LMI-based Techniques Research Articles

A Review of Convex Approaches for Control, Observation and Safety of Linear Parameter Varying and Takagi-Sugeno Systems

This paper provides a review about the concept of convex systems based on Takagi-Sugeno, linear parameter varying (LPV) and quasi-LPV modeling. These paradigms are capable of hiding the nonlinearities by means of an equivalent description which uses a set of linear models interpolated by appropriately defined weighing functions. Convex systems have become very popular since they allow applying extended linear techniques based on linear matrix inequalities (LMIs) to complex nonlinear systems. This survey aims at providing the reader with a significant overview of the existing LMI-based techniques for convex systems in the fields of control, observation and safety. Firstly, a detailed review of stability, feedback, tracking and model predictive control (MPC) convex controllers is considered. Secondly, the problem of state estimation is addressed through the design of proportional, proportional-integral, unknown input and descriptor observers. Finally, safety of convex systems is discussed by describing popular techniques for fault diagnosis and fault tolerant control (FTC).

Robust ℋ 2 controller with parametric uncertainties applied to a reaction wheel unicycle

ABSTRACT A robust controller is designed using an LMI-based technique. In this approach, the controller synthesis is similar to an LQR, but with the possibility of considering parametric uncertainties. The designed controller is applied to a reaction wheel unicycle robot, which is an unstable and sensitive system in terms of parametric errors. An implementation aspect regarding the dynamic torque limitation of the reaction wheel actuator is emphasised. Since the equivalent linear model is decoupled, a decentralised controller structure is fixed during the synthesis. Simulation and practical results are shown. A detailed description of the robot construction is also presented.

Formal Traffic Characterization of LTI Event-Triggered Control Systems

Unnecessary communication and computation in the periodic execution of control tasks lead to overprovisioning in hardware design (or underexploitation in hardware utilization) in control applications, in particular, in networked control systems. To address these issues, researchers have proposed a new class of strategies, named event-driven strategies. Despite their beneficiary effects, matters such as task scheduling and appropriate dimensioning of communication components have become more complicated with respect to traditional periodic strategies. In this paper, we present a formal approach to derive an abstracted system that captures the sampling behavior of a family of event-triggered strategies for the case of LTI systems. This structure approximately simulates the sampling behavior of the aperiodic control system. Furthermore, the resulting abstract system is equivalent to a timed safety automaton. In the construction of the abstraction, the state space is confined to a finite number of convex regions, each of which represents a mode in the quotient system. An LMI-based technique is deployed to derive a sampling time interval associated with each region. Finally, reachability analysis is leveraged to find the transitions of the abstract system.

Conditions of Stabilization of Positive Continuous Takagi–Sugeno Fuzzy Systems with Delay

This paper deals with the problem of stability and stabilization of positive Takagi–Sugeno (T–S) fuzzy systems with fixed delays. The obtained conditions are given under the linear programming technique while imposing positivity constraint for the closed-loop system. New delay-independent stabilization conditions are derived by using a well-appropriated Lyapunov–Krasovskii functional. A real plant model is studied to show the applicability of the design procedure, while a numerical example is used to compare with LMI-based techniques.

A robust control strategy for a class of distributed network with transmission delays

Purpose The purpose of this paper is to concern the design of a robust model predictive controller for distributed networked systems with transmission delays. Design/methodology/approach The overall system is composed of a number of interconnected nonlinear subsystems with time-varying transmission delays. A distributed networked system with transmission delays is modeled as a nonlinear system with a time-varying delay. Time delays appear in distributed systems due to the information transmission in the communication network or transport of material between the sub-plants. In real applications, the states may not be available directly and it could be a challenge to address the control problem in interconnected systems using a centralized architecture because of the constraints on the computational capabilities and the communication bandwidth. The controller design is characterized as an optimization problem of a “worst-case” objective function over an infinite moving horizon. Findings The aim is to propose control synthesis approach that depends on nonlinearity and time varying delay characteristics. The MPC problem is represented in a time varying delayed state feedback structure. Then the synthesis sufficient condition is provided in the form of a linear matrix inequality (LMI) optimization and is solved online at each time instant. In the rest, an LMI-based decentralized observer-based robust model predictive control strategy is proposed. Originality/value The authors develop RMPC strategies for a class of distributed networked systems with transmission delays using LMI-Based technique. To evaluate the applicability of the developed approach, the control design of a networked chemical reactor plant with two sub-plants is studied. The simulation results show the effectiveness of the proposed method.

