Sampled-data Control Systems Research Articles

A Fuzzy Lyapunov–Krasovskii Functional Approach to Sampled-Data Output-Feedback Stabilization of Polynomial Fuzzy Systems

This paper presents an output-feedback exponential stabilization condition of sampled-data polynomial fuzzy control systems under variable sampling rates. Compared with previous work, the proposed method is less conservative because of the newly developed time-dependent fuzzy Lyapunov–Krasovskii functional that is based on the conventional fuzzy Lyapunov function. Moreover, the controller is allowed to contain polynomial gain matrices, thereby improving the control performance and design flexibility. This is realized by assuming the difference between the continuous- and discrete-time state vectors as time-varying norm-bounded uncertainties, which are manipulated using a robust control technique. A new sufficient condition is introduced to cast the stability condition containing the integral term as the sum-of-square conditions. Finally, the effectiveness of the proposed method is validated by simulations.

A Sufficient Condition for Stability of Sampled–data Model Predictive Control using Adaptive Time–mesh Refinement

In this work, we address through model predictive control (MPC) a constrained nonlinear plant described by a continuous-time dynamical model, which naturally leads to a sampled-data control system. The numerical solution of the optimal control problems involved in MPC must utilize, eventually, some form of discretization. Nevertheless, there are several advantages in maintaining a continuous-time model until later stages. One advantage is that we can devise numerical procedures which, by exploiting additional freedom in selecting the discretization points, are more efficient when continuous-time models are used. Here, we discuss an extension to MPC of an Adaptive Mesh Refinement (AMR) algorithm, which has shown to be efficient in solving nonlinear optimal control problems. We derive a sufficient condition that guarantees that an MPC scheme using an adaptive time-mesh refinement algorithm preserves stability.

In Memoriam

In Memoriam

Periodic disturbance rejection to the Nyquist frequency and beyond

In this paper, we address periodic disturbance rejection for sampled-data control systems, where the frequency of the disturbance can be beyond the Nyquist frequency of the limited measured plant output sampling rate. The disturbance effect on steady-state response of the fictitious fast-rate plant output including intersample information is obtained using discrete-time Fourier series. A sufficient condition for disturbance rejection together with a sufficient and necessary condition for perfect disturbance elimination are provided by employing the steady-state response. A simple but effective controller design procedure combining H∞ loop shaping, Youla–Kucera parameterization, and gradient methods is provided to achieve the two conditions. The proposed approach is applied on vibration control beyond the Nyquist frequency in a commercial hard disk drive. The effectiveness of the proposed approach is verified by our simulation results showing disturbance rejection of 62% and perfect disturbance elimination, as well as by our experimental results showing disturbance rejection of 54%.

Event-triggered robust H∞ control for uncertain switched linear systems

ABSTRACTIn this paper, an event-triggering scheme is implemented in uncertain switched linear systems with time-varying delays and exogenous disturbance. Instead of standard periodically time-triggered, sampled-data control systems, the event-triggered control systems sample data only when an event, typically defined as some performance error exceeding a tolerant bound, occurs. Specifically, considering the disturbance existing in the system, the event-triggered robust H∞ control problem is studied. In order to guarantee the robust H∞ performance, the event-triggered full state feedback control, multiple Lyapunov functions method and state-dependent switching law are utilised to construct sufficient conditions in terms of linear matrix inequalities. In particular, since the event-triggered signals and switching signals may interlace with each other, the influence from them on the analysis of robust H∞ performance is clarified. Subsequently, sufficient design conditions of the sub-controllers’ gains are further presented. Moreover, the Zeno problem is discussed to exclude continuously triggering and sampling. Finally, numerical simulations are provided to verify the feasibility of the proposed approach.

