Dynamical Control Systems Research Articles

一类具有季节效应的脉冲控制生物系统动力学研究

基于生态学理论与数学生物学知识，在动态建模过程中加入了Hassell-Varley功能反应函数，建立了一类具有季节效应的脉冲控制生物动力系统。借助脉冲微分方程的Floquet定理与比较定理，分析了系统半平凡周期解的存在性、局部渐近稳定性和全局渐近稳定性，同时讨论了系统生物种群的灭绝性与持久生存性。这些研究结果为进一步研究如何运用脉冲控制策略维持生态种群持久生存提供了一定的理论支撑。 In this paper, firstly, on the basis of ecology theory and mathematical biology knowledge, an impulsive controlled biological dynamical system with seasonal effect has been established by introducing Hassell-Varley functional response in the process of dynamic modeling. Secondly, using the Floquet theory and comparison theorem of impulsive differential equations, the existence, local asymptotic stability and global asymptotic stability of the semi-trivial periodic solution have been analyzed, and then the extinction and permanence of biological populations in the system have also been discussed. Finally, all those results can provide some theoretical support for further researching how to utilize control strategy to maintain the survival of ecological populations.

Estimation problems for uncertain nonlinear dynamical systems with ellipsoidal state constraints

The paper deals with the estimation problems for uncertain nonlinear dynamical systems in the case when a probabilistic description of noise and errors is not available, but only bounds on them known. Such models are found in many applied areas ranged from engineering problems from physics to economics as well as to biological and ecological modeling when it occurs that a stochastic nature of the errors is questionable because of limited data or because of complexity and nonlinearity of the model. As alternative to a stochastic characterization, a so-called set-membership approach has been proposed and intensively developed in the last decades. The solution of many control and estimation problems under uncertainty involves constructing reachable sets and their analogs. For models with linear dynamics under such set-membership uncertainty, there are several constructive approaches, which allow finding effective estimates of reachable sets. Certainly, concrete problems are mostly nonlinear in their parameters and the set of feasible system states is usually non-convex or even non-connected. The key issue in nonlinear set-membership estimation is to find suitable techniques, which produce related bounds for the set of unknown system states without being too computationally demanding. Here the problem of estimating reachable sets of nonlinear dynamical control systems with combined bilinear and quadratic nonlinearity and with uncertainty in initial states is studied. Applying results of the theory of trajectory tubes of control systems and related techniques of differential inclusions theory we present approaches that allow finding the upper ellipsoidal estimates of reachable sets. The main new result consists in obtaining ellipsoidal estimates for reachable sets of nonlinear dynamical system with additional state constraint of ellipsoidal type. Related numerical algorithms, examples and results of computer simulations are included.

Approximate Controllability of Fractional Semilinear Stochastic System of Order α∈ (1,2

A family of dynamical control systems described by nonlinear fractional of order (1,2] stochastic differential equations in Lp spaces is considered. We discussed the approximate controllability of stochastic semilinear fractional control system of order α∈(1,2] under the assumption that the corresponding linear system is approximately controllable. A new set of sufficient conditions for approximate controllability of system are obtained by the theory of strongly continuous α-order cosine family, fixed point theorem, and stochastic analysis techniques. At the end, an example is given to illustrate the theory.

AN OPTIMIZATION OF MAXIMAL INVARIANCE IN A CLASS OF MULTIPLE VALUED ITERATIVE DYNAMICS MODELS OF NONLINEAR DISTURBED CONTROL SYSTEMS

We discuss an optimization problem on the maximal invariance of a class of multiple-valued iterative dynamics (MVID) models of discrete-time nonlinear control dynamical systems with singular disturbance. We study the inner and outer bounds of the maximal invariance, between which all noninterfering MVID models of nonlinear discrete-time control dynamical systems with singular disturbance reside. We also study the invariant fractal structure and an optimization of Lyapunov multipliers associated to it.

Adaptive stabilization of parameter-affine minimum-phase plants under Lipschitz uncertainty

The maximum capability of feedback control for discrete-time systems under a nonparametric Lipschitz uncertainty was first established in Xie and Guo (2000) for the simplest dynamical control system. It was shown that the necessary and sufficient condition for the adaptive stabilizability is of the form L<32+2, where L is the Lipschitz constant of the uncertainty. This result was extended in Huang and Guo (2012) to a basic class of scalar discrete-time minimum-phase control systems under an additional parametric uncertainty, and the adaptive stabilization was achieved with the use of an impracticable infinite memory feedback based on a brute-force search over a sufficiently fine grid in the prior set of unknown parameters. In the present paper, the adaptive stabilization problem is considered for a subclass of parameter-affine minimum-phase systems. The solution of the problem is based on new recurrent objective inequalities enabling to estimate and validate the closed loop system online and to formulate a simple projection-type parameter estimation algorithm instead of the brute-force search used in Huang and Guo (2012). The computational tractability of the proposed finite-memory stabilizing feedback is illustrated via simulations.

