Global sampled-data output feedback control for a class of feedforward nonlinear systems

This paper investigates the problem of global output feedback stabilization for a class of feedforward nonlinear systems via linear sampled-data control. To solve the problem, we first construct a linear sampled-data observer and controller. Then, a scaling gain is introduced into the proposed observer and controller. Finally, we use the sampled-data output feedback domination approach to find the explicit formula for choosing the scaling gain and the sampling period which renders the closed-loop system globally asymptotically stable. A simulation example is given to demonstrate the effectiveness of the proposed design procedure.     

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

In 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.     

Output-feedback stabilization of a class of uncertain non-minimum-phase nonlinear systems

The problem of global output-feedback stabilization for a class of nonlinear systems whose zero dynamics are not necessarily stable is addressed in this paper. It is shown that, using a novel observer design tool together with standard backstepping and small-gain techniques, it is possible to design a stabilizing output feedback controller which ensures robustness with respect to dynamic uncertainties. The proposed stabilization method generalizes existing tools in several directions. As an example, the method is applied to the stabilization of the benchmark translational oscillator/rotational actuator (TORA) using only measurements of the rotational position.     

Lyapunov-based continuous-time nonlinear controller redesign for sampled-data implementation

Given a continuous-time controller and a Lyapunov function that shows global asymptotic stability for the closed-loop system, we provide several results for modification of the controller for sampled-data implementation. The main idea behind this approach is to use a particular structure for the redesigned controller and the main technical result is to show that the Fliess series expansions (in the sampling period T) of the Lyapunov difference for the sampled-data system with the redesigned controller have a very special form that is useful for controller redesign. We present results on controller redesign that achieve two different goals. The first goal is making the lower-order terms (in T) in the series expansion of the Lyapunov difference with the redesigned controller more negative. These control laws are very similar to those obtained from Lyapunov-based redesign of continuous-time systems for robustification of control laws and they often lead to corrections of the well-known “-L_gV” form. The second goal is making the lower-order terms (in T) in the Fliess expansions of the Lyapunov difference for the sampled-data system with the redesigned controller behave as close as possible to the lower-order terms of the Lyapunov difference along solutions of the “ideal” sampled response of the continuous-time system with the original controller. In this case, the controller correction is very different from the first case and it contains appropriate “prediction” terms. The method is very flexible and one may try to achieve other objectives not addressed in this paper or derive similar results under different conditions. Simulation studies verify that redesigned controllers perform better (in an appropriate sense) than the unmodified ones when they are digitally implemented with sufficiently small sampling period T.     

On designing filters for uncertain sampled-data nonlinear systems

This paper is concerned with the problem of nonlinear filtering for sampled-data systems with nonlinear time-varying parameter uncertainty. The aim is to design a digital filter such that the ratio between the energy of the estimation errors and the energy of the exogenous inputs is minimised or guaranteed to be less or equal to a prescribed value for all admissible uncertainties. A nonlinear bounded real lemma for sampled-data systems with nonlinear time-varying parameter uncertainty is provided. Based on this nonlinear bounded real lemma, the robust filtering problem is solved in terms of both continuous and discrete Hamilton–Jacobi equations.     

A discontinuous output feedback controller and velocity observer for nonlinear mechanical systems

In this paper, we develop a new discontinuous output feedback tracking controller for a class of uncertain, nonlinear, multi-input/multi-output, mechanical systems whose dynamics are first-order differentiable. A novel filter design and Lyapunov-type stability analysis are used to prove semi-global asymptotic tracking. As a by-product of the proposed framework, we also present the design of a new simple, discontinuous velocity observer that ensures global asymptotic velocity observation.     

Global sampled-data output feedback stabilisation for a class of nonlinear systems with unknown output function

This paper discusses the problem of global sampled-data output feedback stabilisation for a class of nonlinear systems whose output function is unknown. A systematic design scheme is developed to construct a linear output feedback control law in sampled-data form. An explicit formula for the maximum allowable sampling period is computed to guarantee global stability of the uncertain nonlinear systems under the proposed controller with appropriate gains. Two examples are given to demonstrate the effectiveness of the proposed design procedure.     

非线性不确定系统的直接自适应输出反馈模糊控制

针对一类单输入单输出非线性不确定系统，基于状态观测器并结合自适应模糊系统和滑模控制，提出一种稳定的直接自适应模糊输出反馈控制算法。该算法不需要系统状态可测的条件，并能保证闭环系统稳定。仿真结果表明了该方法的有效性。     

Cooperative output synchronisation of networked feedforward nonlinear systems via linear sampled-data control

This paper studies the problem of cooperative output synchronisation of networked feedforward nonlinear systems via linear sampled-data control. To dominate the unknown nonlinear perturbing terms, a scaling gain is introduced by a change in coordinates. Then, we construct a reduced-order sampled-data observer and use the backstepping method to design a linear sampled-data controller. By using combined graph theory with feedback domination approach, an explicit formula for the sampling period can be obtained under the proposed controller with appropriate gains such that all outputs of the agents in the network can be synchronised. Finally, two examples are provided to verify the effectiveness of the proposed method.     

Conic sectors for sampled-data feedback systems

A multivariable analog system can be controlled by a sampled-data compensator. A conic sector that can be used to analyze the closed-loop stability and robustness of this feedback system is presented in this letter.     