Quantized/Saturated Control for Sampled-Data Systems Under Noisy Sampling Intervals: A Confluent Vandermonde Matrix Approach

In this paper, a unified framework is established to investigate both the quantized and the saturated control problems for a class of sampled-data systems under noisy sampling intervals. A random variable obeying the Erlang distribution is used to describe the noisy sampling intervals. In virtue of the matrix exponential, the sampled-data control system is transformed into an equivalent discrete-time stochastic system, and the aim of this paper is to design a quantized/saturated sampled-data controller such that the resulting discrete-time stochastic system is stochastically stable when the sampling error follows the Erlang distribution. In order to deal with the case of multiple control inputs, a confluent Vandermonde matrix approach is proposed in the design process. By using the Kronecker product operation and the matrix inequality techniques, the desired quantized/saturated controller gains are designed in terms of the solution to certain matrix inequalities. Finally, a simulation example is exploited to verify the effectiveness of the proposed design approach.

A characterization of integral input-to-state stability for hybrid systems

This paper addresses characterizations of integral input-to-state stability (iISS) for hybrid systems. In particular, we give a Lyapunov characterization of iISS unifying and generalizing the existing theory for pure continuous-time and pure discrete-time systems. Moreover, iISS is related to dissipativity and detectability notions. Robustness of iISS to sufficiently small perturbations is also investigated. As an application of our results, we provide a maximum allowable sampling period guaranteeing iISS for sampled-data control systems with an emulated controller.

Input‐delay approach to sampled‐data control of polynomial systems based on a sum‐of‐square analysis

In this study, the authors develop an H ∞ stabilisation condition for polynomial sampled-data control systems with respect to an external disturbance. Generally, continuous-time and sampled state variables are mixed in polynomial sampled-data control systems, which is the main drawback to numerically solving the stabilisation conditions of these control systems. To overcome this drawback, this study proposes novel stabilisation conditions that address the mixed-states problem by casting the mixed states as a time-varying uncertainty. The stabilisation conditions are derived from a newly proposed polynomial time-dependent Lyapunov–Krasovskii functional and are represented as a sum-of-squares, which can be solved using existing numerical solvers. Some additional slack variables are further introduced to relax the conservativeness of the authors' proposed approach. Finally, some simulation examples are provided to demonstrate the effectiveness of their approach.

Disturbance observer-based multirate control for rejecting periodic disturbances to the Nyquist frequency and beyond

Intersample behavior cannot be ignored when a sampled-data control system is subject to periodic disturbances beyond the Nyquist frequency. In this paper, a disturbance observer-based multirate control scheme is proposed to deal with such a periodic disturbance problem. First, using discrete-time Fourier series, the effect of the periodic disturbance on steady-state response of the plant output including intersample information is derived. Next, based on the steady-state output response, a sufficient condition is provided for minimization of the disturbance effect on the output. It turns out that solving the sufficient condition is a problem of quadratic optimization with several equality constraints. The proposed approach is applied on vibration control of mechanical resonant modes beyond the Nyquist frequency in a commercial hard disk drive. Perfect disturbance elimination and disturbance deduction of 72% in fast-rate discrete-time response are observed in the simulation and experiment, respectively.

Minimization of unobservable oscillation in repeatable run-out for magnetic-head positioning system of hard disk drives

A positioning control system for a magnetic head in hard disk drives (HDDs) is a sampled-data control system that has a sampler and a hold. As a result, the control system has unobservable oscillations in a repeatable run-out (RROs) whose frequencies are above the Nyquist frequency. These unobservable oscillations may lead to destruction of user data in HDDs. To solve this problem, this paper presents a minimization method for the unobservable oscillation in the RROs. This minimization method focuses on a relationship between RRO frequencies and a sampling frequency of the sampled-data control system. To estimate amounts of the unobservable RROs beyond the Nyquist frequency, this study employs two types of unobservable magnitudes: a maximum value based magnitude, and a root-mean-square value based magnitude. By using these unobservable magnitudes, we can choose the best suited sampling frequency to minimize the unobservable oscillations in RROs of HDDs.

