Design Of Linear Systems Research Articles

Optimal non-fragile control design for linear systems under amplitude and rate saturation: An LMI approach

In this paper, the problem of optimal non-fragile guaranteed cost control design for linear systems subject to input amplitude and rate saturation is addressed. Sufficient conditions for the existence of a non-fragile state feedback are obtained by Lyapunov stability theory. The designed controller not only guarantees the asymptotic stability of the overall closed-loop system with a minimum upper bound of a cost function, but also ensures the actuator saturation avoidance. This problem is transformed into an optimization problem with linear matrix inequality (LMI) constraints. The proposed method guarantees that the control input amplitude and rate remain within the allowable ranges and do not exceed the considered bounds. The simulation results illustrate the effectiveness and superiority of the proposed theoretical results.

Observer design and interval estimation of time-delay discrete-time linear systems with external disturbance and measurement noise

Observer design and interval estimation of time-delay discrete-time linear systems with external disturbance and measurement noise

Stability of conformable fractional time-varying linear systems

In this paper, we investigate the exponential and asymptotic stability analysis of conformable fractional linear time-varying systems. We propose sufficient conditions for testing the asymptotic and exponential stability of conformable differential systems by using the notion of stable functions and differential Lyapunov inequalities. Furthermore, we apply the developed approach to the problem of conformable stabilisation and observer design for conformable fractional linear time-varying systems.

On the State-Feedback Controller Design for Polynomial Linear Parameter-Varying Systems with Pole Placement within Linear Matrix Inequality Regions

The present paper addresses linear parameter-varying systems with high-order time-varying parameter dependency known as polynomial LPV systems and their controller design. Throughout this work, a procedure ensuring a state-feedback controller from a parameterized linear matrix inequality (PLMI) solution is presented. As the main contribution of this paper, the controller is designed by considering the time-varying parameter rate as a tuning parameter with a continuous control gain in such a way that the closed-loop eigenvalues lie in a complex plane subset, with high-order time-varying parameters defining the system dynamics. Simulation results are presented, aiming to show the effectiveness of the proposed controller design.

Equilibrium controllability analysis and input design of linear systems

Equilibrium controllability analysis and input design of linear systems

Adaptive Fuzzy Boundary Observer Design for Uncertain Linear Coupled Hyperbolic Partial Differential Equation Systems

Joint uncertainties and state estimation of a class of linear coupled hyperbolic partial differential equation systems in the presence of unstructured and structured uncertainties are studied in this paper. For unstructured uncertainties which are completely unknown, by employing Takagi-Sugeno fuzzy logic system to approximate the unstructured uncertainties, a novel adaptive fuzzy boundary observer is developed to estimate both unknown system states as well as unknown weights in the fuzzy logic system, and the estimation errors are ultimately bounded. Therein, in the design of the proposed observer, a set of swapping filters and infinite dimensional backstepping technique are combined. On the other hand, for structured uncertainties that can be described in a concrete parameterized form, the proposed method can easily achieve the exact estimation of weights and states to their true values. The rigorous proof is provided to show that the ultimately bounded estimation errors for the case of unstructured uncertainties and the exponential convergent estimation errors for the case of structured uncertainties can be realized. Finally, three illustrative simulations are carried out to show the feasibility and effectiveness of the developed methods in this paper.

$$H_\infty $$ dynamic observer design for discrete-time linear systems with time varying delays based on generalized reciprocally convex matrix inequality

$$H_\infty $$ dynamic observer design for discrete-time linear systems with time varying delays based on generalized reciprocally convex matrix inequality

Necessary and sufficient conditions for crisp state-feedback design for fuzzy linear systems

In this paper, we examine the uncertain fuzzy continuous time linear systems. There is fuzzy uncertainty in the dynamics of the investigated system in the form of uncertain parameters represented by fuzzy granular numbers. A state feedback is designed to guarantee the stability of the closed-loop system with crisp gains and a necessary and sufficient condition is proposed to guarantee the stability. Furthermore, by using the proposed control input, the fuzzy eigenvalues of the closed-loop system are placed in a way that they have the greatest possibility of occurring in the desired poles. The state feedback gain which is presented in this paper is a crisp number and can be applied to real systems in practical applications. The proposed method ensures closed-loop stability whereas previous methods have presented fuzzy gains which are defuzzified to be applied to a real system without guaranteeing the stability. At the end, two practical simulation examples are given to verify the validity of the theoretical results.

