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Time-delay systems
This book comprehensively presents a recently developed novel methodology for analysis and control of time-delay systems. Time-delays frequently occurs in engineering and science. Such time-delays can cause problems (e.g. instability) and limit the achievable performance of control systems.
eBook
Quantized neural adaptive finite-time preassigned performance control for interconnected nonlinear systems
In this article, the issue of neural adaptive decentralized finite-time prescribed performance (FTPP) control is investigated for interconnected nonlinear time-delay systems. First, to bypass the potential singularity difficulties, the hyperbolic tangent function and the radial basis function neural networks are integrated to handle the unknown nonlinear items. Then, an adaptive FTPP control strategy is developed, where an improved fractional-order filter is applied to tackle the tremendous “amount of calculation” and eliminate the filter error simultaneously. Furthermore, by considering the impact of bandwidth limitation, an adaptive self-triggered control law is designed, in which the next trigger instant is determined through the current information. Ultimately, it can be demonstrated that the proposed control scheme not only guarantees that all states of the closed-loop system are semi-globally uniformly ultimately bounded, but also that the system output is confined to a small area in finite time. Two simulation examples are carried out to verify the effectiveness and superiority of the proposed method.
Journal Article
Discrete-time delay systems: part 1. Global fully actuated case
A basic introduction to the fully actuated system (FAS) approaches for discrete-time systems with delays is given. Firstly, general dynamical discrete-time FAS models with time-varying state delays and constant input delays are proposed. The FAS models are classified into affine ones and non-affine ones, and also ones with and without interconnections. Secondly, controllers for such FASs are designed, which result in constant linear closed-loop systems with arbitrarily assignable eigenstructure. Different from the case of FAS with state delays only, the controller for a discrete-time FAS with an input delay involves a prediction scheme which is constructed based on the open-loop system. The contribution of this paper has laid a fundamental basis for FAS approaches to discrete-time delay systems, and further specific analysis and design problems can be established similar to the continuous-time system case.
Journal Article
Fully actuated system approaches for continuous-time delay systems: part 1. Systems with state delays only
In this paper, the fully actuated system (FAS) approaches for continuous-time systems with time-varying state delays are proposed. Two types of continuous-time high-order FAS models with time delays: single-order time-delay FAS models and multi-order time-delay FASs, are proposed. Particularly, the type of sub-FASs that do not completely but partially satisfy the full actuation is investigated, and the sets of feasible points are defined. When the system states are constrained to the feasible set, a controller can be easily constructed for the sub-FAS such that the closed-loop system is a constant linear system with an arbitrarily assignable eigenstructure. In addition, it is demonstrated that the feasibility constraint can be transformed into a constraint on the initial values of the system, which vanishes when the system is a (global) FAS. Based on the unique control characteristic of the type of FAS models, the concepts of controllability and stabilizability of general dynamical time-delay systems are also proposed. The effect of the proposed theories is illustrated with examples.
Journal Article
Fully actuated system approaches for continuous-time delay systems: part 2. Systems with input delays
In this paper, the fully actuated system (FAS) approaches for continuous-time systems with time-varying state delays and a constant input delay are presented. Two types of continuous-time high-order FASs are proposed: single-order FASs with both state and input delays and multi-order FASs with both state and input delays. Controllers for both types of time-delay FASs are designed based on the full-actuation features of the systems. Unlike the case of FASs with state delays only, a prediction scheme is required and constructed for both types of FASs with input delays. Similar to the case of FASs with state delays only, constant linear closed-loop systems with arbitrarily assignable eigenstructures are also developed. Illustrative examples are provided to demonstrate the effect of the proposed theories.
Journal Article
Memory-based controller design for uncertain nonlinear time-delay system with input saturations
This paper explores the locally exponential stabilization problem for uncertain nonlinear time-delay system via the memory-based saturated controller. By utilizing the distributed-delay polytopic method, augmented Lyapunov–Krasovskii functional and improved integral inequalities, the delay-dependent criteria based on linear matrix inequalities is introduced to guarantee the locally exponential stability of nonlinear time-delay systems subject to actuator saturation. In addition, optimization tasks with reduced conservatism are formulated to enhance the admissible initial condition set. Subsequently, an illustrative instance is employed to demonstrate the validity and practicality of the suggested method.
Journal Article
Discrete-time delay systems: part 2. Sub-fully actuated case
In continuation to the first part of the paper, this second part further investigates the models and control of discrete-time sub-fully actuated systems with time-varying delays. Firstly, a new representation for general linear and nonlinear dynamical discrete-time fully actuated systems (FASs) with time-varying state delays and constant input delays is proposed, and the concept of sub-FAS is defined. The set of feasible points and the set of singular points for a sub-FAS are introduced. Secondly, like the global FAS case, controllers for a discrete-time sub-FAS can also be easily designed, which results in constant linear closed-loop systems with arbitrarily assignable eigenstructures, but unlike the global FAS case, a constraint must be added, which is expressed by the set of feasible points of the system and guarantees the realizability of the designed controllers. Finally, a general definition for controllable dynamical systems with time delays is given.
Journal Article
A FAS approach for stabilization of generalized chained forms: part 1. Discontinuous control laws
In this paper, a type of general nonholonomic systems is proposed, which contains both the Brockett’s two example systems, and their extended
n
-dimensional chained forms, as special cases. For the stabilization of such systems, a stabilizing controller is proposed based on the fully actuated system (FAS) approach, which is discontinuous at the origin but time-invariant when the open-loop system is time-invariant, and drives the feasible trajectories of the system to the origin exponentially. Furthermore, the proposed FAS approach is also extended to the sub-normal system case and the time-delay system case.
Journal Article
Stability analysis of systems with delay-dependent coefficients and commensurate delays
This paper develops a method of stability analysis of linear time-delay systems with commensurate delays and delay-dependent coefficients. The method is based on a D-decomposition formulation that consists of identifying the critical pairs of delay and frequency, and determining the corresponding crossing directions. The process of identifying the critical pairs consists of a magnitude condition and a phase condition. The magnitude condition utilizes the Orlando’s formula, and generates frequency curves within the delay interval of interest. Such frequency curves correspond to the delay-frequency pairs such that the decomposition equation has at least one solution on the unit circle. The delay interval of interest is divided into continuous frequency curve intervals (CFCIs). Under some nondegeneracy assumptions, the number of frequency curves remains constant within each CFCI, and the associated decomposition equation has one and only one solution on the unit circle at any point on a frequency curve. By traversing through the frequency curves, all the crossing points can be identified. The crossing direction is related to the sign of the lowest-order nonzero derivative of the phase angle with respect to the delay, which is a generalization of the existing literature even for the case with single delay. This conclusion allows one to determine the crossing direction by examining the phase angle vs delay diagram. An example is presented to illustrate how a stability analysis can be conducted if some nondegeneracy assumptions are violated.
Journal Article