Optimal control of singular boolean control networks via Ledley solution method

This paper investigates the optimal control problem for a class of Boolean control networks, called singular Boolean control networks (SBCNs), which consist of two parts: difference equations and algebraic equations. By constructing the truth matrix of Ledley solution, necessary and sufficient conditions are provided for the solvability of SBNs (or SBCNs). Then an effective algorithm is presented to design an optimal control sequence by using the controllability matrix of normalized Boolean control networks.     

高阶布尔网络的结构

介绍高阶布尔（控制）网络,并研究了其拓扑结构.以矩阵的半张量积作为工具,把高阶布尔网络的动态过程转化为2种标准离散事件动态系统的代数形式.证明了高阶布尔网络和第1代数形式的一一对应关系,并由此得到其拓扑结构（不动点、极限圈以及暂态期等）.还研究了高阶布尔网络系统与它第2代数形式的关系.     

Data-driven control for switched systems over a vulnerable and resource-constrained network

To alleviate the restriction of system model on control design, data-driven model-free adaptive control (MFAC) is an excellent alternative to model-based control methods. This paper studies event-triggered data-driven control for switched systems over a vulnerable and resource-constrained network. The system is transformed into an equivalent switched data model through dynamic linearization. Resource constraints and denial of service (DoS) attacks in the network are concerned, and a novel joint anti-attack method including resilient event-triggering mechanism and prediction scheme is presented. Furthermore, new event-triggered MFAC algorithms are proposed. In this scenario, by constructing a Lyapunov functional on tracking error, sufficient conditions to ensure its boundedness are derived. This is the first time in the literature to give a complete solution to data-driven control of switched systems. At last, the validity of new algorithms and theoretical results is confirmed by simulations.     

Optimal switching with minimum dwell time constraint

The problem of optimal switching between different subsystems/configurations with minimum dwell time constraints is investigated in this study and a feedback solution, using the framework of approximate dynamic programming, is proposed. The method calls for a tuning stage in which parameters of a function approximator are tuned. Online control will then be conducted with a computational load as low as evaluating a few scalar-valued functions. Finite-horizon and infinite-horizon cost functions are investigated and convergence and stability are analyzed considering the presence of approximation errors. Moreover, the case of applying a full or partial constraint on the mode sequence, as well as having a mode-dependent minimum dwell time are investigated. Finally, performance of the scheme in handling different challenges is numerically evaluated through different examples.     

Data-driven optimal switching of switched systems

Switched systems are complicated due to the switching among the subsystems. When the subsystem models are unknown, control problems on switched systems turn to be more intractable. In this paper, the optimal switching problems are investigated for continuous-time switched autonomous systems with unknown dynamics and a finite-horizon cost function. Firstly, a novel data-driven optimal scheduling approach is proposed based on the estimated insertion gradients. Secondly, aiming at switched systems with a prescribed switching sequence, a data-driven optimal switching time approach is proposed based on the estimated derivatives of the cost with respect to the switching times. The two approaches take advantages of plenty state data containing necessary information instead of the system models. Furthermore, the errors of the approaches are analysed and bounded. Finally, simulation results of two examples are given to show the validity of the two approaches.     

Global asymptotic stability of switched boolean networks with missing data

This paper investigates the global asymptotic stability of a switched Boolean network (SBN) with missing data. Due to the physical constraints of the communication media, data loss often occurs during the transmission. In this paper, the data loss is described as a Bernoulli distribution sequence, and the switching signal sequence is determined by a logical system. Using a semi-tensor product, the dynamics of a SBN with missing data are converted to an algebraic form. Based on this, a necessary and sufficient condition for global asymptotic stability of SBNs with missing data and auxiliary theorems are provided. Two illustrative examples are presented to show the applicability of the developed theorems.     

On the run-time optimization of the Boolean logic of a program

The problem considered here is the optimal scheduling of a Boolean expression on a single-processor system. We consider a Boolean expression in which each Boolean variable represents the binary outcome (or return code) of a program module. The result of the expression may be known without executing all modules (e.g. an OR-operation is terminated as soon as one of the operands returns the value 1), so that the order in which the modules are executed influences the cost involved in finding the result. The optimisation discussed here consists in finding the operand arrangement that minimizes the average execution cost. The cost of each module represents the consumption of resources such as CPU time, elapsed time, number of input-outputs, etc. The assumptions regarding the modules are: (i) No module execution is the pre-requisite for the execution of another module. (ii) At each execution, the return code and the cost of a module do not depend on the sequence of execution. (iii) Over a number of executions, the return code and the cost of a module may be statistically dependent or a deterministic function of return codes and costs of other modules.A prototype scheduler is presented, that implements a sub-optimal strategy. It stores the Boolean expression in tabular form, passes control to a module at a time, as needed for the Boolean computation, measures the cost of execution and decides empirically what operand arrangement is more advantageous.     

