Uncertain Discrete-time Systems Research Articles

Robust multiobserver design for discrete uncertain nonlinear systems with time-varying delay

In this paper, a robust multiobserver is proposed for the state estimation of discrete-time uncertain nonlinear systems with time-varying delay. The designed multiobserver is based on the decoupled multimodel approach. Unlike the classically used multimodel structures, the decoupled multimodel provides a flexibility of modelling. Indeed, the partial models’ structures can be adapted to the complexity of the system in each operating regime, thus the partial models can be with different dimensions. Delay-dependent sufficient conditions for the synthesis of a robust multiobserver against norm-bounded parametric uncertainties and in the presence of measurement noise are established in terms of linear matrix inequalities. A simulation example is given to illustrate the effectiveness of the designed multiobserver.

Robust non-minimal order filter and smoother design for discrete-time uncertain systems

Robust non-minimal order filter and smoother design for discrete-time uncertain systems

Guaranteed Cost Control of Uncertain Discrete Time Systems Subjected to Actuator Saturation via Homogenous Polynomial Lyapunov Function

Estimation of an optimal controller is a fundamental problem in control engineering and is widely known as Optimization. Numerous computation and numerical techniques have been evolved during the past years for the estimation of the optimal solution. Optimal control of a discrete-time system is concerned with optimizing a given objective function using “Homogenous Polynomial Lyapunov Function (HPLF)”. This research focuses upon the design of optimal guaranteed cost controller (GCC) for discrete-time uncertain system using HPLF. The uncertainties are assumed to be norm bounded uncertainties. The effect of actuator saturation is also incorporated in the system. Sufficient conditions for the existence of HPLF are derived in term of Linear Matrix Inequalities (LMI). The LMI approach has the advantage that it can be solved efficiently using Convex Optimization. LMI’s combined with HPLF helps to design the guaranteed cost controller which minimizes the cost by minimizing cost function. Furthermore, the state trajectories and the invariant set is also shown to observe the overall performance.

Robust Stability Analysis and Synthesis for Uncertain Discrete-Time Networked Control Systems Over Fading Channels

This technical note investigates uncertain discrete-time networked control systems over fading channels. It is assumed that the plant is affected by polytopic uncertainty and is connected to the controller in closed-loop via fading channels which are modeled by multiplicative noise processes. Three contributions are proposed as follows. First, it is shown that robust stability in the mean square sense of the uncertain closed-loop networked control system is equivalent to the existence of a Lyapunov function in a certain class. Second, it is shown that the existence of a Lyapunov function in such a class is equivalent to the feasibility of a set of linear matrix inequalities (LMIs). Third, it is shown that the proposed condition can be exploited for the synthesis of robust controllers ensuring robust stability in the mean square sense of the uncertain closed-loop networked control system.

On LMI-based sliding mode control for uncertain discrete-time systems

In this paper, a new approach to design a robust discrete-time sliding mode control (DSMC) is proposed for uncertain discrete-time systems. To this end, an LMI approach is used to develop a new framework to design the sliding function which is linear to the state. Our proposed robust DSMC can be applied to unstable systems, and also there is no need to stabilize the underlying system first. It has been argued in the literature that for the systems involving balanced external disturbances, using switching component is not needed. In this paper, it is shown that with the assumption of smoothness of the external disturbances, a different form of switching element in the controller can outperform the so-called linear controller in terms of the thickness of the boundary layer around the sliding function and the ultimate bound on the system state. Also, this paper extends the idea of disturbance estimation to the uncertain discrete-time systems. The disturbance estimator is exploited in the controller design and the boundedness of the obtained closed-loop system is analyzed. Also, two novel forms of variable structure DSMC are suggested in this paper.

