Uncertain Sampled-data Systems Research Articles

On the reinforcement learning extended state observer for a class of uncertain sampled-data control systems

On the reinforcement learning extended state observer for a class of uncertain sampled-data control systems

Deterministic learning from neural control for a class of sampled-data nonlinear systems

This study investigates the deterministic learning and control issues for uncertain sampled-data nonlinear systems (SDNSs). The problem of how to acquire/learn knowledge from adaptive control for SDNSs with uncertain affine terms is studied. To be specific, an appropriate neural network-based (NNB) control strategy is first presented to ensure tracking performance. To further realize learning, the exponential stability (ES) of the integrated closed-loop system coupled with the estimation error of the NN weights is considered. As the uncertain affine term prevents learning from occurring, the integrated system is converted into a discrete linear time-varying (DLTV) perturbed system by employing the state conversion technique. Tracking convergence allows the persistent excitation condition (PEC) of the NNs to be established, which guarantees the ES of the integrated DLTV system. Thus, accurate modeling of closed-loop sampled dynamics is obtained. By reutilizing the experiential knowledge obtained, a knowledge-based controller is constructed for high-performance control. Finally, simulations are performed to verify the presented strategy.

Fault Detection for a Class of Uncertain Sampled-Data Systems Using Deterministic Learning.

In this article, we propose a learning-based fault diagnosis approach for a class of nonlinear sampled-data systems. First, the unmodeled sampled dynamics is acquired by the using deterministic learning method. The knowledge of the sampled dynamics of the normal and fault patterns is stored in the form of constant neural networks. Second, a fault detection scheme is designed in which memories of the learned knowledge can be recalled to give a rapid response to a fault. Third, analytical results concerning the fault detection condition and detection time are derived. It is shown that the mismatch function plays an important role in the performance properties of the diagnosis scheme. To analyze the effect of mismatch function on the residual, the concept of duty ratio is developed. Moreover, by comparing the constant neural networks of the normal and fault patterns, an extraction operator is designed to capture the feature of the mismatch function. By using this method, the performance of the diagnosis scheme can be improved. A simulation study is included to demonstrate the effectiveness of the approach.

Bounds for the remainders of uncertain matrix exponential and sampled-data control of polytopic linear systems

This paper determines an explicit upper bound to the norm of any given degree of the Taylor’s expansion remainder for the matrix exponential function. It depends on the spectral norm and the corresponding measure of a square matrix. The generalization to cope with uncertain polytopic matrices follows from the definition of a norm and a measure for this mathematical entity and the determination of the corresponding upper bound for the expansion remainder. Naturally, the results are applied to robust stability analysis and state feedback control synthesis of sampled-data polytopic systems. It is shown that a sampled-data uncertain system obtained from a continuous-time polytopic one can be expressed (through a nonconservative sufficient condition) by a feedback interconnection of a discrete-time polytopic system and a norm bounded linear operator. Academical examples illustrate the theoretical results.

Stability analysis of uncertain sampled-data systems with incremental delay using looped-functionals

The robust stability analysis of asynchronous and uncertain sampled-data systems with constant incremental input delay is addressed in the looped-functional framework. These functionals have been shown to be suitable for the analysis of impulsive systems as they allow one to express discrete-time stability conditions in an affine way, enabling then the consideration of uncertain and time-varying systems. The stability conditions are obtained by first reformulating the sampled-data system as an impulsive system, and by then considering a tailored looped-functional along with Wirtinger’s inequality, a recently introduced inequality that has been shown to be less conservative than Jensen’s inequality. Several examples are given for illustration.

Reliable Robust Sampled-Data H∞ Output Tracking Control with Application to Flight Control

This paper is concerned with the problem of robust H ∞ output tracking control for uncertain sampled-data systems with probabilistic actuator failures. By assuming that each actuator fault takes values randomly in a finite set, a new actuator-failure-mode is proposed. Lyapunov-Krasovskii functional combined with the input delay approach as well as the free-weighting matrix approach are employed to establish the H ∞ performance, and the controller design is cast into a convex optimization problem with linear matrix inequality (LMI) constraints. The designed reliable controller can guarantee that the output of the closed-loop sampled-data system tracks the reference signal without steady-state error. An airship model is considered in this paper and its simulation results are given. DOI: http://dx.doi.org/10.5755/j01.itc.43.2.4821

Convex conditions for robust stability analysis and stabilization of linear aperiodic impulsive and sampled-data systems under dwell-time constraints

