LMI Solution Research Articles

The Improved Orbit Solution and Component Masses of bet LMi

Abstract bet LMi is a double-lined visual binary with an orbital period of ∼39 yr. Via a simultaneous fitting to both astrometric and radial velocity measurements, we give a complete and improved orbit solution with high precision. Then, the component masses are precisely determined as 2.98 ± 0.10 M ⊙ and 1.92 ± 0.04 M ⊙ with a relative precision of ∼3%, respectively. The orbital parallax is determined to be 19.6 ± 0.2 mas, which is two times more precise than Hipparcos parallax. With the known apparent magnitudes and magnitude difference of the components, we derive the luminosity of the components as 50.7 ± 1.8 L ⊙ and 9.1 ± 4.1 L ⊙. The estimated radii of the components are 9.4 ± 0.3 R ⊙ and 3.7 ± 1.5 R ⊙.

Robust Guaranteed Cost Control for a Class of Nonlinear 2-D Systems with Input Saturation

In this paper, a robust guaranteed cost controller is designed for a class of two-dimensional(2-D) discrete-time systems described by Roesser model, where the system simultaneously contains input saturation, parametric uncertainty and sector nonlinearity. Firstly, a convex hull representation is used to describe saturated input of the system. Secondly, a sufficient condition for ensuring the asymptotic stability of the closed-loop system and the existence of the robust guaranteed cost controller is given according to the Lyapunov stability theory. Then, this sufficient condition is transformed into a linear matrix inequality form by using Schur complement lemma and the design of robust guaranteed cost controller is realized by the solution of LMI. Finally, a numerical example is given to illustrate the effectiveness of the proposed method.

Unknown input observer design for a class of fractional order nonlinear systems

Analysis and control of fractional order (FO) nonlinear systems is a challenging problem. In earlier works, as highlighted in literature, stability conditions for the FO LTI systems are analytically derived and these results are extended to formulate LMI conditions to express the stability of the FO LTI systems. In present work, design of full order and reduced order observers for imperfect fractional order nonlinear systems is presented. Imperfections in real system are silent dynamics and can be modeled as unknown input. To design observer for such system, unknown input observer (UIO) design concepts are used and LMI conditions for the existence of observer are analytically derived. For this purpose, Differential Mean Value (DMV) theorem is used and nonlinear term in the error dynamics is alternatively expressed in appropriate equivalent form. As a result, error dynamics evolves as Linear Parameter Varying (LPV) system and then stability results for FO LTI systems are extended to stabilize FO nonlinear error dynamical systems. LMI conditions for the existence of unknown input observer for the two cases 0 < α < 1 and 1 < α < 2 are analytically derived. Feasible solution of LMI gives the observer design matrices directly. Finally, results of simulation are presented to authenticate the proposed approach.

Improvement of LMI controllers of Takagi-Sugeno models via Q-learning

This paper presents a preliminary attempt to bridge the conservative (shape-independent) results from guaranteed-cost LMIs and the reinforcement learning setups which learn optimal controllers from data. In this sense, the proposed approach uses an initialization based on the LMI solution and proposes an approximation of the Q-function using polynomials of the membership functions in Takagi-Sugeno models. The resulting controller is shape-dependent, that is, uses the knowledge of membership functions and data to clearly improve LMI solutions.

Optimal input design for continuous-time system identification: application to fractional systems

An optimal input design framework for continuous-time system identification using fractional models is presented. This framework extends some existing results in discrete-time systems. The problem is formulated in convex finite dimensional form. Input spectrum decomposition in Laguerre polynomial basis is applied and an LMI solution is proposed. This method permits to synthesize optimal input spectrum for LTI continuous-time systems including fractional ones.

A state feedback input constrained control design for a 4-semi-active damper suspension system: a quasi-LPV approach

This paper addresses a semi-active suspension control of the full vehicle equipped with 4 controlled semi-active dampers by using a full 7 degree of freedom (DOF) vertical model. First, the dissipativity conditions of the semi-active dampers are recast as saturation conditions on the control inputs. Then, the suspension controller is derived by solving a state feedback control design problem for a class of linear parameter-varying (LPV) system in the presence of actuator saturation. To this aim, a generalized sector condition for LPV system is applied to treat the nonlinearity, caused by the input saturation and to relax the stability condition. The proposed control law ensures the disturbance attenuation by reducing the L2 gain from the disturbance to the controlled output. This controller, derived in the LPV/H∞ framework, is based on the LMI solution for polytopic systems. Some realistic simulation results are presented in order to illustrate the effectiveness of the proposed approach.

An LPV Fault Tolerant control for semi-active suspension - scheduled by fault estimation

In this paper, a novel fault tolerant control is proposed to accommodate damper faults (oil leakages) in a semi-active suspension system based on a quarter-car vehicle model. The fault accommodation is based on the Linear Parameter Varying (LPV) control strategy and involves two steps. At first, a fast time-varying fault is estimated by using the fast adaptive fault estimation (FAFE) algorithm, based on an unknown input adaptive observer. Thanks to information about the estimated fault, the dissipativity domain of the semi-active suspension is adapted according to the fault. Then a single LPV fault tolerant controller is developed to manage the system performances. The controller solution, derived in the LPV/H∞ framework, is based on the LMI solution for polytopic systems. Some simulation results are presented that show the effectiveness of this approach.

