Polytopic Uncertainties Research Articles

Robust PD-type iterative learning control for discrete systems with multiple time-delays subjected to polytopic uncertainty and restricted frequency-domain

This paper proposes the PD-type iterative learning control (ILC) for multiple time-delays systems with polytopic parameter uncertainty. Based on repetitive process framework, the system under study is equivalently converted into a class of uncertain repetitive processes with multiple time-delays. This approach accounts for effective inclusion of both time and trial domain objectives and hence some requirements on transient dynamics and trial-to-trial error convergence are incorporated for robust design procedures. Additionally, this approach can easily avoid the need for computation with very large dimensioned matrices as it is required for the lifting approach. Also, the proposed controller is designed with the generalized Kalman-Yakubovich-Popov lemma to ensure the monotonic trial-to-trial error convergence in finite frequency domain. This allows us to reduce the conservatism inherent to entire frequency range approaches since the reference signal spectrum reside in a known frequency range. Moreover, the sufficient conditions for the convergence of the resulting scheme are expressed by linear matrix inequalities and hence they are amenable to effective algorithmic solution. Finally, numerical simulations of different scenarios are presented to illustrate the effectiveness of the proposed method. In particular, to highlight the potential interest in PD-type ILC the robust tracking performance is compared with the results for P and D types of ILC.

Resilient distributed MPC for systems under synchronous round-robin scheduling

This paper is concerned with the resilient dynamic output-feedback (DOF) distributed model predictive control (DMPC) problem for discrete-time polytopic uncertain systems under synchronous Round-Robin (RR) scheduling. In order to alleviate the computation burden and improve the system robustness against uncertainties, the global system is decomposed into several subsystems, where each subsystem under synchronous RR scheduling communicates with each other via a network. The RR scheduling is adopted to avoid data collisions, however the updating information at each time instant is unfortunately reduced, and the underlying RR scheduling of subsystems are deeply coupled. The main purpose of this paper is to design a set of resilient DOF-based DMPC controllers for systems under the consideration of polytopic uncertainties and synchronous RR scheduling, such that the desirable performance can be obtained at a low cost of computational time. A novel distributed performance index dependent of the synchronous RR scheduling is constructed, where the last iteration information from the neighbor subsystems is used to deal with various couplings. Then, by resorting to the distributed RR-dependent Lyapunov-like approach and inequality analysis technique, a certain upper bound of the objective is put forward to establish a solvable auxiliary optimization problem (AOP). Moreover, by using the Jacobi iteration algorithm to solve such a problem online, the distributed feedback gains are directly obtained to guarantee the convergence of system states. Finally, two examples including a distillation process example and a numerical example are employed to show the effectiveness of the proposed resilient DMPC strategy.

Blending based multiple-model adaptive control of multivariable systems with application to lateral vehicle motion control

This paper develops multiple fixed model blending based adaptive parameter identification schemes for multi-input multi-output (MIMO) systems with polytopic parameter uncertainty. The developed identification schemes are proven to be asymptotically stable for uncertain linear time-invariant (LTI) MIMO systems, and is shown to provide fast adaptation for even uncertain linear time-varying (LTV) systems. Furthermore, utilizing the proposed parameter identification schemes, a linear-quadratic (LQ) optimal multiple-model adaptive control (MMAC) scheme is developed for linear MIMO systems with polytopic uncertainties. The proposed MMAC scheme is proven to be asymptotically stable for LTI MIMO systems and applied to tracking control of uncertain lateral vehicle dynamics. A set of simulation test results are presented to verify the stability, effectiveness, and comparison of the proposed MMAC scheme.

A Systematic Optimization Design of New Constrained Robust Model Predictive Fault-Tolerant Control for Industrial Processes

A comprehensive optimization design method of new constrained robust model predictive fault-tolerant control is proposed for industrial processes with partial actuator failures and unknown disturbances. A new state space model which is composed of differential state variables, output tracking errors, and new state variables related to output tracking errors is first constructed according to the multiple single-input single-output (SISO) models. Considering the uncertainties existing in the system, the reproduced model is represented by a discrete switched model with polytopic uncertainties. Subsequently, the model predictive controller with min-max optimization is designed to ensure the performance improvement and solve the drawback that the controller gain is not adjustable. To further enhance the system performance, the designed controller is optimized in two steps based on the switching strategy. In addition, the corresponding switching strategy is designed to realize the mutual switching between different models of the system. Finally, taking continuous stirred tank and injection molding processes as examples, the effectiveness of the proposed method is verified by comparing with the traditional control method.

