A sliding mode control for linear fractional systems with input and state delays

In this paper, a sliding mode control design for fractional order systems with input and state time-delay is proposed. First, we consider a fractional order system without delay for which a sliding surface is proposed based on fractional integration of the state. Then, a stabilizing switching controller is derived. Second, a fractional system with state delay is considered. Third, a strategy including a fractional state predictor input delay compensation is developed. The existence of the sliding mode and the stability of the proposed control design are discussed. Numerical examples are given to illustrate the theoretical developments.     

Markov ratio decision processes

A finite-state Markov decision process, in which, associated with each action in each state, there are two rewards, is considered. The objective is to optimize the ratio of the two rewards over an infinite horizon. In the discounted version of this decision problem, it is shown that the optimal value is unique and the optimal strategy is pure and stationary; however, they are dependent on the starting state. Also, a finite algorithm for computing the solution is given.     

分数阶时滞微分系统的滑模控制(英文)

The problem of sliding mode control for fractional differential systems with statedelay is considered.A novel sliding surface is proposed and a controller is designed correspondingly,such that the state starting from any initial value will move toward the switching surface and reach the sliding surface in finite time and the state variables on the sliding surface will converge to equilibrium point.And the stability of the proposed control design is discussed.     

Sliding mode control of inventory management systems with bounded batch size

In this paper, variable structure control of discrete time systems is considered and the idea of reaching law based sliding mode control is presented. Then the idea is applied to design a control strategy for a class of supply chains with multiple suppliers. In the considered inventory management systems, goods are delivered to a single warehouse with limited capacity. Suppliers themselves have finite manufacturing capabilities, but are also not willing to accept orders of negligible size. The reaching law proposed for such systems ensures full satisfaction of the unpredictable consumers’ demand while adhering to state and input constraints.     

Phenomena in Inverse Stackelberg Games,Part 1: Static Problems

Games are considered in which the role of the players is a hierarchical one. Some players behave as leaders, others as followers. Such games are named after Stackelberg. In the current paper, a special type of these games is considered, known in the literature as inverse Stackelberg games. In such games, the leader (or: leaders) announces his strategy as a mapping from the follower (or: followers) decision space into his own decision space. Arguments for studying such problems are given. The routine way of analysis, leading to a study of composed functions, is not very fruitful. Other approaches are given, mainly by studying specific examples. Phenomena in problems with more than one leader and/or follower are studied within the context of the inverse Stackelberg concept. As a side issue, expressions like “two captains on a ship” and “divide and conquer” are given a mathematical foundation.     

Phenomena in Inverse Stackelberg Games,Part 2: Dynamic Problems

Games are considered in which the role of the players is a hierarchical one. Some players behave as leaders, others as followers. Such games are named after Stackelberg. In the current paper, a special type of these games is considered, known in the literature as inverse Stackelberg games. In such games, the leader (or: leaders) announces his strategy as a mapping from the follower (or: followers) decision space into his own decision space. Arguments for studying such problems are given. The routine way of analysis, leading to a study of composed functions, is not very fruitful. Other approaches are given, mainly by studying specific examples. Phenomena in problems with more than one leader and/or follower are studied within the context of the inverse Stackelberg concept. As a side issue, expressions like “two captains on a ship” and “divide and conquer” are given a mathematical foundation.     

Noninferior Nash Strategies for Multi-Team Systems

This paper is concerned with the optimization of systems that are controlled by several teams of decision makers. The decision makers within each team cooperate for the benefit of their team. On the other hand, the teams compete among themselves in order to achieve an objective that relates to the overall performance of the system. An approach that merges concepts from team theory and game theory for dealing with such systems and a solution called the noninferior Nash strategy are introduced. This multi-team solution provides a new framework for analyzing hierarchically controlled systems so as to address complicated coordination problems among the decision makers. The properties of the noninferior Nash solution in static multi-team systems are investigated and necessary conditions for its existence are derived. Analytical expressions for the noninferior Nash strategies are derived for a class of linear-quadratic static multi-team games. In order to deal with the issue of nonuniqueness of the solution, the concept of a noninferior Nash strategy with a team leader is introduced. Several examples are presented to illustrate the results.     