An improved digital redesign for sampled-data fuzzy control systems: Fuzzy Lyapunov function approach

This paper proposes an improved digital redesign (DR) technique for sampled-data fuzzy controllers in nonlinear systems, based on a Takagi–Sugeno (T–S) fuzzy model. To improve the performance of the DR technique, two methodologies are used: a state-matching error cost function, and a continuous-time fuzzy Lyapunov function. Using these two methodologies, a novel DR technique is proposed to guarantee both the stability and state-matching conditions of the sampled-data fuzzy control system. Further, the proposed DR technique is represented as an optimal problem using the linear matrix inequality (LMI) format. Finally, some simulation examples are provided to verify the effectiveness of the proposed technique in comparison with previous techniques.

Output-feedback control for sampled-data systems with variable sampling rate

ABSTRACTIn this paper, we propose design method of controller for sampled-data systems with variable sampling rate. First, we give design method for both H2 and H∞ controller. For H2 control, performance of the system is introduced according to a standard sampled-data setting. A discrete-time H2 control problem is employed for solving the original problem. Its solvability condition is then established as a parameter-dependent linear matrix inequality. A probabilistic approach is taken for coping with the parameter-dependency. H∞ controller is designed by almost the same manner. Applying both results, we have design method for multi-objective control.

Robust stability bounds for multi-delay networked control systems

ABSTRACTIn this paper, the robust stability of a perturbed linear continuous-time system is examined when controlled using a sampled-data networked control system (NCS) framework. Three new robust stability bounds on the time-invariant perturbations to the original continuous-time plant matrix are presented guaranteeing stability for the corresponding discrete closed-loop augmented delay-free system (ADFS) with multiple time-varying sensor and actuator delays. The bounds are differentiated from previous work by accounting for the sampled-data nature of the NCS and for separate communication delays for each sensor and actuator, not a single delay. Therefore, this paper expands the knowledge base in multiple inputs multiple outputs (MIMO) sampled-data time delay systems. Bounds are presented for unstructured, semi-structured, and structured perturbations.

합성된 리아프노프 함수법을 통한 샘플링 된 데이터 제어 시스템의 향상된 안정화 조건 및 제어기 설계

This paper investigates improved stability and stabilization criteria for sampled-data control systems. By using a suitable and newly constructed augmented Lyapunov-Krasovskii functional and some recent mathematic techniques such as auxiliary function-based integral inequalities, sufficient conditions for stability and stabilization conditions are derived within the framework of linear matrix inequalities(LMI) form. The superiority and validity of the proposed results are illustrated by three numerical examples.

Improved criteria for sampled-data synchronization of chaotic Lur’e systems using two new approaches

In this paper, the problem of the sampled-data synchronization of two identical chaotic Lur’e systems is studied in which the controller is designed by using sampled output of the systems with variable sampling rates. Two novel approaches, sampling-instant-to-present-time fragmentation and free-matrix-based time-dependent discontinuous Lyapunov approach, are proposed for the first time. The first one makes us to utilize more information of inner sampling behavior and later one helps handling a hybrid feature of sampled-data control systems. Based on the presented two new approaches, novel synchronization conditions are developed in the form of linear matrix inequalities. The obtained conditions ensure the master–slave synchronization of chaotic Lur’e systems under larger sampling period than remarkable existing works which can be found by two numerical examples.