Robust Recursive Regulator for Systems Subject to Polytopic Uncertainties

We present a robust recursive framework for the regulation of discrete-time linear systems subject to polytopic uncertainties. Based on regularized least-squares with a penalty parameter, we formulate a convex optimization problem and weight the polytope vertices altogether. In this sense, the main contribution of this paper consists of a robust recursive framework for the computation of stabilizing feedback gains. The solution does not require numerical optimization packages and relies ultimately on a single penalty parameter which is easily tuned. Moreover, the gains are obtained recursively through algebraic expressions, as opposed to related works which employ linear matrix inequalities. Under observability and controllability conditions, we demonstrate convergence and stability of the closed-loop system in terms of an algebraic Riccati equation. We provide numerical and real-world examples to validate the proposed approach and for comparison with a robust $H_{\infty }$ controller.

Iterative LMI Approach to Robust Hierarchical Control of Homogenous Linear Multi-Agent Systems Subject to Polytopic Uncertainty and External Disturbance

This paper investigates design of robust hierarchical control for linear multi-agent systems (MAS) subject to polytopic uncertainty and external disturbance. Each agent of MAS is described by a homogeneous linear time-invariant dynamic model. The control structure has two layers, namely, an upper layer and a lower layer. Local actions are executed in the lower layer. Each agent shares information through an undirected graph with neighboring agents in the upper layer to achieve the global stabilization and disturbance attenuation. We employ a parameter-dependent Lyapunov function to formulate the robust control design of the local and global feedback in terms of bilinear matrix inequalities and incorporate constraints on disturbance attenuation. We propose the sufficient condition, where system matrices and Lyapunov variables are separated. The parameterization of the controller depends on a common slack variable instead of the Lyapunov matrices. We develop an iterative approach based on the coordinated optimization to solve sub-problems over linear matrix inequalities. Numerical examples are provided to demonstrate the effectiveness of the proposed robust control designs. It is shown that our proposed robust control designs outperform other robust control designs in terms of achievable disturbance attenuation and maximum admissible uncertainty bound.

Finite-time boundedness of two-dimensional positive continuous-discrete systems in Roesser model

This paper is concerned with the finite-time boundedness of two dimensional (2-D) positive continuous-discrete systems in Roesser model. By constructing an appropriate co-positive type Lyapunov function, sufficient conditions of finite-time stability for the nominal 2-D positive continuous-discrete system are established. Sufficient conditions of finite-time boundedness for the addressed system with external disturbances are also proposed. The proposed results are then extended to uncertain cases, where the interval and polytopic uncertainties are considered respectively. Finally, three examples are provided to illustrate the effectiveness of the proposed results.

Robust finite frequency H∞ distributed memory filter design for networked control systems with polytopic uncertainty

AbstractThis paper addresses the robust finite frequency (FF) distributed filtering problem for uncertain networked control system (NCS) that consists of heterogeneous subsystems. By using past output measurements and considering the frequency information of disturbance signals, the designed distributed memory filter is able to guarantee that the filtering error system is well‐posed, stable and has the FF performance. Based on the extended finite frequency bounded realness lemma for uncertain NCSs, the existence condition of robust FF distributed memory filter is derived. Moreover, it is shown that by taking advantage of more past output measurements of NCS, the proposed design procedure can derive a distributed filter that achieves a lower performance bound. Finally, a practical example is given to show the effectiveness of the proposed filter design method.

LMI Criteria for Admissibility and Robust Stabilization of Singular Fractional-Order Systems Possessing Poly-Topic Uncertainties

The issue of robust admissibility and control for singular fractional-order systems (FOSs) with polytopic uncertainties is investigated in this paper. Firstly, a new method based on linear matrix inequalities (LMIs) is presented to solve the admissibility problems of uncertain linear systems. Then, a solid criterion of robust admissibility and a corresponding state feedback controller are derived, which overcome the conservatism of the existing results. Finally, for the sake of demonstrating the validity of proposed results, some relevant examples are provided.