Controlling the Temporal Pulse Shape of the Passively Q-Switched Laser by Nonlinear Feedback Control

Q-switched lasers are high intensity laser pulses with extremely short durations of a few nanoseconds. The application of such laser pulses is ubiquitous [1,2]. In many dermatological procedures, intense energy pulses of Q-switched lasers are used to evaporate pigmented cells with high precision while the ultra-short pulse duration prevents damaging the surrounding healthy tissues. These lasers are also used in many industrial applications that require precision cutting, ranging from laser ablation and micromachining to the high-speed drilling of holes. However, the necessary precision of desired pulse characteristics has become increasingly demanding. Ever shrinking dimensions of micromachining call for reliable pulses with predictable properties. Currently, the difficulty of producing identical pulses of prescribed intensity, shape, and duration limits the use of Q-switched lasers. While the authors have previously worked on actively Q-switched lasers [3], this work focuses on passive Q-switching, where saturable absorber materials function as the internal switch in the laser cavity. In this paper theoretical tools from the field of nonlinear dynamical control systems [4] are applied to design a feedback controller circuit, which can produce a Q-switched pulse with customized characteristics by varying the pump rate, which can be influenced by the pump power. The pump power is considered as the input to the system and the photon number is the output of the system. The population inversion, the saturable absorber concentration and the photon number are considered as the states of the system. First it is demonstrated that by applying nonlinear state feedback, the Q-switched laser system can be transformed into a pair of two cascaded integrators. Therefore, the desired output can be customized by applying its second derivative as the input. Cr:YSO Q-switched Cr:LiSAF laser is used as an example to demonstrate our method. Both theoretical analysis of the method and the numerical simulation results are presented.

Study of different optimization strategies for analogue circuits

Purpose In this paper, we propose further development of the generalized methodology for analogue circuit optimization. This methodology is based on optimal control theory. This approach generates many different circuit optimization strategies. We lead the problem of minimizing the CPU time needed for circuit optimization to the classical problem of minimizing a functional in optimal control theory. Design/methodology/approach The process of analogue circuit optimization is defined mathematically as a controllable dynamical system. In this context, we can formulate the problem of minimizing the CPU time as the minimization problem of a transitional process of a dynamical system. To analyse the properties of such a system, we propose to use the concept of the Lyapunov function of a dynamical system. This function allows us to analyse the stability of the optimization trajectories and to predict the CPU time for circuit optimization by analysing the characteristics of the initial part of the process. Findings We present numerical results that show that we can compare the CPU time for different circuit optimization strategies by analysing the behaviour of a special function. We establish that, for any optimization strategy, there is a correlation between the behaviour of this function and the CPU time that corresponds to that strategy. Originality/value The analysis shows that Lyapunov function of optimization process and its time derivative can be informative sources for searching a strategy, which has minimal processor time expense. This permits to predict the best optimization strategy by analyzing only initial part of the optimization process.

Digital Signal Processing and Control for the Study of Gene Networks.

Thanks to the digital revolution, digital signal processing and control has been widely used in many areas of science and engineering today. It provides practical and powerful tools to model, simulate, analyze, design, measure, and control complex and dynamic systems such as robots and aircrafts. Gene networks are also complex dynamic systems which can be studied via digital signal processing and control. Unlike conventional computational methods, this approach is capable of not only modeling but also controlling gene networks since the experimental environment is mostly digital today. The overall aim of this article is to introduce digital signal processing and control as a useful tool for the study of gene networks.