Sampled-data filtering of Takagi–Sugeno fuzzy neural networks with interval time-varying delays

This paper is concerned with sample-data filtering of T–S fuzzy neural networks with interval time-varying delays, which is formed by a fuzzy plant with time delay and a sampled-data fuzzy controller connected in a closed loop. A Takagi–Sugeno (T–S) fuzzy model is adopted for the neural networks and the sampled-data fuzzy controller is designed for a T–S fuzzy system. To develop the guaranteed cost control, a new stability condition of the closed-loop system is guaranteed in the continuous-time Lyapunov sense, and its sufficient conditions are formulated in terms of linear matrix inequalities. By using a descriptor representation, the sampled-data fuzzy control system with time delay can be reduced to ease the stability analysis, which effectively leads to a smaller number of LMI-stability conditions. Information of the membership functions of both the fuzzy plant model and fuzzy controller are considered, which allows arbitrary matrices to be introduced, to ease the satisfaction of the stability conditions. By a newly proposed inequality bounding technique, the fuzzy sampled-data filtering performance analysis is carried out such that the resultant neural networks is asymptotically stable. Numerical example and simulation result are given to illustrate the usefulness and effectiveness of the proposed theoretical results.

Formula omitted] and [formula omitted] control of time-varying delay switched linear systems with application to sampled-data control

This paper deals with switched linear systems subject to time-varying delay. The main goal is to design state and output feedback switching strategies preserving closed-loop stability and a guaranteed H2 or H∞ performance. The switching strategies are based on a generalization of a recent extended version of the small gain theorem and do not require any assumption on the continuity of the delay and its time-variation rate. The key point to obtain the design conditions is the adoption of an equivalent switched linear system where the time-varying delay is modeled as a norm-bounded perturbation. Moreover, with this approach, it is possible to deal with sampled-data control systems. All conditions are formulated in terms of Lyapunov–Metzler inequalities, which allow the maximization of an upper bound on the time-delay preserving stability and guaranteed performance. Numerical examples are discussed in order to illustrate the effectiveness of the design approach.

Optimizing a sampled-data submarine motion control system over a set of reduced order controllers

The paper proposes a method for optimizing sampled-data systems over a set of reduced order controllers. The method is based on the concept of parametric transfer function and finding a subset of solutions for polynomial Diophantine equation with the order not exceeding the preset number. The method is applied to optimization of H2-norm of sampled-data submarine motion control system.

Decentralized $$\mathscr{H}_{\infty }$$ H ∞ Sampled-Data Control for Continuous-Time Large-Scale Networked Nonlinear Systems

The decentralized \({\mathscr{H}}_{\infty }\) sampled-data control problem is investigated for a class of continuous-time large-scale networked nonlinear systems with interconnection. Each nonlinear subsystem in the considered large-scale system is represented by a Takagi–Sugeno model and is closed by a communication channel with transformed time delay. Our objective is to design a decentralized sampled-data fuzzy controller such that the resulting fuzzy control system is asymptotically stable with an \({\mathscr{H}}_{\infty }\) performance. Firstly, using an input delay approach, the sampled-data control system is formulated into the system with time-varying delay, and a two-term approximation method is proposed such that the delayed system is reformulated into an interconnected framework with input and output. Then, we introduce a Lyapunov–Krasovskii functional that all Lyapunov matrices are no longer required to be positive definite. Combined with the scaled small gain theorem, the less conservative solutions to the decentralized \({\mathscr{H}}_{\infty }\) sampled-data control problem for the considered system are derived in the form of linear matrix inequalities. Finally, the effectiveness of the proposed methods is illustrated by two numerical examples.

Stability analysis and stabilization of aperiodic sampled-data systems based on a switched system approach

This paper investigates the stability analysis and controller design problems for aperiodic sampled-data control systems. The time-varying sampling period is assumed to take only a finite number of values, and the considered system is modeled as a discrete-time switched system with both stable and unstable subsystems. A sufficient condition is derived for the system to be exponentially stable, and a state feedback stabilizing controller is designed such that the system is exponentially stable and achieves an optimal guaranteed cost performance. The obtained exponential decay rate and guaranteed cost performance level critically depend on both the lengths and activation frequencies of the varying sampling periods, and it is revealed that nonuniformly sampled control systems can remain to be stable even in the appearance of a very large sampling period, provided that the activation frequency of the large sampling period is small enough. Finally, an illustrative example is given to show the effectiveness of the proposed approach.