Sampling Dependent Stability Results for Aperiodic Sampled-Data Systems

This paper investigates sampling dependent stability for aperiodic sampled-data systems by employing a Lyapunov-like functional that is time-dependent, and not imposed to be definite positive. Based on the system information on the sampling interval wholly rather than partly, a new Lyapunov-like functional is constructed, which extends existing ones by introducing the integral of the system state and the cross terms among this integral and the sampled state. To take advantage of the integral of the system state, integral equations of the sampled-data system are explored when estimating the derivative of the extended functional. By the Lyapunov-like functional theory, a new sampling dependent stability result is obtained for sampled-data systems without uncertainties. Then, the stability result is applied to sampled-data systems with polytopic uncertainties and a robust stability result is derived. At last, numerical examples are given to illustrate that the stability results improve over some existing ones.

Delayed state feedback predictive control of uncertain nonlinear discrete‐time switched systems with input constraint and state delays

This study addresses the robust predictive control of a class of discrete-time switched systems under arbitrary switching signals. The subsystems of the considered switched system involve polytopic uncertainties, the state delay, non-linear terms, and input constraint. The main goal is to provide two switched delayed state feedback controllers for the cases of known and unknown state delays based on a constrained robust model predictive control method. An appropriate Lyapunov–Krasovskii functional is used to design the controller via an optimisation problem developed as linear matrix inequalities (LMIs). Both approaches are delay dependent because the online LMIs depend on the value of state delay in the first case and the upper bound of the state delay in the second one. The other advantages of the proposed method are considering a non-constrained switching signal, its ability to handle constraints, and shaping a transient response. Finally, numerical examples are provided to illustrate the effectiveness of the theoretical results and also to compare the results with previous researches.

Distributed preview control for large-scale systems with time-varying delay

A distributed preview controller (DPC) design problem is discussed for discrete-time large-scale systems with time-varying delay and polytopic uncertainty in this paper. The original time-varying delay system is reformulated as a constant delay systems via a model transformation. The difference operator method is extended to derive an augmented error system (AES). The preview control problem is converted into a stabilization problem based on state augmentation technique. Sufficient conditions are derived from the scaled small-gain theorem (SSG). Additionally, a DPC is designed through some linear matrix inequality (LMI) techniques. Finally, two examples are provided to show the effectiveness of our controller for large-scale systems.

Robust H∞ control for nonlinear course system of unmanned surface vessel with polytopic uncertainty based on sum of squares

In this paper, the nonlinear robust [Formula: see text] control is investigated for nonlinear course control systems of unmanned surface vessel (USV) with uncertain parameters and external disturbance. Firstly, we suppose that the part or all of the system parameters are unknown but within some ranges, due to the effect of different conditions such as the loading of ship. Then, the course system is modeled as a polynomial one with time invariant polytopic uncertainty. With the aid of parameter dependent Lyapunov function method and positive polynomial theory, the sufficient conditions are given for stability and stabilization with [Formula: see text] performance. These conditions are formulated in terms of parameter-dependent nonlinear matrix inequalities which can be verified by semidefinite programming relaxations based on the sum of squares technique. Finally, simulation results show the effectiveness of the approach.

Synchronization of Cohen-Grossberg fuzzy cellular neural networks with time-varying delays

Abstract In this paper, a class of Cohen-Grossberg fuzzy cellular neural networks (CGFCNNs) with time-varying delays are considered. Initially, the sufficient conditions are proposed to ascertain the existence and uniqueness of the solutions for the considered dynamical system via homeomorphism mapping principle. Then synchronization of the considered delayed neural networks is analyzed by utilizing the drive-response (master-slave) concept, in terms of a linear matrix inequality (LMI), the Lyapunov-Krasovskii (LK) functional, and also using some free weighting matrices. Next, this result is extended so as to establish the robust synchronization of a class of delayed CGFCNNs with polytopic uncertainty. Sufficient conditions are proposed to ascertain that the considered delayed networks are robustly synchronized by using a parameter-dependent LK functional and LMI technique. The restriction on the bounds of derivative of the time delays to be less than one is relaxed. In particular, the concept of fuzzy theory is greatly extended to study the synchronization with polytopic uncertainty which differs from previous efforts in the literature. Finally, numerical examples and simulations are provided to illustrate the effectiveness of the obtained theoretical results.