位相リセットが多足歩行に及ぼす影響のシンプルモデルを用いた解析

Multi-legged animals show several types of ipsilateral interlimb coordination. Millipedes show the direct wave gait in which the swing leg movements propagate from posterior to anterior. On the other hand, some centipedes show the retrograde wave gait in which the swing leg movements propagate from anterior to posterior. Interestingly, when some millipede walks in a specific way, it is reported that both direct and retrograde waves of the leg movements can coexist with a source part of the waves (we call it as source wave gaits). However, the mechanism behind the gait generation is still unclear because of the complex nature of the interaction between neural control and body dynamic systems. In this paper, we propose a simple model to gain a better understanding of the mechanism, especially how a local sensory feedback affects multi-legged locomotion. We design a planar multi-legged model and its locomotion control system based on biologically-inspired oscillators with a local sensory feedback, phase resetting. Each oscillator controls each leg, and there are no direct interactions among oscillators. Our simulation results reveal three types of gaits, which have different ipsilateral phase relationships (Direct, retrograde and source wave gaits like animals). These gaits are neither predesigned or predetermined, but emerge through the interaction between the neural control and body dynamic systems through phase resetting. These results suggest that the local sensory feedback is important to form proper interlimb coordination and thereby effectively generates multi-legged gaits. In addition, our mathematical analysis with the simple model successfully extracts the essential feature of these gaits, and suggests that these types of locomotion can exist regardless of the number of legs in our system.

From semi-tensor product of matrices to logical control systems

The logical control system theory (LCST) based on semi-tensor product (STP) of matrices has become a new direction in control field. The purpose of this paper is to give a comprehensive introduction to the logical control system, from the basic mathematical tools and analysis methods to the main results. First we introduce the STP of matrices. Meanwhile, a digging discussion is made to reveal some of its insides. Then we explain how to use STP to convert a logic expression into algebraic form. Then an itemized introduction to the main achievements in analysing and control design of LCSs in last few years is presented, which consists of the topological structure of logical systems, controllability, observability, and stabilization, the stability of disturbance decoupling, optimal control, identification of LCSs. Next, the extension from classical Boolean logic to $k$-valued logic, to multi-valued logic, and to mixed-valued logic is explained. All these results form the theoretical foundation of this new discipline. In addition, the concepts, notations, and the fundamental method/tool have been uniformly normalized. Then some current developments of LCST and its applications or potential applications have been discussed. Some open problems and possible research directions have also been presented. Finally, a personal prediction about the development of control theory is given as: The combination of logic control systems and dynamic control systems is expected to generate a ``information-control system, it is what Tsien Hsueshen predicted ``theorical control theory, and is also the next generation of control theory proposed by American discipline development report.

Neural network based semi-empirical models for dynamical systems described by differential-algebraic equations

We analyzed the problem of mathematical modeling and computer simulation of nonlinear controlled dynamical systems usually described by differential-algebraic equations. The problem is proposed to be solved in the framework of the semi-empirical approach combining theoretical knowledge for the plant with training tools of artificial neural network field. The results are presented for a semi-empirical model that simulate the reentry hypersonic vehicle and confirm the efficiency of this approach.

Trajectory Controllability of Semilinear Systems with Delay in Control and State

In this paper we consider the finite-dimensional dynamical control system described by scalar semilinear ordinary differential state equation with variable delay. The semilinear state equation contains both pure linear part and nonlinear perturbation. We extend the concept of controllability on trajectory controllability for systems with point delay in control and in nonlinear term. Moreover, we present remarks and comments on the relationships between different concepts of controllability. Finally we propose the possible extensions.

Control of a PCM ventilated facade using reinforcement learning techniques

Artificial intelligence techniques have been successfully applied to control dynamic systems looking for an optimal control. Among those techniques, reinforcement learning has been shown as particularly effective at reducing the dimensionality of some real problems and solving control problems by learning from experience. The use of thermal energy storage active systems in the building sector is identified as suitable option to reduce their energy demand for heating and cooling. However, these systems might be expensive and require appropriate control strategies in order to improve the performance of the building. In this paper a ventilated facade with PCM is controlled using a reinforcement learning algorithm. The ventilated facade uses mechanical ventilation during nighttime to solidify the PCM and releases this cold stored to the inner environment during the peak demand period. It is crucial to decide correctly the schedule of charge and discharge process of the PCM according to the weather and indoor conditions. An experimentally validated numerical model is used to test the performance of the control algorithm under different weather conditions. Important improvements on the energy savings due to the use of control strategies were found and supported by the data under the different tested climatic conditions.

Building up time-consistency for risk measures and dynamic optimization

In stochastic optimal control, one deals with sequential decision-making under uncertainty; with dynamic risk measures, one assesses stochastic processes (costs) as time goes on and information accumulates. Under the same vocable of time-consistency (or dynamic-consistency), both theories coin two different notions: the latter is consistency between successive evaluations of a stochastic processes by a dynamic risk measure (a form of monotonicity); the former is consistency between solutions to intertemporal stochastic optimization problems. Interestingly, both notions meet in their use of dynamic programming, or nested, equations.We provide a theoretical framework that offers (i) basic ingredients to jointly define dynamic risk measures and corresponding intertemporal stochastic optimization problems (ii) common sets of assumptions that lead to time-consistency for both. We highlight the role of time and risk preferences — materialized in one-step aggregators — in time-consistency. Depending on how one moves from one-step time and risk preferences to intertemporal time and risk preferences, and depending on their compatibility (commutation), one will or will not observe time-consistency. We also shed light on the relevance of information structure by giving an explicit role to a state control dynamical system, with a state that parameterizes risk measures and is the input to optimal policies.