A novel two-stage strategy for robust H∞ filter design of uncertain discrete-time systems

This paper studies the robust H∞ filter design problem for discrete-time linear system with polytopic uncertainty. Differing from existing ideas in the literature to reduce filtering conservatism, the present article proposes a less conservative two-stage algorithm to handle this issue by stepwisely recovering and utilizing matrix variable information of analysis condition. This algorithm is formulated by virtue of the combined matrix inequality with a prefixed binary choice signal, which is composed of direct design condition with nonlinear matrix variable inequality and its corresponding linearized one. In general, a more relaxed matrix variable structure is derived based on improved scalar parameter approach from the perspective of eigenvalue theory, which is then applied to obtain less conservative filter design condition with linearized matrix variable inequality in the first stage of provided algorithm. With some solved variables in stage one, that nonlinear matrix variable inequality based design condition is transformed into linear version, and in the second stage it will be used to further optimize the filtering performance level via picking up the lost matrix variable information of stage one. Finally, the advantages of the given algorithm are clearly illustrated by two examples.

Robust [formula omitted] filter design with past output measurements for uncertain discrete-time systems

This paper is concerned with the design of robust filters for uncertain discrete-time linear systems. The uncertainty is assumed to be time-invariant belonging to a polytope. An upper bound to the H∞ norm of the transfer-function from the system input to the filtering error is used as performance criterion. The novelty is that the resulting robust filter has order greater than the order of the system being filtered by incorporating past output measurements. The design conditions are expressed in terms of convex problems constrained by Linear Matrix Inequalities. Performance is assessed through parameter-dependent Lyapunov functions. The results generalize existing robust filtering procedures without bringing in any additional conservatism. Simple numerical examples illustrate the procedure.

Indefinite LQ optimal control with equality constraint for discrete-time uncertain systems

Based on uncertainty theory, this paper studies a kind of discrete-time uncertain linear quadratic (LQ) optimal control with equality constraint for the terminal state, allowing the state and control weighting matrices in the cost function to be indefinite. First, we transform the uncertain LQ optimal control problem into an equivalent deterministic optimal control problem. Then, a necessary condition for the existence of optimal linear state feedback control is presented by means of matrix minimum principle. Moreover, the well-posedness of the uncertain LQ problem is proved by applying the technique of completing squares. Finally, an example is provided to demonstrate the effectiveness of our theoretical results.

Design of adaptive fuzzy backstepping sliding mode control for MIMO uncertain discrete-time nonlinear systems based on noisy measurements

This paper presents an adaptive fuzzy backstepping sliding mode control for multi-input and multi-output uncertain nonlinear systems in semi-strict feedback form. The systems are described by a discrete-time state equation with uncertainties viewed as the modeling errors and the unknown external disturbances, and the observation of the states is taken with independent measurement noises. Combining the adaptive fuzzy backstepping control with the sliding mode control approach for the comprehensive improvement in the stability and the robustness, the adaptive fuzzy backstepping sliding mode control is approximately designed where the design parameters are selected using an appropriate Lyapunov function. The uncertainities are approximated as fuzzy logic systems using the fuzzy inference approach based on the extended single input rule modules to reduce the number of the fuzzy IF-THEN rules. The estimates for the un-measurable states and the adjustable parameters are taken by the proposed simplified weighted least squares estimator. It is proved that the trajectory of the tracking error and the sliding surface is uniformly ultimately bounded. The effectiveness of the proposed approach is indicated through the simulation experiment of a simple numerical system.

Neural estimation using a stable discrete-time MLP observer for a class of discrete-time uncertain MIMO nonlinear systems

This paper has proposed a novel class of the stable discrete-time multilayer perceptron (MLP) neural observer for a class of discrete-time multiple-input multiple-output uncertain nonlinear systems. It is trained online and is used to estimate the states of the system especially when there is no prior knowledge about the dynamics of the system and can be applied as a basis for designing an intelligent control. The weight updating for the MLP is the developed backpropagation algorithm. Online training, convergence of the observer error to neighborhood of origin, robustness against uncertainties and disturbance, low computational expense and fast convergence rate are the main qualities of the suggested method. Lyapunov’s direct method is used to guarantee the stability of the proposed system. To demonstrate the performance of the discrete-time MLP observer, two discrete-time nonlinear dynamic systems are simulated in MATLAB/Simulink. Simulation results confirm the proficiency of the system even at different operating conditions and the presence of disturbance and measurement noise.

