Control Of Discrete Nonlinear Systems Research Articles

Robust Control of Nonlinear Discrete Systems With Perturbations Based on Estimated State Feedback

Robust Control of Nonlinear Discrete Systems With Perturbations Based on Estimated State Feedback

A Discrete Integral Sliding Manifold for a Nonlinear System with Time Delay: An Event-Triggered Scheme

This paper presents a new approach to integral sliding mode control for discrete nonlinear systems with time delay. The approach is based on an event-triggered scheme and is applied to Takagi–Sugeno fuzzy models. In the first step, a new integral sliding function is constructed, which avoids the limited assumptions of most existing fuzzy sliding mode control schemes. The design parameter matrices defining the sliding surface are obtained by solving linear matrix inequalities. In the second step, an event trigger-based integral sliding mode control protocol is developed to ensure the state trajectories of the Takagi–Sugeno fuzzy systems with time delays. Finally, the proposed strategies are evaluated through a simulation example to demonstrate their effectiveness.

Symbolic Regulator Sets for a Weakly Nonlinear Discrete Control System with a Small Step

For a class of discrete weakly nonlinear state-dependent coefficient (SDC) control systems, a suboptimal synthesis is constructed over a finite interval with a large number of steps. A one-point matrix Padé approximation (PA) of the solution of the initial problem for the discrete matrix Riccati equation is constructed based on the state-dependent Riccati equation (SDRE) approach and the asymptotics by the small-step of the boundary layer functions method. The symmetric gain coefficients matrix for Padé control synthesis is constructed based on the one-point PA. As a result, the parametric closed-loop control is obtained. The results of numerical experiments illustrate, in particular, the improved extrapolation properties of the constructed regulator, which makes the algorithm applicable in control systems for a wider range of parameter variation.

Real‐time model‐free resilient control for discrete nonlinear systems

AbstractMotivated by the increasing complexity of systems to be controlled and different system components that cause uncertainties, threats, and disturbances, among other system stressing phenomena. Resilient control is an important design paradigm that has attracted attention from academics, practitioners, and the industrial sector. Therefore, this paper proposes the design of a model‐free resilient control for unknown discrete‐time nonlinear systems based on a recurrent high order neural network trained with an on‐line extended Kalman filter‐based algorithm for output trajectory tracking in the presence of uncertainties, disturbances, and unmodeled dynamics. This paper also includes the stability proof of the entire proposed scheme; its applicability is shown via simulation and experimental results including a comparative analysis of the proposed controller against well‐known controllers for a three‐phase induction motor.

Synergetic synthesis of aggregated discrete regulators for induction motors

The paper presents the method of synergetic synthesis of a nonlinear discrete control system for induction motors. The proposed approach is based on using the methods of the synergetic control theory and nonlinear mathematical models of induction motors. This approach allows to create nonlinear closed-loop piecewise-continuous control systems which guarantee the asymptotic stability of the controlled induction motors, accomplishment of the determined technological and electromagnetic invariants and selective invariance to the unknown external disturbances acting on the system. The invariance of the designed systems is ensured due to the usage of a dynamic discrete regulator which increases the astatism of the synthesized system.

Observer-based sliding mode control for discrete nonlinear systems with packet losses: an event-triggered method

In this paper, the observer-based output feedback sliding mode control (SMC) problem is investigated for discrete delayed nonlinear systems subject to packet losses under the event-triggered strategy. It is assumed that the packet losses may occur in the control channel from the sensor to the observer. A suitable compensation strategy via the Bernoulli distributed random variable is used to reduce the effects of packet losses. In order to avoid the phenomenon of network congestion during the networked transmission, an event-triggered mechanism is introduced to determine if the last released measurement needs to be updated. Based on the zero-order-hold (ZOH) measurement, an output feedback observer is designed to reconstruct the system state. This method can facilitate the design of the discrete-time sliding surface. A sufficient condition is proposed to guarantee the stochastic stability of sliding mode dynamics systems by using linear matrix inequality (LMI) method, and a novel observer-based sliding mode controller is synthesized to force the trajectories of the error systems onto the pre-designed sliding mode surface within finite time. Finally, an example is given to illustrate the validity of the proposed theoretical result.