Stability analysis and control of linear impulsive systems is addressed in a hybrid framework, through the use of continuous-time time-varying discontinuous Lyapunov functions. Necessary and sufficient conditions for stability of impulsive systems with periodic impulses are first provided in order to set up the main ideas. Extensions to the stability of aperiodic systems under minimum, maximum and ranged dwell-times are then derived. By exploiting further the particular structure of the stability conditions, the results are non-conservatively extended to quadratic stability analysis of linear uncertain impulsive systems. These stability criteria are, in turn, losslessly extended to stabilization using a particular, yet broad enough, class of state-feedback controllers, providing then a convex solution to the open problem of robust dwell-time stabilization of impulsive systems using hybrid stability criteria. Relying finally on the representability of sampled-data systems as impulsive systems, the problems of robust stability analysis and robust stabilization of periodic and aperiodic uncertain sampled-data systems are straightforwardly solved using the same ideas. Several examples are discussed in order to show the effectiveness and reduced complexity of the proposed approach.

Robust guaranteed cost control of uncertain fuzzy systems under time-varying sampling

In practice, the system is often modeled as a continuous-time fuzzy system, while the control input is applied only at discrete instants. This system is called a sampled-data control system. In this paper, robust guaranteed cost control for uncertain sampled-data fuzzy systems is discussed. A guaranteed cost control where a quadratic cost function is bounded by a certain scalar, not only stabilizes a system but also considers a control performance. A typical sampled-data control is the zero-order input, which can be represented as a piecewise-continuous delay. Here we take a delay system approach to the sampled-data guaranteed cost control problem. The closed-loop system with a sampled-data state feedback controller becomes a system with time-varying delay. First, guaranteed cost control performance conditions for the closed-loop system are given in terms of linear matrix inequalities (LMIs). Such conditions are derived by using Leibniz–Newton formula and free weighting matrix method for fuzzy systems under the assumption that sampling time is not greater than some prescribed scalar. Then, a design method of robust guaranteed cost state feedback controller for uncertain sampled-data fuzzy systems is proposed. Examples are given to illustrate our robust sampled-data guaranteed cost control design.

Robust backstepping for the Euler approximate model of sampled-data strict-feedback systems

Stabilization of uncertain sampled-data strict-feedback systems is addressed. The stability study is carried out on the Euler approximation of the exact discretized model of the plant. Firstly, a class of state-feedback controllers is developed that guarantees an input-to-state stability property for the closed-loop system. Additionally, assuming some hypotheses on the uncertain terms hold, a practical asymptotic stability property is ensured by designing an appropriate class of controllers.

Exponential stability of impulsive systems with application to uncertain sampled-data systems

We establish exponential stability of nonlinear time-varying impulsive systems by employing Lyapunov functions with discontinuity at the impulse times. Our stability conditions have the property that when specialized to linear impulsive systems, the stability tests can be formulated as Linear Matrix Inequalities (LMIs). Then we consider LTI uncertain sampled-data systems in which there are two sources of uncertainty: the values of the process parameters can be unknown while satisfying a polytopic condition and the sampling intervals can be uncertain and variable. We model such systems as linear impulsive systems and we apply our theorem to the analysis and state-feedback stabilization. We find a positive constant which determines an upper bound on the sampling intervals for which the stability of the closed loop is guaranteed. The control design LMIs also provide controller gains that can be used to stabilize the process. We also consider sampled-data systems with constant sampling intervals and provide results that are less conservative than the ones obtained for variable sampling intervals.

Robust nonlinear control of sampled-data systems

This paper investigates the control problem for a class of uncertain nonlinear sampled-data systems which are affine in the inputs. 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 control problem is solved in terms of both continuous and discrete Hamilton–Jacobi equations.

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.

Stochastic stability and robust control for sampled-data systems with Markovian jump parameters

In this paper, the problems of stochastic stability and robust control for a class of uncertain sampled-data systems are studied. The systems consist of random jumping parameters described by finite-state semi-Markov process. Sufficient conditions for stochastic stability or exponential mean square stability of the systems are presented. The conditions for the existence of a sampled-data feedback control and a multirate sampled-data optimal control for the continuous-time uncertain Markovian jump systems are also obtained. The design procedure for robust multirate sampled-data control is formulated as linear matrix inequalities (LMIs), which can be solved efficiently by available software toolboxes. Finally, a numerical example is given to demonstrate the feasibility and effectiveness of the proposed techniques.

Quantitative feedback synthesis of sampled-data systems with time-delay by approximate Z-transform

In this paper, the equivalent disturbance rejection (EDR) in QFT design methodology is proposed for dealing with sampled-data systems with time-delay. This EDR is mainly to overcome the non-minimum phase zero generated by the first order Pade' approximation of the time-delay factor. Due to plant parameter uncertainty, the analogue controller is to be designed so that the system response lies within permissible bounds. By approximate Z-transform, the analogue controller can be transformed directly into a digital one and then the analogue plant is transformed into the digital plant, with sampling time as a free parameter. By adjusting the sampling time, the uncertain sampled-data system can be stabilized. In comparison with other approaches, our design framework is much more systematic by using only algebraic manipulations and transparent enough to guide the designer to realize the physical controller for the plant with prescribed bounds on its parameters.

