Observer‐based fuzzy adaptive optimal control for nonlinear continuous‐time saturation interconnected systems

A fuzzy adaptive optimal output‐feedback control problem is investigated for nonlinear continuous‐time interconnected systems with saturation constraints. The system dynamics and the mismatched interconnections of each subsystem are unknown, and each subsystem contains unavailable states. Based on fuzzy logic systems, a fuzzy state observer is designed to approximate the unknown system states and the interconnections of the nonlinear interconnected system. By using adaptive dynamic programming technology, the decentralized optimal controller of each subsystem is given and the saturation control input is updated via the critic fuzzy logic systems. The proposed fuzzy adaptive observer‐based optimal control scheme can guarantee that the closed‐loop interconnected system is ultimately uniformly bounded stable. A simulation example validates the effectiveness of the presented scheme.     

LMI-based cooperative distributed model predictive control for Lipschitz nonlinear systems

In this paper, a distributed model predictive control is proposed to control Lipschitz nonlinear systems. The cooperative distributed scheme is considered where a global infinite horizon objective function is optimized for each subsystem, exploiting the state and input information of other subsystems. Thus, each control law is obtained separately as a state feedback of all system's states by solving a set of linear matrix inequalities. Due to convexity of the design, convergence properties at each iteration are established. Additionally, the proposed algorithm is modified to optimize only one control input at a time, which leads to a further reduction in the computation load. Finally, two application cases are studied to show the effectiveness of the proposed method.     

A decentralized receding horizon optimal approach to formation control of networked mobile robots

This paper presents a receding horizon optimal controller with guaranteed stability for multirobot formation, taking into account collision and obstacle avoidance. The proposed scheme is based on synchronous decentralized strategy wherein all the vehicles that are connected via a packed‐delaying network solve a finite horizon–constrained optimal control problem to obtain their own control action at each sampling instant. First, each robot is modeled by a single integrator dynamics; then, by defining a control law for each robot and considering the effect of communication delay, the closed‐loop dynamics is described as a delay differential equation with tunable parameters. Afterwards, a novel finite‐horizon optimal control setup is established to obtain these adjustable gains such that a desirable formation is achieved. The efficiency and applicability of the suggested scheme are demonstrated by simulation results.     

Passivity‐based H∞ control for a class of switched nonlinear systems

In this paper, we investigate the H_∞ control problem for a class of switched nonlinear systems based on passivity. The solvability conditions of the H_∞ control problem are obtained by designing a state‐dependent switching law and state feedback controller of each subsystem. In addition, if all subsystems are not passive, we make a partition of the state space and design controllers for subsystems such that each subsystem has the passivity property on the associated region, and then obtain solvability conditions of the H_∞ control problem. An example is provided to demonstrate the effectiveness of the proposed design method. Copyright © 2016 John Wiley & Sons, Ltd.     

Near‐optimal control for multiparameter singularly perturbed stochastic systems

In this paper, the linear quadratic optimal stochastic control problem is investigated for multiparameter singularly perturbed stochastic systems in which N lower‐level fast subsystems are interconnected by a higher‐level slow subsystem. After establishing the asymptotic structure of the solution for the multiparameter stochastic algebraic Riccati equation (MSARE), a near‐optimal controller that is independent of small unknown parameters is obtained by neglecting these parameters. The stability of a closed‐loop stochastic system is investigated. Furthermore, it is shown that the resulting controller achieves an O(∥ν∥²) approximation to the optimal cost of the original optimal control problem. Finally, in order to demonstrate the efficiency of the proposed algorithm, a numerical example—a practical multi‐area power system—is solved. Copyright © 2010 John Wiley & Sons, Ltd.     

The stabilizing system of the spine. Part I. Function, dysfunction, adaptation, and enhancement.

Presented here is the conceptual basis for the assertion that the spinal stabilizing system consists of three subsystems. The vertebrae, discs, and ligaments constitute the passive subsystem. All muscles and tendons surrounding the spinal column that can apply forces to the spinal column constitute the active subsystem. The nerves and central nervous system comprise the neural subsystem, which determines the requirements for spinal stability by monitoring the various transducer signals, and directs the active subsystem to provide the needed stability. A dysfunction of a component of any one of the subsystems may lead to one or more of the following three possibilities: (a) an immediate response from other subsystems to successfully compensate, (b) a long-term adaptation response of one or more subsystems, and (c) an injury to one or more components of any subsystem. It is conceptualized that the first response results in normal function, the second results in normal function but with an altered spinal stabilizing system, and the third leads to overall system dysfunction, producing, for example, low back pain. In situations where additional loads or complex postures are anticipated, the neural control unit may alter the muscle recruitment strategy, with the temporary goal of enhancing the spine stability beyond the normal requirements.     