Robust dynamic feedback stabilization for linear systems with disturbances

In this paper, we are concerned with the dynamic feedback design for linear systems with input disturbance. We propose a new approach to design dynamic feedback such that the disturbance in the control channel can be compensated effectively. An interesting characteristic about the disturbance robustness of dynamic feedback is found. Thanks to this interesting characteristic, we just need to consider the disturbance-free system to make the dynamic feedback design. This fact is well validated by several dynamic feedback laws proposed in this paper. Our results are available for the regular linear system with harmonic disturbance. Moreover, the stabilization of an unstable heat equation with general periodic disturbance is also investigated. In order to validate the theoretical results visually, some numerical simulations are given to show the effectiveness of the proposed dynamic feedback.

Lyapunov-based stabilization mobile control design of linear parabolic PDE systems

This article considers the exponential mobile stabilization control of linear parabolic partial differential equation (PDE) systems. Firstly, a stabilization scheme based on static output feedback (SOF) control and mobile actuator/sensor guidance is proposed. Next, the operator theory is used to discuss the well-posedness of closed-loop PDE systems. Thus, the SOF control and mobile guidance design approach is simultaneously proposed to guarantee that the closed-loop PDE system is exponentially stable. In final, the effectiveness of the design method is verified by numerical simulation.

Beamline and vacuum system design of HEBT for the A-FNS accelerator

The Advanced Fusion Neutron Source (A-FNS) project is progressing at the QST Rokkasho institute, Japan. The A-FNS will conduct fusion neutron irradiation tests of materials for a fusion demonstration reactor (DEMO reactor). For these tests a high intensity deuteron beam accelerator is used to produce a high neutron flux with the neutron energies around 14 MeV. The accelerator system accelerates a deuteron beam to a beam energy of 40 MeV, guides the beam towards a liquid lithium target and shapes the uniform beam at the Li target using a magnet system.Two of the main considerations for the A-FNS high energy beam transport (HEBT) design are protection of the Superconducting Radio-Frequency linear accelerator (SRF) and vacuum system design for the interface of the HEBT and the target system. For the A-FNS, back streaming of Li vapor from the windowless free surface of the Li target is a concern. In addition, widely different vacuum pressure must be maintained between the accelerator system and the target system. This paper shows the detailed design of the A-FNS HEBT section regarding these considerations.

Robust virtual sensors design for linear and nonlinear systems under external disturbances

SummaryThe problem of robust virtual sensors design in linear and nonlinear dynamic systems is studied. To design such sensors, two different canonical forms are used: identification and Jordan canonical forms. The problems generally are solved in three steps: at the first step, the linear model invariant with respect to the disturbance is designed; at the second step, a possibility to take into account the nonlinear term and to estimate the given variable is checked; finally, stability of the observer is obtained. The relations allowing to design virtual sensor of minimal dimension estimating the prescribed component of the state vector of the system are obtained. The problem of virtual sensor location is studied and solved. The theoretical results are illustrated by the example of three tank system.

The Robust Model Predictive Control Design for Linear Interconnected Systems

In this paper, we discuss the design of robust model predictive control for linear interconnected systems by several constraints. Linear interconnected system is a complex systems which consist of several subsystems and the dynamic of subsystem is influenced by the states or outputs of the other subsystems. The systems are controlled by formulating and applying the model predictive control on each subsystems. We formulate the optimization problem that minimize the cost function for each subsystems. The optimization problem is solved by gradient method to get the minimum cost function. Numerical simulation was conducted to show the effectiveness and performance of robust model predictive control. Based on the results of the numerical simulation and test the robustness, it can be shown that the robust model predictive control is effective to control the linear interconnected systems.