Robust Stability and Stabilization of 2D Positive System Employing Saturation

This work is concerned with the issue of stability analysis and controller synthesis for a class of Fornasini–Marchesini second-type systems with polytopic uncertainty, state delays and saturation nonlinearity. Firstly, by utilizing the co-positive Lyapunov function method, sufficient conditions in the linear programming setting are presented assuring the positivity and robust asymptotic stability of the proposed systems. Then, both the state feedback controller and the observer-based state feedback controller are considered based on the obtained results. In addition, the design schemes of the related controller gain matrices are also explicitly provided. Finally, two illustrative examples are given to demonstrate the effectiveness of the method outlined in this paper.

Robust state feedback for uncertain 2-D discrete switched systems in the Roesser model

The design of robust controllers is considered here for a class of two-dimensional (2-D) discrete switched systems described by the Roesser model with polytopic uncertainties. Attention focuses on the design of a switched state feedback controller, which guarantees the robust asymptotic stability and a prescribed performance for the closed-loop system. By using multiple parameter-dependent Lyapunov functionals, and introducing some switched free-weighting matrices, a new sufficient condition for the robust performance analysis of uncertain 2-D discrete switched systems is developed. Furthermore, the design of switched state feedback controller is proposed in terms of linear matrix inequalities (LMIs). Illustrative examples are given to illustrate the effectiveness of the developed theoretical results.

Robust Static Output Feedback H2/H∞ Control Synthesis with Pole Placement Constraints: An LMI Approach

This paper studies the robust static output feedback (SOF) problem considering pole placement constraints for linear systems with polytopic uncertainty as well as linear parameter varying (LPV) systems. New linear matrix inequality (LMI) approaches are proposed for the SOF controller design while the pole placement, H2, and H∞ constraints are guaranteed. In addition, the gain-scheduled SOF controller will be designed for LPV systems if system parameters are measured. The proposed methods can be applied to general linear systems without imposing any constraints on system matrices. The performance and effectiveness of the proposed methods are shown using two examples.

Robust model predictive control for Markovian jump systems under Round-Robin protocol

In this paper, a robust model predictive control problem is investigated for a class of Markovian jump systems with polytopic uncertainties. The Round-Robin protocol is utilised to schedule data transmission from the controllers to the actuator in order to reduce the burden of communication and the occupancy of network effects. Moreover, two kinds of transition probability matrices for the Markovian process are considered due to the practical application process, namely the one with polytopic uncertainties and the other with partially unknown entries. Sufficient conditions are established by means of the mixed-mode and token-dependent Lyapunov-like technique such that the closed-loop system is stable in the mean-square sense. In addition, a set of mixed-mode and token-dependent state feedback controllers are designed in terms of minimising a certain upper bound of the worst-case infinite horizon cost function. Finally, some simulation examples are implemented to verify the effectiveness of the proposed design scheme.

Robust model predictive control of heterogeneous time-delay multi-agent systems with polytopic uncertainties and input amplitude constraints

This article studies the robust model predictive control of heterogeneous multi-agent systems with polytopic uncertainties and time delay. Moreover, some constraints on the amplitude of the control inputs are considered for each agent. The proposed distributed controllers are designed as state feedback. The goal is to design the feedback gains such that the multiagent system achieves consensus in the presence of time-delay and model uncertainties. For this purpose, an optimization problem is proposed, and by using the constrained robust model predictive control and the appropriate Lyapunov–Krasovskii functional, sufficient conditions are obtained to solve the optimization problem through solving the linear matrix inequalities. In this regard, a theorem is presented, and it is proved that the consensus errors converge to zero. Finally, the effectiveness of the proposed method is illustrated using numerical simulations.

Regional stabilization of TCP/AQM system with polytopic uncertainties and homogeneous segmented time delay

In this paper, new local stabilization analysis for TCP/AQM process based on segmented delay is proposed. The new approach consists in describing the time delay as a sum of homogeneous loads delays plus the variation of the queuing delay resulting from the made actions inside the router buffer. By employing an appropriate new Lyapunov–Krasovskii functional that depends on the upper bounds of the loads, new segmented delays dependent local stabilization conditions are proposed. Furthermore, new results concerning the unsymmetrical saturation input are obtained. Finally, the theory is experimented on NS 3, which proves that the proposed Segment Controller (SegCont) mechanism is strong and robust.