Feedback passivity‐based control of discrete nonlinear systems with time‐delay for variable geometry truss manipulator

AbstractIn this paper, the feedback passivity‐based control of nonlinear discrete time‐delay systems for variable geometry truss manipulators is investigated. To determine an appropriate communication channel in the sense of feedback passivation, we first model the dynamics of the variable geometry truss manipulator as a generalized discrete nonlinear system with time‐delay. Then we further prove that when the infinite norm of estimated error is bounded, as long as there is a controller enables the closed‐loop system to be input‐strictly passive, there must be a deterministic equivalent controller to ensure that the system is stochastically quasi passive. After that, on the basis of the conclusion obtained, a more conclusive corollary is addressed for linear plants. Though passivity is a stricter condition than stability, feedback passivation does not impose more restrictions on estimate errors, and therefore does not require more communication channel information than mean square stability. Finally, we simplify the variable geometry truss dynamics to a linear plant to simulate to verify the validity of our method, and also compared the experimental results with the methods in the existing literature.

Fejér Polynomials and Control of Nonlinear Discrete Systems

We consider optimization problems associated with a delayed feedback control (DFC) mechanism for stabilizing cycles of one-dimensional discrete time systems. In particular, we consider a delayed feedback control for stabilizing T-cycles of a differentiable function $$f: \mathbb {R}\rightarrow \mathbb {R}$$ of the form $$\begin{aligned} x(k+1) = f(x(k)) + u(k), \end{aligned}$$where $$\begin{aligned} u(k) = (a_1 - 1)f(x(k)) + a_2 f(x(k-T)) + \cdots + a_N f(x(k-(N-1)T)), \end{aligned}$$with $$a_1 + \cdots + a_N = 1$$. Following an approach of Morgul, we associate with each periodic orbit of f, $$N \in \mathbb {N}$$, and $$a_1$$, ..., $$a_N$$ an explicit polynomial whose Schur stability corresponds to the stability of the DFC on that orbit. We prove that, given any 1- or 2-cycle of f, there exist N and $$a_1$$, $$\ldots $$, $$a_N$$ whose associated polynomial is Schur stable, and we find the minimal N that guarantees this stabilization. The techniques of proof will take advantage of extremal properties of the Fejer kernels found in classical harmonic analysis.

Robust Fuzzy Model Predictive Control of Discrete-Time Takagi–Sugeno Systems With Nonlinear Local Models

Robust fuzzy model predictive control of discrete nonlinear systems is investigated in this paper. A recently developed Takagi–Sugeno (T–S) fuzzy approach which uses nonlinear local models is adopted to approximate the nonlinear systems. A critical issue that restricts the practical application of classical model predictive control is the online computational cost. For model predictive control of T–S fuzzy systems, the online computational burden is even worse. Especially for complex systems with severe nonlinearities, parametric uncertainties, and disturbances, existing model predictive control of T–S fuzzy systems usually leads to a very conservative solution or even no solution in some occasions. However, more relaxed results can be achieved by the proposed fuzzy model predictive control approach which adopts T–S systems with nonlinear local models. Another advantage is that online computational cost of the optimization problem through solving matrix inequalities can be significantly reduced at the same time. Simulations on a numerical example and a two-tank system are presented to verify the effectiveness and advantages of the proposed method. Comparisons among several T–S fuzzy approaches are illustrated and show that the best settling time is achieved via the proposed method.

Generalization of nonlinear control for nonlinear discrete systems

Generalization of nonlinear control for nonlinear discrete systems

An online identification algorithm of unknown time-varying delay and internal multimodel control for discrete non-linear systems

ABSTRACTIn this paper, an online algorithm is proposed for the identification of unknown time-varying input delay in the case of discrete non-linear systems described by decoupled multimodel. This method relies on the minimization of a performance index based on the error between the real system and the partial internal models outputs. In addition, a decoupled internal multimodel control is proposed for the compensation of discrete non-linear systems with time-varying delay. This control scheme incorporates partial internal model controls. Each partial controller is associated to a specified operating zone of the non-linear system. The switching between these controllers is ensured by a supervisor that contains a set of local predictors. A simulation example is carried out to illustrate the significance of the proposed time-varying delay identification algorithm and the proposed internal multimodel control scheme.