Stability analysis of networked and quantized linear control systems

The presence of a communication network in a control loop induces imperfections, such as quantization effects, packet dropouts, time-varying transmission intervals, time-varying transmission delays and communication constraints. The objectives of this paper are to provide a unifying modeling framework that incorporates all these imperfections simultaneously, and to present novel techniques for the stability analysis for these networked control systems (NCSs). In contrast to many other papers that consider quantization in NCSs, we incorporate quantization effects in the modeling framework by modeling them as norm-bounded additive disturbances on both plant and controller signals. We focus on linear plants and controllers, and periodic and quadratic protocols, which leads to a modeling framework for NCSs based on discrete-time switched linear uncertain systems. Using an overapproximated system in the form of a polytopic model with additive norm-bounded uncertainty, we propose LMI-based techniques to analyze the input-to-state stability (ISS) and the ℓ2-gain properties of the obtained NCS models with respect to the norm-bounded additive disturbances induced by quantization. These ISS and ℓ2-gain conditions will be used to assess closed-loop stability and performance for two classes of quantizers. We illustrate the effectiveness of the developed theory on a benchmark example of a batch reactor.

Stability analysis of networked control systems with periodic protocols and uniform quantizers

The presence of a communication network in a control loop induces imperfections, such as quantization effects, packet dropouts, time-varying transmission intervals, time-varying transmission delays and communication constraints. The objectives of this paper are to provide a unifying modeling framework that incorporates all these imperfections, and to present novel techniques for the stability analysis for these networked control systems (NCSs). We focus on linear plants, linear controllers and periodic protocols, which leads to a modeling framework for NCSs based on discrete-time switched linear uncertain systems. Using an overapproximated system in the form of a polytopic model with additive norm-bounded uncertainty, we use LMI-based techniques to analyze the input-to-state stability (ISS) of the obtained NCS models with respect to the norm-bounded additive disturbances on plant and controller signals induced by quantization. These ISS conditions will be used to assess closed-loop stability and performance for periodic communication protocols and uniform quantizers, although the framework allows for extensions towards other types of protocols and other types of quantizers as well. We illustrate the effectiveness of the developed theory on a benchmark example of a batch reactor.

State and Parameter Estimation for Nonlinearly Parameterized Systems: An H∞-Based Approach

AbstractWe present a framework for estimating states and parameters in systems that can be described by a detectable linear system perturbed by a nonlinear function of the states, exogenous signals, and a vector of unknown, constant parameters. The estimators designed in this framework consist of two interconnected modules: a parameter estimator that is constructed as though the states and the nonlinear perturbation were directly available for measurement; and an observer/perturbation estimator that estimates the states as well as the perturbation. The design methodology is based on satisfying an H∞ condition, which leaves the designer with a wide range of options for carrying out the design. We discuss the use of LMI-based techniques in particular, and illustrate their application on a simulation example. We also discuss how the results of the paper can be applied to a more general class of cascaded nonlinear systems.

A Design Method of Critical Control Systems Utilizing Genetic Algorithms and LMI-based Regional Pole Assignment Technique

A methodology for designing critical systems subject to magnitude- and rate-limited reference inputs is proposed. The worst-case tracking error is minimized under the constraint on the control effort. The LMI-based technique developed by Chilali and Gahinet is utilized to assign the resulting closed-loop poles into the intersection of vertical strips and a conic sector. The optimal pole region is searched by means of the simple genetic algorithm. An illustrative design example of the position control system for a two-inertia system is provided to demonstrate the proposed design methodology.

State and input simultaneous estimation for a class of nonlinear systems

This paper addresses the problem of estimating simultaneously the state and input of a class of nonlinear systems. Here, the systems nonlinear part comprises a Lipschitz nonlinear function with respect to the state and input, and a state-dependent unknown function including additive disturbance as well as uncertain/nonlinear/time-varying terms. Upon satisfying some conditions, the observer design problem can be solved via a Riccati inequality or a LMI-based technique with asymptotic estimation guaranteed. A numerical example is included for illustration.