Optimal decentralized control of a wind turbine and diesel generator system

This article presents a decentralized optimal controller design technique for the frequency and power control of a coupled wind turbine and diesel generator. The decentralized controller consists of two proportional-integral (PI)-lead controllers which are designed and optimized simultaneously using a quasi-Newton based optimization technique, namely, Davidon–Fletcher–Powell algorithm. The optimal PI-lead controllers are designed in such a way that there are no communication links between them. Simulation results show the superior performance of the proposed controller with a lower order structure compared to the benchmark decentralized linear-quadratic Gaussian integral controllers of orders 4 and 11. It is also shown that the proposed controller demonstrates an effective performance in damping the disturbances from load and wind power, as well as a robust performance against the parameter changes of the power system.     

Subsystem‐level optimal control of weakly coupled linear stochastic systems composed of N subsystems

In this paper we introduce a transformation for the exact closed‐loop decomposition of the optimal control and Kalman filtering tasks of linear weakly coupled stochastic systems composed of N subsystems. In addition to having obtained N completely independent reduced‐order subsystem Kalman filters working in parallel, we have obtained the exact solution of the algebraic regulator and filter Riccati equations in terms of the solutions of the corresponding reduced‐order subsystem algebraic Riccati equations. The introduced transformation produces a lot of savings especially for on‐line computations since it allows parallel processing of information with lower‐order‐dimensional Kalman filters. The methodology presented is applied to a 17th‐order cold‐rolling mill. Copyright © 1999 John Wiley & Sons, Ltd.     

基于腰椎间盘退变的脊柱稳定性改变的MRI研究进展

腰椎间盘是位于两个相邻椎体之间的圆盘状纤维软骨,是维持脊柱稳定性的重要解剖结构。目前,维持脊柱稳定性的解剖结构分为被动亚系、主动亚系和神经控制亚系,称为"三亚系模型",腰椎间盘退变(intervertebral disc degeneration,IVDD)会引起该模型其它组织的病理学改变,且彼此相互作用导致脊柱稳定性下降,是下腰痛最常见的原因。IVDD患者常伴有椎小关节及韧带的退变、邻近椎体Modic改变、椎体血流量减少、椎旁肌肉脂肪浸润增加、神经轴向牵拉损伤的代偿性减少等。磁共振成像(magnetic resonance imaging,MRI)是评估脊柱稳定性首选的影像学方法,常规MRI能完整显示IVDD患者三亚系模型相关组织形态学变化,MRI功能成像能定量分析其病理生理学变化的程度。本文综述IVDD患者腰椎间盘、椎小关节、韧带、椎体、肌肉、神经的MRI形态学及定量值变化,阐述IVDD引起脊柱稳定性改变的相关机制,旨在为下腰痛患者的精准诊疗提供更全面的信息。     

Hierarchical optimal control of a binary distillation column

This paper presents a two‐level optimal control for the binary distillation column. From the control point of view, the binary distillation column is a high‐order system consisting of several interconnected subsystems (trays) that aim to maximize output purity. Controlling the system in a hierarchical manner not only decreases complexity and solution time but also can improve the control structure's reliability. In this study, the distillation column is decomposed into N_T second‐order subsystems, each representing one stage (one tray). Accordingly, the cost function is decomposed, and thus, the overall problem is converted into N_T lower‐order subproblems where each tray has its own controller. A two‐level interaction prediction approach provides optimal control for the overall system. The task of the first level is to solve the subproblems using the predicted values of the coordination parameters, whereas the second level acts as a coordinator to update the coordination parameters. Simulation results show the capability and efficacy of the proposed two‐level control method in finding the optimal solution with less complexity and lower solution time than those of the centralized method.     

Decentralized output‐feedback stabilization for interconnected discrete systems with unknown delays

The decentralized feedback stabilization problem of a class of nonlinear interconnected discrete‐time systems is considered. This class of systems has unknown‐but‐bounded state‐delay and uncertain nonlinear perturbations satisfying quadratic constraints that are functions of the overall state and delayed state vectors. A decentralized output feedback scheme is proposed and analyzed such that the overall closed‐loop system guarantees global delay‐dependent stability condition, derived in terms of local subsystem variables. Incorporating feedback gain perturbations, new resilient decentralized feedback scheme is subsequently developed. The proposed approach is formulated within the framework of convex optimization over linear matrix inequalities. Simulation results illustrate the effectiveness of the proposed decentralized output‐feedback controllers. Copyright © 2009 John Wiley & Sons, Ltd.     

Low‐order multi‐rate linear time‐invariant decentralized trackers using the new observer‐based sub‐optimal method for unknown sampled‐data nonlinear time‐delay system with closed‐loop decoupling

This paper presents the low‐order multi‐rate linear time‐invariant decentralized trackers using the new observer‐based sub‐optimal method for a class of unknown sampled‐data nonlinear time‐delay system with closed‐loop decoupling. For the unknown sampled‐data nonlinear time‐delay system, we assume that the inner time delay is clearly known. Under this prerequisite, the appropriate (low‐) order decentralized linear observer for the unknown sampled‐data nonlinear system is determined by the off‐line observer/Kalman filter identification (OKID) method with artificial delay input and actual delay output. Then, the above observer has been further improved based on the proposed new observer‐based sub‐optimal approach. Sequentially, the decentralized tracker with the high gain property is proposed, so that the closed‐loop system has the decoupling property. The proposed approach constructs complete mathematics method including the concept of optimal control theory and state‐matching digital redesign technique and is quite useful for the complicated interconnected large‐scale sampled‐data nonlinear time‐delay system with unknown system equation. Copyright © 2010 John Wiley & Sons, Ltd.     

