any given subset with the necessary and sufficient condition for asymptotical set stabilizability in terms of obtaining the reachability matrix. In addition, we propose a method to design stabilizing feedback based on a state-space partition. Finally, the results were applied to solve asymptotical feedback output tracking and asymptotical feedback synchronization of PBCNs. Examples were detailed to demonstrate the feasibility of the proposed method and results.

In this article, the design and control of a new coaxial tilt-rotor unmanned aerial vehicle (CTRUAV) are presented. The CTRUAV is an electric-powered unmanned aerial vehicle with a special configuration, which is composed of two pairs of tiltable coaxial rotors and a rear rotor. A CTRUAV prototype has been designed by 3-D computer-aided design software and constructed according to the designing scheme. The dynamic model of a CTRUAV is derived by utilizing the Euler–Lagrange equation, which considers the special features of the coaxial rotors and air drag forces on the CTRUAV. An adaptive controller is developed to realize motion control for the CTRUAV. The adaptive controller includes two subcontrollers: an inner-loop attitude controller and an outer-loop velocity controller. The stability of the resulting closed-loop CTRUAV system is analyzed via the Lyapunov method. Finally, several simulations and real experimental tests are implemented to validate the effectiveness of the developed CTRUAV system.

This paper is concerned with the motion control for a quadrotor with a cable-suspended load (QCSL). A fixed-time control strategy is presented to improve the transient response and robustness of the QCSL with external disturbance. The overall control scheme is designed with a cascade structure to better cope with the underactuated property of the QCSL and the indirect effect of the control force on the load’s velocity through the tensile force on the cable. The simulation results are given to demonstrate the performance of the proposed scheme. Furthermore, actual flight tests were performed on a new experimental QCSL to validate the effectiveness of the proposed control strategy.