Input–output decoupling control design for switched Boolean control networks

We investigate the input–output decoupling problem of switched Boolean control networks (SBCNs) in this paper. Based on the matrix expression of Boolean functions, the dynamics of SBCNs are converted into an algebraic form via semi-tensor product of matrices first. Then, using the redundant variable separation technique, we give the necessary and sufficient conditions for the existence of three kinds of controllers to detect whether an SBCN can be input–output decomposed or not, respectively, including the open-loop controllers, the state feedback controllers, and the output feedback controllers. Meanwhile, a constructive procedure is presented to construct the open-loop controllers, as well as the state feedback controllers and output feedback controllers. Finally, an illustrative example is given to show that the new results obtained are effective.     

Adaptive neural control for nonlinear switched systems with improved MDADT and its applications

In this paper, a new framework of the robust adaptive neural control for nonlinear switched stochastic systems is established in the presence of external disturbances and system uncertainties. In the existing works, the design of robust adaptive control laws for nonlinear switched systems mainly relies on the average dwell time method, while the design and analysis based on the model-dependent average dwell time (MDADT) method remains a challenge. An improved MDADT method is developed for the first time, which greatly relaxes the requirements of Lyapunov functions of any two subsystems. Benefiting from the improved MDADT, a switched disturbance observer for discontinuous disturbances is proposed, which realizes the real-time gain adjustment. For known and unknown piecewise continuous nonlinear functions, a processing method based on the tracking differentiator and the neural network is proposed, which skillfully guarantees the continuity of the control law. The theoretical proof shows that the semiglobal uniform ultimate boundedness of all closed-loop signals can be guaranteed under switching signals with MDADT property, and simulation results of the longitudinal maneuvering control at high angle of attack are given to further illustrate the effectiveness of the proposed framework.     

Modelling and optimal control of a time-delayed switched system in fed-batch process

The main control goal of the fed-batch process is to maximize the yield of target product as well as to minimize the operation costs simultaneously. Considering the existence of time delay and the switching nature in the fed-batch process, a time-delayed switched system is proposed to formulate the 1,3-propanediol (1,3-PD) production process. Some important properties of the system are also discussed. Taking the switching instants and the terminal time as the control variables, a free terminal time delayed optimal control problem is then presented. Using a time-scaling transformation and parameterizing the switching instants into new parameters, an equivalently optimal control problem is investigated. A numerical solution method is developed to seek the optimal control strategy by the smoothing approximation method and the gradient of the cost functional together with that of the constraints. Numerical results show that the mass of target product per unit time at the terminal time is increased considerably.     

Modeling and stabilization of a wireless network control system with packet loss and time delay

The problem of modeling and stabilization of a wireless network control system (NCS) is considered in this paper, where packet loss and time delay exist simultaneously in the wireless network. A discrete-time switched system with time-varying delay model is first proposed to describe the system closed by a static state feedback controller. A sufficient criteria for the discrete-time switched system with time-varying delay to be stable is proposed, based on which, the corresponding state feedback controller is obtained by solving a set of linear matrix inequalities (LMIs). Numerical examples show the effectiveness of the proposed method.     

Optimal control of nonlinear switched system in an uncoupled microbial fed-batch fermentation process

The bio-dissimilation of glycerol to 1,3-propanediol (1,3-PD) is a complex bioprocess due to the multiple inhibitions of substrate and products onto the cell growth. In consideration of both the inhibition mechanisms of 3-hydroxypropionaldehyde (3-HPA) and the transport modes of glycerol and 1,3-PD across the cell membrane, we establish a novel switched system which is represented by a ten-dimensional nonlinear dynamical equation containing both extracellular and intracellular environments. The uncoupled microbial fed-batch fermentation process are modeled using the switched system which the glycerol and alkali are respectively poured into. Taking the feeding rates of glycerol and alkali, the switching times and the mode sequence as the control variables, an optimal control model is proposed with the concentration of the terminal time 1,3-PD as performance index. In order to maximize the yield of 1,3-PD, the control parameterization technique and the exact penalty function method are used to solve the considered problem. Numerical results show that under the obtained optimal feeding rates of glycerol and alkali, switching times and mode sequence, the productivity of 1,3-PD at the terminal time is increased significantly compared with previous results.     

Set stability and synchronization of logical networks with probabilistic time delays

Using the algebraic state space representation (ASSR) method, this paper investigates the set stability and synchronization of Boolean networks with probabilistic time delays (PTDs). Firstly, an equivalent stochastic system is established for the Boolean network with PTDs by using the ASSR method. Secondly, based on the probabilistic state transition matrix of equivalent stochastic system, a necessary and sufficient condition is proposed for the set stability of Boolean networks with PTDs. Thirdly, as an application of set stability, the synchronization of coupled Boolean networks with PTDs is studied, and a necessary and sufficient condition is presented. Finally, an illustrative example is given to demonstrate the effectiveness of the obtained new results.     

Observability of singular Boolean control networks with state delays

This paper investigates the observability of singular Boolean control networks (SBCNs) with state delays. First, via Cheng product, the considered system is converted into its algebraic form. Then, under the uniqueness of the solution, two methods are proposed to transform the system into a general Boolean control network (BCN). Therefore, the considered system’s observability is equivalent to the BCN’s observability. Subsequently, the restricted input-state incidence matrix is introduced and some necessary and sufficient conditions are presented for the observability of BCNs with state delays. Finally, two illustrative examples are presented to show that the main results obtained are effective in analyzing the observability of SBCNs with state delays.     