基于公平关切的网络零售商店内推介策略研究

研究了公平关切下网络零售商店内推介策略选择问题。首先,以无公平关切模型为基准,发现无公平关切情形下两零售商均采取推介策略。其次,考虑跟随者(零售商2)公平关切,发现在信息不对称情况下,随着零售商2公平关切程度的增大均衡推介策略依次为:都不推介、仅跟随者(零售商2)推介和都推介,由于信息的不对称公平关切能够诱导跟随者采取推介策略;在信息对称情况下,随着公平关切程度的增大均衡推介策略依次为:仅领导者(零售商1)推介和都推介,信息的透明化能够促使领导型零售商采取推介策略。最后,分析了两零售商都公平关切情形下均衡推介策略选择问题。     

Existence theorems of equilibrium points in stackelberg

A two players static. Stackelberg game is considered with constraints on the decision variables. Existence theorems of equilibrium points are given when the reaction set of the follower to the strategy of the leader, is a singleton. Some definition are presented and discussed and a simple existence theorem is given also in the case when the follower has more than one element in his reaction set. Finally an example of dynamic Stackelbebg game- is analized to emphasize some features arising when constraints are present on control variables.     

Chaos synchronization and chaos control of quantum-CNN chaotic system by variable structure control and impulse control

In this paper, we derive some less stringent conditions for the exponential and asymptotic stability of impulsive control systems with impulses at fixed times. These conditions are then used to design an impulsive control law for the Quantum Cellular Neural Network chaotic system, which drives the chaotic state to zero equilibrium and synchronizes two chaotic systems. An active sliding mode control method is synchronizing two chaotic systems and controlling chaotic state to periodic motion state. And a sufficient condition is drawn for the robust stability of the error dynamics, and is applied to guiding the design of the controllers. Finally, numerical results are used to show the robustness and effectiveness of the proposed control strategy.     

Second-order cluster consensus of multi-agent dynamical systems with impulsive effects

This paper discuss the cluster consensus of multi-agent dynamical systems (MADSs) with impulsive effects and coupling delays. Some sufficient conditions that guarantee cluster consensus in MADS are derived. In each cluster, agents update their position and velocity states according to a leader’s instantaneous information, and interactions among agents are uncertain. Furthermore, switching topology problem in MADS is considered by impulsive stability and adaptive strategy. Finally, numerical simulations are given to verify our theoretical analysis.     

Chaos synchronization in noisy environment using nonlinear filtering and sliding mode control

This paper presents an algorithm for synchronizing two different chaotic systems, using a combination of the extended Kalman filter and the sliding mode controller. It is assumed that the drive chaotic system has a random excitation with a stochastically chaotic behavior. Two different cases are considered in this study. At first it is assumed that all state variables of the drive system are available, i.e. complete state measurement, and a sliding mode controller is designed for synchronization. For the second case, it is assumed that the output of the drive system does not contain the whole state variables of the drive system, and it is also affected by some random noise. By combination of extended Kalman filter and the sliding mode control, a synchronizing control law is proposed. As a case study, the presented algorithm is applied to the Lur’e-Genesio chaotic systems as the drive-response dynamic systems. Simulation results show the good performance of the algorithm in synchronizing the chaotic systems in presence of noisy environment.     

Control of a novel class of fractional-order chaotic systems via adaptive sliding mode control approach

In this paper, an adaptive sliding mode controller for a novel class of fractional-order chaotic systems with uncertainty and external disturbance is proposed to realize chaos control. The bounds of the uncertainty and external disturbance are assumed to be unknown. Appropriate adaptive laws are designed to tackle the uncertainty and external disturbance. In the adaptive sliding mode control (ASMC) strategy, fractional-order derivative is introduced to obtain a novel sliding surface. The adaptive sliding mode controller is shown to guarantee asymptotical stability of the considered fractional-order chaotic systems in the presence of uncertainty and external disturbance. Some numerical simulations demonstrate the effectiveness of the proposed ASMC scheme.     

