Driving cellular biological systems to one of desired long-term behaviors, an important subject in systems biology, can be interpreted as the set stabilization problem. This article presents a realistic control approach to set stabilization of complex biological networks modeled by Boolean networks (BNs) wherein only open-loop control is applied. First, the considered BN is transformed into an auxiliary BN having redundant state variables. Based on the similarity between desired attractors and Boolean algebra, a number of reduced BNs are constructed from the auxiliary BN in favor of set stabilization. Next, the feedback vertex set (FVS) control law is applied to reduced BNs for obtaining open-loop control inputs that take partial state variables toward desired values. This procedure continues in a recursive way until ensuring that the controlled BN converges to an unspecified desired attractor. The proposed scheme has the superiority that both fixed-point and cyclic attractors can be included in the problem setting, and that it can tackle complex BNs with moderate computational burdens. Extensive numerical experiments on random BNs and real biological systems are provided to demonstrate the applicability of the proposed scheme.

This study introduces the notion of interval of confidence (IoC) for the modeling of fuzzy controllers and presents three novel mathematical models of interval type-2 fuzzy proportional-integral-derivative (IT2FPID) controllers by utilizing the concept of IoC and various types of footprints of uncertainty (FoUs) having parallelogram, bottom-wide triangle, and top-wide triangle shapes. The properties and computational aspects of the proposed controllers are analyzed mainly in terms of IoCs and FoUs. All the developed controllers with various types of FoUs are plant-model-free nonlinear controllers with variable gains and structures. It is proved that more generalized models of IT2FPID controllers can be attained by replacing the fuzzy singletons with IoCs. The suitability of introducing IoC in IT2FPID controllers is verified by showing that IoC does not play any role in the mathematical modeling of type-1 (T1) fuzzy PID controllers. To demonstrate the effectiveness of the proposed controllers, extensive simulation studies and numerical and hardware experiments are conducted. The simulation and experimental results affirm the proposed controllers' superiority over conventional and fuzzy PID ones, opening up new possibilities for improved performance in real-world control applications.

This article presents attractor-transition control of complex biological networks represented by Boolean networks (BNs) wherein the BN is steered from a prescribed initial attractor toward a desired one. The proposed approach leverages the similarity between attractors and Boolean algebraic properties embedded in the underlying state transition equations. To enhance the clarity of expression regarding stabilization toward the desired attractor, a simple coordinate transformation is performed on the considered BN. Based on the characteristics of transformed state equations, self-stabilizing state variables requiring no control efforts are derived in the first. Next, by applying the feedback vertex set (FVS) control scheme, control inputs stabilizing the remaining state variables are determined. The proposed control scheme exhibits versatility by accommodating both fixed-point and cyclic attractors. We validate the effectiveness of the proposed strategy through extensive numerical experiments conducted on random BNs as well as complex biological systems. In adherence to the reproducible research initiative, detailed results of numerical experiments and all the implementation codes are provided on the authors' website: https://github.com/choonlog/AttractorTransition.

Output stabilizing control of biological systems is of utmost importance in systems biology since key phenotypes of biological networks are often encoded by a small subset of their phenotypic marker nodes. This study addresses the challenge of output stabilizing control for complex biological systems modeled by Boolean networks (BNs). The objective is to identify a set of constant control inputs capable of driving the BN toward a desirable long-term behavior with respect to specified output nodes. Leveraging the algebraic properties of Boolean logic, we develop a novel control algorithm that reformulates the output stabilizing control problem into a simple graph theoretic problem involving auxiliary BNs, the scale of which significantly decreases compared to the original BN. The proposed method ensures superiority over previous results in terms of both the number of control inputs and computational loads, since it searches for the solution within the reduced BNs while retaining essential structures needed for output stabilization. The efficacy of the proposed control scheme is demonstrated through extensive numerical experiments with complex random BNs and real biological networks. To support the reproducible research initiative, detailed results of numerical experiments are provided in the supplementary material, and all the implementation codes are made accessible at https://github.com/choonlog/OutputStabilization.

This article presents a reconfiguration strategy for the corrective controller achieving model matching control of an input/state asynchronous sequential machine (ASM). The considered controller is vulnerable to permanent faults that degenerate a subset of the controller's states. If the controller has a certain amount of redundancy in terms of its states, one can build a reconfiguration scheme in which the functionality of degenerated states is taken over by supplementary states. The proposed reconfiguration scheme is superior to conventional methods of fault tolerance with hardware redundancy since the required number of redundant states is much smaller. Hardware experiments on field-programmable gate array (FPGA) circuits are provided to validate the applicability of the proposed scheme. The present study serves as the first research report on the reconfigurable corrective controller.