Modelling and Passivity Based Control of switched systems from bond graph formalism: Application to multicellular converters

This paper addresses the modelling and control of switched systems with Boolean inputs. A generalization of Passivity Based Control (PBC) is proposed and fitted to bond graph formalism. The state equations of the equivalent average model are first deduced from the original bond graph using the notion of commutation cells and then interpreted according to Port Controlled Hamiltonian formalism. The whole approach is presented in a formal way. This method is then applied on a multicellular serial converter, which is widespread in power systems and of growing interest. The application of PBC associated to a modelling approach using commutation cells on a non-trivial example shows its efficiency to determine a generic controller, the number of elementary cells being considered as a parameter.     

Observability of Boolean control networks with stochastic disturbances

In this paper, the observability problem of Boolean control networks (BCNs) with stochastic disturbances is investigated via two kinds of control schemes: deterministic control and state feedback control. Firstly, based on the proposed indicator matrix, a simplified system of the original augmented Boolean system is constructed. Based on the analysis of the auxiliary system, observability of the original BCN is converted to determine whether an observable set can be reached from another unobservable set. After that, some necessary and sufficient conditions are obtained to judge the observability of BCNs. At the same time, two algorithms are proposed for designing these two types of control sequences. Finally, numerical simulations are also provided to demonstrate feasibility of the theoretical results.     

Robust suboptimal feedback control for a fed-batch nonlinear time-delayed switched system

The optimal control strategy constructed in the form of a state feedback is effective for small state perturbations caused by changes in modeling uncertainty. In this paper, we investigate a robust suboptimal feedback control (RSPFC) problem governed by a nonlinear time-delayed switched system with uncertain time delay arising in a 1,3-propanediol (1,3-PD) microbial fed-batch process. The feedback control strategy is designed based on the radial basis function to balance the two (possibly competing) objectives: (i) the system performance (concentration of 1,3-PD at the terminal time of the fermentation) is to be optimal; and (ii) the system sensitivity (the system performance with respect to the uncertainty of the time-delay) is to be minimized. The RSPFC problem is subject to the continuous state inequality constraints. An exact penalty method and a novel time scaling transformation approach are used to transform the RSPFC problem into the one subject only to box constraints. The resulting problem is solved by a hybrid optimization algorithm based on a filled function method and a gradient-based algorithm. Numerical results are given to verify the effectiveness of the developed hybrid optimization algorithm.     

Co-design of output-based security control and dynamic event-triggered mechanism for NCSs under hybrid cyber attacks

This paper investigates output-based dynamic event-triggered control for networked control systems (NCSs), in which hybrid cyber attacks randomly occur in communication network. First, a gain adjustable dynamic output feedback (DOF) controller is designed for NCSs and relaxes state-available constraint in presence of three types of attacks, including stochastic deception attacks, replay attacks and aperiodic denial-of-service (DoS) attacks. Second, a output-based dynamic event-triggered mechanism (DETM) is designed to optimize limited network resources under the cyber attacks. Third, a new switched system is established to describe the effect of hybrid cyber attacks, the DOF controller and the DETM simultaneously. Then, criteria for guaranteeing asymptotically stability of the switched system are obtained. Furthermore, the co-design method of DETM and DOF controller is provided to maintain the NCSs stability. Finally, an example is presented to show the effectiveness of the proposed methods in this paper.     

Model reference adaptive control for switched linear systems using switched multiple models control strategy

In this paper, the multiple model strategy is applied to the adaptive control of switched linear systems to improve the transient performance. The solvability of the adaptive stabilization problem of each subsystem is not required. Firstly, the two-layer switching mechanism is designed. The state-dependent switching law with dwell time constraint is designed in the outer-layer switching to guarantee the stability of the switched systems. During the interval of dwell time constraint, the parameter resetting adaptive laws are designed in the inner-layer switching to improve the transient performance. Secondly, the minimum dwell time constraint providing enough time for multiple model adaptive control strategy to work fully and maintaining the stability of the switched systems is found. Finally, the proposed switched multiple model adaptive control strategy guarantees that all the closed-loop system signals remain bounded and the state tracking error converges to zero.     

Matrix-weighted consensus for multi-agent systems with sampled-data

This paper researches the consensus issue for multi-agent systems on matrix-weighted directed fixed and undirected switching network topologies by sampled data control method which saves resources and is more practical. Using the sampled information, the distributed control laws are designed under two network topologies, respectively. Under directed fixed network topology, the consensus conditions based on the sampling period and the eigenvalues of Laplacian matrix are deduced by matrix theory and analysis theory. Under undirected switching network topology, by using Lyapunov stability theory, the consensus conditions based on the sampling period and switched network topologies are built. Lastly, two simulation examples are offered to verify the validity of the obtained results.