Event-triggered sliding mode control for singular systems with disturbance

This paper investigates the event-triggered sliding mode control (SMC) problem for singular systems with disturbance. Firstly, an event-triggered sliding mode control law is designed to guarantee the reachability of sliding surface. Different from the related methods, in order to deal with the difficulty caused by event-triggered SMC strategy, a novel Lemma is proposed in this paper. Secondly, the admissibility of sliding motion is presented, which is used to solve the controller gain. Then, a positive lower bound of the inter execution time can be guaranteed and the Zeno behavior is avoided. Finally, two simulation examples are presented to show the effectiveness of derived theoretical results.     

带有限反馈下层的二层规划问题的部分合作模型

对下层最优反馈为离散有限多个的二层规划问题的部分合作模型进行探讨. 当下层的合作程度依赖于上层的决策变量时, 给出一个确定合作系数函数的一般方法, 进而得到一个新的部分合作模型. 在适当地假设下, 可保证所给的部分合作模型一定可以找到比悲观解要好的解, 并结合新的部分合作模型对原不适定问题进行分析, 得到了一些有益的结论. 最后以实际算例说明了所给部分合作模型的可行性.     

Stackelberg strategies in linear-quadratic stochastic differential games

This paper obtains the Stackelberg solution to a class of two-player stochastic differential games described by linear state dynamics and quadratic objective functionals. The information structure of the problem is such that the players make independent noisy measurements of the initial state and are permitted to utilize only this information in constructing their controls. Furthermore, by the very nature of the Stackelberg solution concept, one of the players is assumed to know, in advance, the strategy of the other player (the leader). For this class of problems, we first establish existence and uniqueness of the Stackelberg solution and then relate the derivation of the leader's Stackelberg solution to the optimal solution of a nonstandard stochastic control problem. This stochastic control problem is solved in a more general context, and its solution is utilized in constructing the Stackelberg strategy of the leader. For the special case Gaussian statistics, it is shown that this optimal strategy is affine in observation of the leader. The paper also discusses numerical aspects of the Stackelberg solution under general statistics and develops algorithms which converge to the unique Stackelberg solution.This work was performed while the second author was on sabbatical leave at the Department of Applied Mathematics, Twente University of Technology, Enschede, Holland.     

Event-triggered dual-mode predictive control for constrained nonlinear systems with continuous/intermittent detection

This paper investigates the problem of event-triggered model predictive control for constrained nonlinear systems. A dual-mode control strategy combined with two different event-triggered mechanisms are introduced to reduce computational and communication loads. For the event-triggered mechanisms, two cases, continuous detection and intermittent detection, are considered, respectively. In order to avoid the transmission of continuous predicted control input trajectories, the actual control signals are generated under a sample-and-hold manner. A decreasing prediction horizon is introduced to reduce the complexity of optimization problems and a tightened state constraint is designed to achieve robust constraint satisfaction. The sufficient conditions are derived to guarantee the feasibility and stability of the closed-loop system. The performance of the proposed strategy is illustrated by a simulation example.     

Hierarchic control of a linear heat equation with missing data

The paper is devoted to the Stackelberg control of a linear parabolic equation with missing initial condition. The strategy involves two controls called follower and leader. The objective of the follower is to bring the state to a desired state while the leader has to bring the system to rest at the final time. The results are obtained by means of Fenchel–Legendre transform and appropriate Carleman inequalities.     

A decomposition approach to solve a bilevel capacitated facility location problem with equity constraints

In this paper, we study a capacitated facility location problem with two decision makers. One (say, the leader) decides on which subset of facilities to open and the capacity to be installed in each facility with the goal of minimizing the overall costs; the second decision maker (say, the follower), once the facilities have been designed, aims at maximizing the profit deriving from satisfying the demands of a given set of clients beyond a certain threshold imposed by the leader. The leader can foresee but cannot control the follower’s behavior. The resulting mathematical formulation is a discrete–continuous bilevel optimization problem. We propose a decomposition approach to cope with the bilevel structure of the problem and the integrality of a subset of variables under the control of the leader. Such a proposal has been tested on a set of benchmark instances available in the literature.     

On maximizing the average time at a goal

In a decision process (gambling or dynamic programming problem) with finite state space and arbitrary decision sets (gambles or actions), there is always available a Markov strategy which uniformly (nearly) maximizes the average time spent at a goal. If the decision sets are closed, there is even a stationary strategy with the same property.Examples are given to show that approximations by discounted or finite horizon payoffs are not useful for the general average reward problem.