Robust model predictive control of discrete nonlinear systems with time delays and disturbances via T–S fuzzy approach

In this paper, robust fuzzy model predictive control of a class of nonlinear discrete systems subjected to time delays and persistent disturbances is investigated. Based on the modeling method of delay difference inclusions, nonlinear discrete time-delay systems can be represented by T–S fuzzy systems comprised of piecewise linear delay difference equations. Moreover, Lyapunov–Razumikhin function (LRF), instead of Lyapunov–Krasovskii functional (LKF), is employed for time-delay systems due to its ability to reflect system original state space and its advantages in controller synthesis and computation. The robust positive invariance and input-to-state stability with respect to disturbance under such circumstances are investigated. A robust constraint set is adopted that the system state is converged to this set round the desired point. In addition, the controller synthesis conditions are derived by solving a set of matrix inequalities. Simulation results show that the proposed approach can be successfully applied to the well-known continuous stirred tank reactor (CSTR) systems subjected to time delay.

On the Robust Stabilization of One Class of Nonlinear Discrete Systems

We study the problem of robust linear stabilization of a family of nonlinear discrete control systems with uncertainties and nonlinearly dependent control. We establish sufficient conditions for the robust stabilization and synthesize linear regulators of state engaged in the robust stabilization. The obtained necessary conditions for the robust stabilization are close to sufficient.

Iterative Learning Control for discrete nonlinear systems with randomly iteration varying lengths

This note proposes ILC for discrete-time affine nonlinear systems with randomly iteration varying lengths. No prior information on the probability distribution of random iteration length is required prior for controller design. The conventional P-type update law is used with a modified tracking error because of randomly iteration varying lengths. A novel technical lemma is proposed for the strict convergence analysis in pointwise sense. An illustrative example verifies the theoretical results.

The null controllability of nonlinear discrete control systems with degeneracy

The null controllability of nonlinear discrete control systems with degeneracy

Регулирование нелинейных дискретных систем управления

Регулирование нелинейных дискретных систем управления

Robust Stabilization and Evaluation of the Performance Index of Nonlinear Discrete Control Systems

Robust Stabilization and Evaluation of the Performance Index of Nonlinear Discrete Control Systems

Convergence of PD-Type Iterative Learning Control of Nonlinear Discrete Systems and its Robustness

Abstract: For the control problem of nonlinear discrete systems, this paper describes the status of current research and analyzes the advantages and disadvantages of open-loop and closed-loop iterative learning controller. A class of nonlinear discrete systems will be extended to the general nonlinear discrete systems. To the general nonlinear discrete systems, a open-closed-loop PD-type iterative learning controller which based on current and last output error instead of last output error only is proposed. It makes use of information on system operation more fully and accurately. Besides, based on norm of λ and mathematical induction, its sufficient condition for convergence is given. In order to test its robustness, a simulation is done in the case of a persistent interference. Simulation results show that it is efficient.

Internal model control based on a novel least square support vector machines for MIMO nonlinear discrete systems

To improve the robustness of the traditional inverse system method, the internal model control based on a novel least square support vector machines (LS-SVM) is proposed. The novel LS-SVM considers general errors that include noises of input variables and output variables as empirical errors. The data of original MIMO discrete system is exploited to approximate its inverse model by the novel LS-SVM. By cascading the inverse model and the original system to constitute a decoupling pseudo-linear system, the internal model control strategy is carried out to the pseudo-linear system to realize the effective control. Simulation validates that the novel LS-SVM used in the inverse system identification is effective and shows that the internal model control of nonlinear discrete systems has better robustness of anti-interference and parameters varying than that of the open-loop system only based on inverse control.

Robust Stability and Synthesis of Nonlinear Discrete Control Systems under Uncertainty

With the use of Lyapunov functions chosen as the norm of state vector, we obtain the robust stability sufficient conditions for a wide class of nonlinear, and generally nonstationary, discrete-time control systems with the given set-valued parameter estimates. For a strictly monotone nonlinear function, validation of these conditions is equivalent to solution of a series of combinatorial problem in the state space.Synthesis of robustly stable control systems in a domain is performed on the basis of the obtained sufficient conditions of robust stability.