Digital modelling and robust digital redesign of sampled-data uncertain systems via the interval tuning bilinear approximation method

Based on the bilinear approximation method, we present an interval tuning bilinear approximation method to do the digital model conversion and digital redesign of sampled-data uncertain systems. The tuning bilinear method together with interval arithmetic operation is employed to obtain the approximate discrete-time model and the digital robust control law from the continuous-time uncertain state equation and the given continuous-time robust control law, respectively. The proposed digitally tuning redesigned control law with one parameter can be adjusted so that the resulting dynamic states of the digitally controlled sampled-data uncertain system are able to closely match those of the original continuous-time well-designed uncertain system for a relatively longer sampling period.

A genetic approach to hybrid control of sampled-data uncertain system with input time delay

This paper utilizes genetic algorithms (GAs) to convert a continuous-time uncertain system with input time delay to an equivalent discrete-time interval model. Also, the GAs are used to find the interval control law for a sampled-data uncertain system with input time delay. The developed discrete-time interval model match closely the exact discrete-time uncertain system with input time delay. Based on the principle of equivalent areas and GAs, a new implementable digital control law, taking into account the intersample behavior and implementation errors, is developed for digital control of the input time-delay continuous-time uncertain system so that the states of the digitally controlled sampled-data uncertain system optimally match those of the originally well-designed continuous-time uncertain system.

Design of sampled-data systems with large plant uncertainty using quantitative feedback theory

This paper proposes a new quantitative feedback theory (QFT) design framework for dealing with sampled-data systems with large plant uncertainty. After the QFT-based design in the continuous-time domain is completed, the analogue controller can be transformed directly into a rational discrete-time transfer function via approximate Z transform, with the sampling time as a free parameter. The sampling time can therefore be adjusted to make the uncertain sampled-data system robustly stable. In comparison with other approaches, our approach is much more systematic without the solvability problem and yet significant enough to guide the designer to realize the physical controller in which the plant transfer function has prescribed bounds on its parameters. Several examples are used to illustrate the proposed approach and excellent results are obtained.

On designing filters for uncertain sampled-data nonlinear systems

This paper is concerned with the problem of nonlinear H ∞ 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 H ∞ filtering problem is solved in terms of both continuous and discrete Hamilton–Jacobi equations.

OBSERVER-BASED HYBRID CONTROL OF SAMPLED-DATA UNCERTAIN SYSTEM WITH INPUT TIME DELAY

This paper proposes a new digital redesign method for determining the hybrid controller of a continuous-time system with input time delay using an observer-based digital controller. The proposed method together with the genetic algorithms is used to determine: (1) the interval digital model of a continuous-time uncertain system with input time delay, (2) the interval digital redesign control law and (3) the interval digital observer of the original continuous-time uncertain observer with input time delay. Moreover, the result is less conservative than those obtained by the existing interval methods. A discrete-time observer is built by the original continuous-time observer with input-time-delay control law and a predictor such that the estimated states of the redesigned discrete-time observer closely match those of the original continuous-time observer with input time delay not only at sampling instants but also the behavior of the system state during the sampling interval is optimal by minimizing the hybrid performance index. The digitally redesigned observer-based controller can closely match the states of the digitally redesigned uncertain sampled-data system with those of the original continuous-time observer-based controlled uncertain system with input time delay.

Model conversion of discrete-time uncertain systems via the interval geometric-series method

This paper presents a geometric-series approximation method using interval arithmetic operations to convert a discrete-time uncertain system to an equivalent continuous-time uncertain model. The system matrices characterizing the state-space representation of the original uncertain systems are assumed to be interval matrices. The logarithm matrix-valued functions with respective interval system matrices are approximated by appropriate rational interval matrix-valued functions using the geometric-series approximation method. Then, the desired enclosing analog interval approximant is obtained by adding an additional error interval matrix which accounts for the approximation error to the rational interval approximant. The model thus constructed is guaranteed to tightly enclose the precise original interval model. The proposed method can be employed to convert an identified discrete-time uncertain model of the original analog uncertain system, to an equivalent continuous-time uncertain model. Also, the proposed method can be utilized to convert a sampleddata uncertain system to an equivalent purely continuous-time uncertain model so that the well-developed analog robust control theories and design methods based on H 2 / H ∞ can be applied.