FCPN Approach for Uncertain Nonlinear Dynamical System with Unknown Disturbance

In this work, we have used a fuzzy counter-propagation network (FCPN) model to control different discrete-time, uncertain nonlinear dynamic systems with unknown disturbances. Fuzzy competitive learning (FCL) is used to process the weight connection and make adjustments between the instar and the outstar of the network. FCL paradigm adopts the principle of learning, used for calculation of the Best Matched Node (BMN) in the instar–outstar network. FCL provides a control of discrete-time uncertain nonlinear dynamic systems having dead zone and backlash. The errors like mean absolute error (MAE), mean square error (MSE), and best fit rate, etc. of FCPN are compared with networks like dynamic network (DN) and back propagation network (BPN). The FCL foretells that the proposed FCPN method gives better results than DN and BPN. The success and enactments of the proposed FCPN are validated through simulations on different discrete-time uncertain nonlinear dynamic systems and Mackey–Glass univariate time series data with unknown disturbances over BPN and DN.

Guaranteed cost control of discrete-time uncertain systems with both state and input delays

ABSTRACTThe paper proposes a guaranteed cost feedback control for discrete-time uncertain systems with both state and input delays. The delays are assumed to be time-varying and bounded. In addition to norm-bounded parametric uncertainties, the class of admissible uncertainties and nonlinearities of the system comprehend several types of uncertainties frequently investigated in the literature. Using some recent developments, new sufficient conditions for the existence of the guaranteed cost control are given by bilinear matrix inequalities. Numerical examples illustrate the effectiveness of the proposed method.

A modified robust self-tuning controller for Hammerstein nonlinear systems with asymmetric deadzone input nonlinearity

This article presents a novel adaptive control method for a class of uncertain discrete-time Hammerstein nonlinear systems with asymmetric deadzone input nonlinearity and bounded external disturbance. Based on the parameterization model of Hammerstein systems, the unknown parameters are updated by a robust recursive least squares algorithm with a deadzone weighted factor. Then, by introducing an estimate of the unmodeled dynamics as a feedback, the deadzone compensating control law is derived without an adaptive deadzone inverse. Theoretical results show that all the signals in the closed-loop system are bounded and the output tracking error is convergent with a relatively small residue. To show the usefulness of the developed results, simulation examples including an electro-hydraulic servo system and a DC motor subjected to a nonlinear friction are studied.

Robust Stability and $$H_{\infty }$$ H ∞ Control of Discrete-Time Uncertain Impulsive Systems with Time-Varying Delay

This paper considers the robust stability and $$H_{\infty }$$Hź control problems for a class of discrete-time uncertain impulsive systems with time-varying delay. Sufficient conditions for the robu...

An Extended Zonotopic and Gaussian Kalman Filter (EZGKF) merging set-membership and stochastic paradigms: Toward non-linear filtering and fault detection

A framework merging the set-membership and the stochastic paradigms is formalized and used to design an Extended Zonotopic and Gaussian Kalman Filter (EZGKF) dealing with the robust state estimation and the fault detection of uncertain discrete-time nonlinear systems. The so-called Set-membership and Gaussian Mergers (SGM) are introduced and particularized to Zonotopes (ZGM). They provide a constructive and computationally efficient solution to propagate random uncertainties with incompletely specified probability distributions combining set-based support enclosures and upper covariance matrix bounds formalized as matrix inequalities. Based on a full time-varying LPV enclosure featuring structured state matrix uncertainties, and given some confidence level expressed in probabilistic terms (maximal false alarm rate), a detection test is developed and shown to merge the usually mutually exclusive benefits granted by set-membership techniques (robustness to the worst-case within specified bounds, domain computations) and stochastic approaches (taking noise distribution into account, probabilistic evaluation of tests). A numerical example illustrates the state estimation capabilities of EZGKF and the improved tradeoff between the sensitivity to faults and the robustness to disturbances/noises.