A measurement method of nonlinear strength for dynamical model of SRLV

In the re-entry process of a suborbital reusable launch vehicle (SRLV), the strong nonlinear and uncertainty have a negative impact on the dynamical modelling and control system design. The paper introduces a nonlinearity index method to analyse the dynamical model of SRLV. The nonlinearity index method was first developed to control error propagation in a nonlinear system. The nonlinearity indices access the boundary between the strong and the weak nonlinearity of the system model. Applying this method on SRLV dynamics is an effective way to measure the nonlinear strength of dynamics model over the full flight envelope. The algorithm of nonlinearity index according to engineering applications is first proposed in this paper. The expressions of static and dynamic nonlinearity indices are given, which can qualitatively and quantitatively measure the nonlinear strength of dynamical model in the re-entry phase. The simulation results show the method is correct and appropriate.

Short-Term Traffic Flow Local Prediction Based on Combined Kernel Function Relevance Vector Machine Model

Short-term traffic flow prediction is one of the most important issues in the field of adaptive traffic control system and dynamic traffic guidance system. In order to improve the accuracy of short-term traffic flow prediction, a short-term traffic flow local prediction method based on combined kernel function relevance vector machine (CKF-RVM) model is put forward. The C-C method is used to calculate delay time and embedding dimension. The number of neighboring points is determined by use of Hannan-Quinn criteria, and the CKF-RVM model is built based on genetic algorithm. Finally, case validation is carried out using inductive loop data measured from the north–south viaduct in Shanghai. The experimental results demonstrate that the CKF-RVM model is 31.1% and 52.7% higher than GKF-RVM model and GKF-SVM model in the aspect of MAPE. Moreover, it is also superior to the other two models in the aspect of EC.

Controllability of Nonlinear Impulsive Stochastic Evolution Systems Driven by Fractional Brownian Motion

We consider the infinite-dimensional dynamical control systems described by nonlinear impulsive stochastic evolution differential equations. Sufficient conditions for the complete controllability of nonlinear impulsive stochastic systems are formulated and proved under the reasonable assumption that the corresponding linear system is completely controllable.

Controllability of time-delayed Boolean multiplex control networks under asynchronous stochastic update.

In this article, the controllability of asynchronous Boolean multiplex control networks (ABMCNs) with time delay is studied. Firstly, dynamical model of Boolean multiplex control networks is constructed, which is assumed to be under Harvey' asynchronous update and time delay is introduced both in states and controls. By using of semi-tensor product (STP) approach, the logical dynamics is converted into an equivalent algebraic form by obtaining the control-depending network transition matrices of delayed system. Secondly, a necessary and sufficient condition is proved that only control-depending fixed points of the studied dynamics can be controlled with probability one. Thirdly, respectively for two types of controls, the controllability of dynamical control system is investigated. When initial states and time delay are given, formulae are obtained to show a) the reachable set at time s under specified controls; b) the reachable set at time s under arbitrary controls; c) the reachable probabilities to different destination states. Furthermore, an approach is discussed to find a precise control sequence which can steer dynamical system into a specified target with the maximum reachable probability. Examples are shown to illustrate the feasibility of the proposed scheme.

A Mayer-type optimal control for multivalued logic control networks with undesirable states

A fundamental problem for all dynamical control systems is to determine a control that is optimal in some sense. Based on semi-tensor product, we consider a Mayer-type optimal control problem for multi-valued logical control networks with time delays in states. A necessary condition for a control to be optimal is derived while avoiding a set of forbidden states. Examples are provided to illustrate the effectiveness of the obtained results.

The Psychology of Dynamic Balance and Peak Performance in Sport: Correction Theory

This article introduces a new approach to understanding peak performance and dysfunctional performance in sport, correction theory. Correction theory, based within a control theory and dynamical systems perspective, assumes that dynamic balance (a state in which a robust complex system will self-correct in response to imbalance) underwrites individual functioning. The central thesis presented in this article is that an interdependent relationship exists between peak performance and dysfunctional performance in sport. Peak performance is, in part, a (corrective) response to dysfunctional performance and vice versa. An overview of correction theory is presented, based on two propositions relating to balance. Implications of correction theory for understanding sporting performance are briefly considered.