On the Lyapunov-based adaptive control redesign for a class of nonlinear sampled-data systems

Stabilization of the exact discrete-time models of a class of nonlinear sampled-data systems, with an unknown parameter, is addressed. Given a Lyapunov-based continuous-time adaptive controller that ensures some stability properties for the closed-loop system, a sufficient condition for the design of high order discrete-time controllers is given. The stability analysis is carried out considering the truncated Fliess series of the Lyapunov difference equation. Due to the appearance of power terms of the unknown parameter, the problem is reparameterized in a convex-like form and an estimation law for the new unknown parameter is derived with no need of overparametrization or projection techniques. Then, assuming appropriate conditions hold, high order controllers can be designed. The boundedness of the extended state vector is ensured under some conditions, for a sufficiently small sampling period. It is shown how increasing the controller order can improve system performance.     

Disturbance-observer-based sampled-data adaptive output feedback control for a class of uncertain nonlinear systems

In this paper, a sampled-data adaptive output feedback controller is proposed for a class of uncertain nonlinear systems with unmeasured states, unknown dynamics and unknown time-varying external disturbances. To approximate uncertain nonlinear functions, radial basis function neural networks (RBFNNs) are employed. The state observer and the disturbance observer (DO) are constructed to estimate the unmeasured state and the external disturbance, respectively. Then, the sampled-data adaptive output feedback controller and adaptive laws are designed by using the backstepping design technique. The allowable sampling period T is derived to guarantee that all states of the resulting closed-loop system are semi-globally uniformly ultimately bounded. Finally, two simulation examples are presented to illustrate the effectiveness of the proposed approach.     

Control of sampled-data systems with variable sampling rate

This paper addresses stability and performance of sampled-data systems with variable sampling rate, where the change between sampling rates is decided by a scheduler. A motivational example is presented, where a stable continuous time system is controlled with two sampling rates. It is shown that the resulting system could be unstable when the sampling changes between these two rates, although each individual closed-loop system is stable under the designed controller that minimizes the same continuous loss function. Two solutions are presented in this paper. The first solution is to impose restrictions on switching sequences such that only stable sequences are chosen. The second solution presented is more general, where a piecewise constant state feedback control law is designed which guarantees stability for all possible variations of sampling rate. Furthermore, the performance defined by a continuous time quadratic cost function for the sampled-data system with variable sampling rate can be optimized using the proposed synthesis method.     

New conic sectors for sampled-data feedback systems

New conic sectors are presented which can be used to analyze sampled-data feedback systems. First, a cone is constructed which contains just the sampler. Next, by using conic sector results for interconnected systems, the cone is propagated to the entire sampled-data operator. The new cone result is less conservative (has a smaller radius) and removes the restriction of an open-loop stable sampled-data compensator.     

A multirate controller design of linear periodic time delay systems

This paper presents a multirate controller design for a linear periodic system with multiple delays at input and output. The approach first converts the periodic time-delay system into a periodic delay-free system, and then stabilizes and optimizes it by a multirate controller with pulse compensation. A significant advantage of this approach is that by using multirate sampling, the controller can provide more substantial design freedoms, so that although the system does not provide complete state information, it remains possible to convert the controller design into the dual of a regular complete state feedback problem. This enables one to derive a simple algorithm for choosing the optimal parameters of the controller and, by use of the optimal pulse compensation, to improve the transient response.     

Robust sampled-data control for Markovian jump linear systems

In this paper, we consider the problem of robust control for uncertain sampled-data systems that possess random jumping parameters which is described by a finite-state Markov process. The conditions for the existence of a stabilizing control and optimal control for the underlying systems are obtained. The desired controllers are designed which are in terms of matrix inequalities. Finally, a numerical example is given to show the potential of the proposed techniques.     

TS-based sampled-data model predictive controller for continuous-time nonlinear systems

This paper proposes a new fuzzy model predictive control approach for continuous-time nonlinear systems in terms of linear matrix inequalities (LMIs). The proposed approach is based on the Takagi–Sugeno fuzzy modeling, a quadratic Lyapunov function, and a sampled-data parallel distributed compensation controller with constant sampling time. The goal is designing the sampled-data controller such that at each sampling time, the stability of the closed-loop system is guaranteed and an infinite horizon cost function is minimised. The main advantage of the proposed approach is to eliminate the approximations induced from discretizing the original system and cost function upper bound minimisation. Consequently, a lower bound of the cost function is obtained and the performance of the proposed model predictive controller is improved compared to the recently published papers in the same field of interest. In addition, the Euclidean norm constraint of the control input vector is derived in terms of LMIs. To illustrate the merits of the proposed approach, the proposed technique is applied to a continuous stirred tank reactor system.     

Stability connection between sampled-data fuzzy control systems with quantization and their approximate discrete-time model

This paper concerns the stability of a sampled-data Takagi-Sugeno (T-S) fuzzy control system with quantization, when a controller design is based on an approximate discrete-time model of the plant without quantization. The motivations come from the facts that digital devices for interfacing a plant with a controller quantize signals and an exact discrete-time model of the T-S fuzzy system is generally not amenable to synthesis process. We show that the concerned system is Lagrange stabilizable by the controller asymptotically stabilizing the approximate discrete-time model. A constructive design algorithm for the developed stability analysis is proposed in terms of linear matrix inequalities.     

Input-to-state stabilization for nonlinear dual-rate sampled-data systems via approximate discrete-time model

The problem of state feedback stabilization of nonlinear sampled-data systems is considered under the “low measurement rate” constraint. A dual-rate control scheme is proposed that utilizes a numerical integration scheme to approximately predict the current state. Given an approximate discrete-time model of a sampled nonlinear plant and given a family of controllers that stabilizes the plant model in input-to-state sense, we show that under some standard assumptions the closed loop dual-rate sampled data system is input-to-state stable in the semiglobal practical sense.