КОМПЛЕКСНЫЙ АНАЛИЗ ПРОЕКТА ПЛАНИРОВКИ ТЕРРИТОРИИ ЛИНЕЙНОГО ОБЪЕКТА СИСТЕМЫ ВОДОСНАБЖЕНИЯ ЗАМАРАЙСКОГО МЕСТОРОЖДЕНИЯ ПОДЗЕМНЫХ ВОД С ЦЕЛЬЮ БЕЗОПАСНОГО РАЗВИТИЯ ТЕРРИТОРИИ

Issues of quality water supply are always relevant, because water is the source of life on Earth. The article deals with the design of linear water supply systems and identifies the main problems of their functioning. The authors present the results of studies of the projected reserve water pipeline from the Zamarayskoye groundwater deposit to the pumping stations in the Serovsky urban district. It is found that the preparation of urban planning documentation is currently an important condition for the safe development of the territory. The purpose of such documentation is to form the boundaries of land for the placement of new engineering networks, in particular the water supply system. Safe water use is one of the main aspects of social state policy.

Robust Output Feedback Control Design in the Presence of Sporadic Measurements

Output feedback control design for linear time-invariant systems in the presence of sporadic measurements and exogenous perturbations is addressed. To cope with the sporadic availability of measurements of the output, a hybrid dynamic output feedback controller equipped with a holding device whose state is reset when a new measurement is available is designed. The closed-loop system, resulting from the interconnection of the controller and the plant, is augmented with a timer variable triggering the arrival of new measurements and its properties are analyzed using hybrid system tools. Building upon Lyapunov theory for hybrid systems, sufficient conditions for internal and L2 input-to-output stability are proposed. An LMI-based design methodology for the co-design of the gains of the controller and the parameters of the holding device is presented. The effectiveness of the proposed LMI-based design approach is showcased in a numerical example.

Distributed Cooperative LQR Design for Multi-Input Linear Systems

Distributed Cooperative LQR Design for Multi-Input Linear Systems

Interval observers design for systems with ostensible Metzler system matrices

This paper attempts to resolve the problem concerning the interval observers design for linear systems with ostensible Metzler system matrices. Because system dynamics matrices are partially different from strictly Metzler structures, a solution is achieved by constructing a composed system matrix representation, which combines pre-compensated interval matrix structures fixed with a prescribed region of D-stability and the reconstructed strictly Metzler matrix structure, related to the original interval system matrix parameter definition. A novel design procedure is presented, which results in a strictly positive observer gain matrix and guarantees that the lower estimates of the positive state variables are non-negative when considering the given system structure and the non-negative system state initial values. The design is computationally simple since it is reduced to the feasibility of the set of linear matrix inequalities.

Interval observer–based compensators design for linear systems with uncertain time-varying parameters

This paper proposes a novel approach to design interval observer–based compensator for linear systems with uncertain parameters and measurement noises. Based on monotone system theory, existence decoupled conditions of observers gain design to guarantee cooperativity and input-to-state stability of error dynamics system are proposed in terms of a set of linear matrix inequalities. Moreover, a compensator consisting of the observers and output feedback controller is designed within interval observer design framework. Such an observer-based compensator has a simple separation structure, which shows that interval observers and feedback controller can be simultaneously designed based on separation principle. The developed techniques on observer-based compensator design are illustrated through a practical example.

Non-fragile PD control of linear time-delay positive discrete-time systems

This paper addresses the issue of proportional-derivative (PD) controllers design for positive linear systems in the discrete-time domain, which still remains a challenging problem in positive systems theory. The specific aim is to design a PD controller for a system with constant time delay, which simultaneously ensures closed-loop system stability and preserves positivity. Moreover, additive gain variation of the controller is considered in the synthesis process. Systematic formulation and tractable algorithms are developed to find the PD controller gains for positive stabilization. The performance of such methods is validated by numerical examples.

Robust Output Regulation and Reinforcement Learning-Based Output Tracking Design for Unknown Linear Discrete-Time Systems

In this article, we investigate the optimal output tracking problem for linear discrete-time systems with unknown dynamics using reinforcement learning (RL) and robust output regulation theory. This output tracking problem only allows to utilize the outputs of the reference system and the controlled system, rather than their states, and differs from most existing works that depend on the state of the system. The optimal tracking problem is formulated into a linear quadratic regulation problem by proposing a family of dynamic discrete-time controllers. Then, it is shown that solving the output tracking problem is equivalent to solving output regulation equations, whose solution, however, requires the knowledge of the complete and accurate system dynamics. To remove such a requirement, an off-policy RL algorithm is proposed using only the measured output data along the trajectory of the system and the reference output. By introducing reexpression error and analyzing the rank condition of the parameterization matrix, we ensure the uniqueness of the proposed RL-based optimal control via output feedback.