This article investigates robust stabilizing control of biological systems modeled by Boolean networks (BNs). A population of BNs is considered where a majority of BNs have the same BN dynamics, but some BNs are inflicted by mutations damaging particular nodes, leading to perturbed dynamics that prohibit global stabilization to the desired attractor. The proposed control strategy consists of two steps. First, the nominal BN is transformed and curtailed into a sub-BN via a simple coordinate transformation and network reduction associated with the desired attractor. The feedback vertex set (FVS) control is then applied to the reduced BN to determine the control inputs for the nominal BN. Next, the control inputs derived in the first step and mutated nodes are applied to the nominal BN so as to identify residual dynamics of perturbed BNs, and additional control inputs are selected according to the canalization effect of each node. The overall control inputs are applied to the BN population, so that the nominal BN converges to the desired attractor and perturbed BNs to their own attractors that are the closest possible to the desired attractor. The performance of the proposed robust control scheme is validated through numerical experiments on random BNs and a complex biological network.

This article proposes a resilient corrective control scheme for input/state asynchronous sequential machines (ASMs) against a class of actuator faults in which certain actuator outputs cannot be generated temporarily. We first present a mathematical formulation to describe the reachability of the controlled ASM damaged by the intermittent loss of actuator outputs. Based on the mathematical formulation, we address the existence condition and design procedure for a state-feedback corrective controller and a diagnoser that achieve resilience, that is, to make the closed-loop system exhibit normal input/state behaviors despite the intermittent loss of actuator outputs. To validate the applicability of the proposed concept and methodology, the closed-loop system of a practical asynchronous digital system is implemented on a field-programmable gate array (FPGA) and experimental verifications are provided.

Fault-tolerant corrective control for input/output asynchronous sequential machines (ASMs) is studied in this article. In the present problem setting, not only the controlled ASM but also the corrective controller itself is vulnerable to transient faults. The fault outcome is aggravated when the transient fault occurs to the controller, since the adverse effect of the fault is propagated toward the controlled ASM. We first address a scheme of diagnosing transient faults by designing the state observer that induces the resultant faulty state based on the output burst. We then present the existence condition and design algorithm for a corrective controller that recovers the normal behavior of the closed-loop system against transient faults at the ASM, while achieving self-repair against those faults occurring to the controller. Hardware experiments on field-programmable gate array (FPGA) circuits are provided to validate the applicability of the proposed control methodology.

This paper presents a scheme of correcting transient faults in finite state machines with asynchronous mechanism. The considered system is cascade composition of two finite state machines and is exposed to transient faults that cause unauthorized state transitions. Using the theory of corrective control for asynchronous sequential machines, the proposed framework yields an output feedback controller that diagnoses and tolerates any transient faults occurring to the system so that the closed-loop system can continue the normal behavior. With no observation module added, the controller can determine which component experiences a transient fault. An illustrative example is provided for sketching the design procedure of the proposed controller.

Corrective control can compensate the stable-state behavior of asynchronous sequential machines without involving redesign of the inner logic of the machine. In this paper, we apply the corrective control scheme to a space-borne dual ring counter subject to Single Event Upset (SEU) faults. By virtue of hardware redundancy lying in the dual ring counter, we design a corrective controller that tolerates any SEU fault that causes unauthorized state transitions. Since the output of the counter is unavailable to the controller, input/output control methodology is required for realizing fault diagnosis and tolerance. As a case study, we implement the proposed controller and a 4-bit dual ring counter in VHDL code, and conduct an experiment on the procedure of fault tolerance under a synthetic fault scenario.

This paper addresses the issue of tolerating a locked joint failure in gait planning for hexapod robots which have symmetric structures and legs in the form of an articulated arm with three revolute joints. A locked joint failure is one for which a joint cannot move and is locked in place. If a failed joint is locked, the workspace of the resulting leg is constrained, but hexapod walking machines have the ability to continue static walking. A strategy of fault tolerant tripod gait is proposed. In particular, a periodic gait is proposed as a special form of the proposed algorithm and its existence and efficiency are analytically proven. A case study on applying the proposed scheme to the standard tripod gait verifies its applicability and capability.

In this paper, we propose a framework of Virtual Architectural Engineering (VAE) as a pilot service of the SHINE (SHared INternet Environment) system, which is a middleware for implementing distributed network virtual environments. In the proposed service, three-dimensional (3-D) building models drawn in CAD are exported to the XML database (DB), which stores geometry and shared properties of each building component. The SHINE browser parses XML documents from the XML DB and renders 3D models using Java 3D APIs and JavaBeans virtual component library. Users participating in VAE can view and design 3D models with a sense of sharing space, presence and time.

This paper presents the SHINE (Shared Internet Environment) system, which is middleware for implementing distributed networked virtual environments and virtual architectural engineering (VAE) as a pilot service of Internet collaboration. In the proposed service, three-dimensional (3D) building models drawn with CAD are exported to the XML database (DB), which stores geometry and shared properties of each building component. The SHINE browser parses XML documents from the XML DB and renders 3D models using X3D components and the JavaBeans virtual component library. Users participating in VAE can view and design 3D models with a sense of sharing space, presence and time.

In this paper, fault detection and tolerance in static walking of legged robots are addressed. A kind of fault events, locked joint failure, is defined and its properties are investigated in the frame of gait study and robot kinematics. For the purpose of tolerating a locked joint failure, an algorithm of fault tolerant gaits for a quadruped robot is proposed in which the robot can continue its walking after a locked failure occurs to a joint of a leg. A case study on applying the proposed scheme to wave gaits verifies its applicability and capability.