A combined state and state estimate feedback solution to the ship positioning control problem

A stochastic linear quadratic optimal control problem is considered in which some of the plant states may be measured without a measurement noise component. This set of states are assumed to be associated with the plant inputs and force transducers. The optimal controller is shown to include state feedback from this part of the system. The states which cannot be measured are assumed to be combined in noisy output signal. The optimal controller corresponding to this second subsystem is shown to include a Kalman filter and state-estimate feedback. The combination of state and state-estimate feedback has the advantage that the dimension of the Kalman filter is equal to that of the second subsystem mentioned above. In the conventional solution to this problem, no states are assumed measurable, and the dimension of the Kalman filter is equal to the dimension of the complete system. In many industrial control problems, the combined control law enables a significant reduction in the dimension of the filter to be achieved. The technique has been proposed for use in dynamic ship positioning control systems, and this problem is discussed.     

Guaranteed cost control for switched LPV systems via parameter and state‐dependent switching with dwell time and its application

This paper is concerned with the problem of guaranteed cost control for switched linear parameter‐varying (LPV) systems. A parameter and state‐dependent switching law with dwell time is designed. The guaranteed cost control problem for switched LPV systems is still solvable even though this problem for each subsystem is unsolvable. First, a sufficient condition ensuring the solvability of the guaranteed cost control problem for switched LPV systems is presented via multiple parameter‐dependent Lyapunov functions. Then, the parameter‐dependent controller is designed, such that the closed‐loop system is asymptotically stable with the guaranteed cost index. Finally, the effectiveness of the proposed control design scheme is illustrated by its application to an aero‐engine. Copyright © 2016 John Wiley & Sons, Ltd.     

Continuous and inverse optimal control designs for chained systems: A global state‐scaling transformation and a time‐scaling method

In this paper, the inverse optimal control designs for chained systems are investigated. The presented designs are based on the thorough study of controllability of chained systems. Particularly, two methods are proposed to recover uniform complete controllability for the chained system. One involves a global singularity‐free state‐scaling transformation, the other is based on a time transform, and both of them require an innovative design of dynamic control component for its subsystem. Using either of the approaches, the chained system is mapped into a controllable linear time‐varying system for which control can systematically be designed to ensure exponential convergence or asymptotic stability. Both state‐feedback and output‐feedback designs are presented and literally shown to be inversely optimal. Simulation results are used to verify the effectiveness of the proposed controls. Copyright © 2008 John Wiley & Sons, Ltd.     

Time-scale decoupling and order reduction for linear time-varying systems

The class of time-varying linear systems which are two-time-scale on an interval may be decoupled by a transformation of variables into separate subsystems containing the slow and fast dynamic parts. The transformation is obtained by solving a non-symmetric Riccati differential equation forward in time and a linear matrix differential equation backward in time. Small parameters are identified which measure the strength of the time-scale separation and the stability of the fast subsystem. As these parameters go to zero, the order of the system is reduced, and a useful approximate solution to the original system is obtained. The transformation is illustrated for examples with strong and weak fast subsystem stability.     

A unified approach to reduced-order modelling and control of large-scale systems with multiple decision makers

This paper presents a unified approach to reduced-order modelling and control of large-scale systems with multiple decision makers. The ‘core’ of a large game problem is identified through the information structure and the class of structure preserving strategies. The induced decomposition results in a low-order game problem and two decentralized optimal control problems. An example of a two-area power system demonstrates the computational attractiveness of the proposed design methodology.     

Decentralized control strategies for dynamic routing

The routing problem in multi‐destination data communication networks is considered. A dynamic model, which can incorporate arbitrary, different, time‐varying processing delays at different nodes, is developed to describe the network dynamics. Based on this model, controllers for routing control are proposed. The structures of the proposed controllers are motivated by an optimal control problem. These proposed controllers are completely decentralized in the sense that all necessary on‐line computations are done locally at each node. Furthermore, the information needed for these computations is related only to the queue lengths at the present node and the adjacent downstream nodes. Both cases when the controls can be continuously changed and when the controls are updated at discrete time instants are considered. In the latter case the controls at different nodes may be updated at different time instants (i.e. the network is not necessarily synchronous). It is shown that the controllers enjoy many desirable properties; in particular, they clear all the queues of the network in the absence of external message arrivals, in finite time. Furthermore, the controllers do not direct messages around a loop. They also have certain robustness properties. Some simulation results relating to a number of realistic problems are presented to illustrate various features of the controllers. Copyright © 2002 John Wiley & Sons, Ltd.