Nonfragile Robust Model Predictive Control for Uncertain Constrained Systems with Time-Delay Compensation

This study investigates the problem of asymptotic stabilization for a class of discrete-time linear uncertain time-delayed systems with input constraints. Parametric uncertainty is assumed to be structured, and delay is assumed to be known. In Lyapunov stability theory framework, two synthesis schemes of designing nonfragile robust model predictive control (RMPC) with time-delay compensation are put forward, where the additive and the multiplicative gain perturbations are, respectively, considered. First, by designing appropriate Lyapunov-Krasovskii (L-K) functions, the robust performance index is defined as optimization problems that minimize upper bounds of infinite horizon cost function. Then, to guarantee closed-loop stability, the sufficient conditions for the existence of desired nonfragile RMPC are obtained in terms of linear matrix inequalities (LMIs). Finally, two numerical examples are provided to illustrate the effectiveness of the proposed approaches.

A Novel Fuzzy Sliding-Mode Control for Discrete-Time Uncertain System

This paper considers the sliding-mode control problem for discrete-time uncertain systems. It begins by presenting a discrete variable speed reaching law and a discrete-time sliding-mode controller (DSMC) designed using the proposed reaching law, followed by an analysis of their stability and dynamic performance. A sliding-mode controller with simple fuzzy logic is then proposed to further strengthen the dynamic performance of the proposed sliding-mode controller. Finally, the presented DSMC and the DSMC with fuzzy control for adjusting the parameters in this paper are compared with one of the previous proposed classic DSMC systems. The results of this simulation show that the DSMC presented here can suppress chatter and ensure good dynamic performances when fuzzy logic is used to tune the parameters.

Robust quantized H∞ filtering for discrete-time uncertain systems with packet dropouts

This paper considers the problem of H∞ filtering for uncertain discrete-time systems with quantized measurements and packet dropouts. The time-invariant uncertain parameters are supposed to reside in a polytope. The system measurement outputs are quantized by a memoryless logarithmic quantizer before being transmitted to the filter and the performance of packet dropouts is described by Bernoulli random binary distribution. Attention is focused on the design of H∞ filter to mitigate the effects of quantization and packet dropouts, which ensured not only stochastically stability but also a prescribed H∞ noise attenuation level. Via parameter-dependent Lyapunov function approach and introducing some slack variables, sufficient conditions for the existence of an H∞ filter are expressed in terms of linear matrix inequalities (LMIs). Two examples are provided to demonstrate the effectiveness and applicability of the proposed method.

Robust admissibility and admissibilisation of uncertain discrete singular time-delay systems

abstractThis paper is concerned with the characterisation of robust admissibility and admissibilisation for uncertain discrete-time singular system with interval time-varying delay. Considering the norm-bounded uncertainty and the interval time-varying delay, a new comparison model is introduced to transform the original singular system into two connected subsystems. After this transformation, a singular system without uncertainty and delay can be handled by the Lyapunov–Krasovskii functional method. By virtue of the scaled small gain theorem, an admissibility condition of the original singular system is proposed in terms of linear matrix inequalities. Moreover, the problem of robust admissibilisation of uncertain discrete singular time-varying system is also studied by iterative linear matrix inequality algorithm with initial condition optimisation. Several numerical examples are used to illustrate that the results are less conservative than existing ones.

Mean Square Stability Based on H∞ Control for Uncertain Networked Control Systems with Random Data Loss

This paper studies the design of uncertain linear discrete-time Networked Control Systems over imperfect communication channels with time-varying data loss. This leakage is modeled as stochastic parameter and norm-bounded uncertainties. In addition, this paper defines the necessary conditions for the design of the dynamic output feedback controller; subsequently, an iterative LMI approach is specified to compute the controller state parameters. The simulation results show that the designed controller improves the H∞ disturbance attenuation performance of the concerned uncertain system.