Design of Robust Fault Detection Observers for Discrete-time Linear Switched Systems

AbstractThis work addresses the design of a robust hybrid observer for discrete-time switched linear systems subject to unknown inputs and modeling errors. The observer herein proposed is synthesized, for the case when the active mode is unknown and in the purpose of robust fault detection. We'll show that a suitable trade-off between the robustness to unknown inputs and sensitivity to faults can be obtained through a H∞ performance index. The latter is optimized using an iterative LMI solution procedure. The efficiency of the proposed approach is illustrated by a numerical example.

Design of a robust fault detection based observer for linear switched systems with external disturbances

This paper concerns the design of a robust hybrid observer for switched linear systems with unknown inputs and modeling error. It extends some previous results to a more general class of switched-state jump linear hybrid systems. The observer herein proposed is synthesized for the task of robust fault detection without the knowledge of the active mode. Moreover, the robust fault detection problem has been considered as a standard H ∞ model matching. Then, a suitable trade-off between the robustness of the unknown inputs and the sensitivity to faults has been obtained thanks to a H ∞ performance index. The latter is finally optimized using an iterative LMI solution procedure.

Stability and [formula omitted] objective characterizations in control: A comparative study

This paper is concerned with stability and H 2 objective characterizations in control. New forms of alternative LMI characterizations are presented for continuous-time stability and H 2 objective. A key relationship between the alternative characterizations for continuous-time systems and the existing discrete-time versions is illustrated. The existing enhanced LMI characterization for continuous-time systems, called the reciprocal projection lemma, is revisited and an alternative proof is provided with a new interpretation. An ϵ -embedded LMI characterization is presented for a comparative study with the reciprocal projection lemma and for numerical analysis on the conservativeness of synthesis conditions. Through an application in control, it is discussed that, when applied to multi-objective problems in control, the alternative characterizations in this paper lead to an LMI solution with further significant conservativeness reduction, compared to the reciprocal projection lemma. In addition, through the comparison with the existing dilated LMI condition, it is shown that the dilated condition is an equivalent continuous-time counterpart of the existing discrete-time versions.

Generalized asymptotic regulation with guaranteed [formula omitted] performance: An LMI solution

A multi-objective controller synthesis problem is considered in which a set of generalized asymptotic regulation constraints are to be satisfied while also guaranteeing a desired level of performance measured in terms of the asymptotic variance of a performance output in response to a white noise random process with zero mean and identity covariance matrix. The generalized regulation constraints are expressed as bounds on the state-steady peak in response to disturbances generated by an anti-stable autonomous exogenous system with nonzero initial states. The controllers that guarantee these constraints can be realized by replicating the dynamics of the exogenous system within a certain structure formed by gain matrices, which are subject to convex constraints, and an accompanying controller with which the feedback loop is to be stabilized. Formulating the design of the accompanying controller in a way to guarantee the additional performance objective, the overall design is rendered tractable over a set of free variables, in terms of which the synthesis of a suitable controller is also outlined. The order of the controller is equal to the order of the plant plus the order of the exogenous system. By an adaptation of the developed techniques, a solution is also provided for the problem of generalized asymptotic regulation with suboptimal transient response.

Robust Fault Detection Based-Observer for Linear Switched Systems

Abstract This paper deals with the design of a robust hybrid observer for switched linear systems with unknown inputs and modeling error. The proposed observer is synthesized for the task of robust fault detection and concerns the case when the active mode is unknown. The basic idea of our approach is to formulate the design of the robust fault detection observer as a H∞ model-matching problem. Then, some results of H∞ optimization are exploited and an LMI solution procedure is proposed to synthesize the desired robust observer.

A new LMI solution in the L1 optimal problem for wind turbine-induction generator unit

An application of a new L 1-optimal control technique based on linear matrix inequality optimization to a wind turbine-induction generator unit is presented. The new technique, which is proposed as an algorithm, combines the original concept of peak-to-peak gain of designed system with optimal control theory and employs a free design parameter allowing for a flexible management of the tradeoff between robustness to disturbance signals and magnitude of the worst peak-to-peak gain of the design system. For solving this non convex problem,, using several transfer function for linearization and linear matrix inequality optimization approach. For the convergence of this algorithm, a scope is found on the basis of the H ∞-norm. If the length of this interval is small, we have a good estimate of the actual optimal peak-to-peak gain that is achievable by control. Application to the wind turbine-induction generator unit provides fast response with a good steady state error, suitable settling time and stability upon severe wind gust.

Exponential Dissipativity of Discrete-time Stochastic Systems and Robust Simultaneous Stabilization via Output Feedback

The paper studies robust simultaneous stabilization problem via output feedback for a set of nonlinear discrete-time uncertain systems. New version of dissipativity called exponential dissipativity is defined for discrete-time stochastic system with Markovian switching. It is proved that if this stochastic system with special choice of its parameters is exponentially dissipative then the original set of uncertain system is simultaneously stabilizable and the stabilizing control has robustness properties in the sense that it admits some feedback uncertainties. The linear robust simultaneous stabilization problem is considered as a particular case. In this case the results are obtained in the form of convergent algorithm for computing of output feedback gain, based on iterative solution of LMI's. This algorithm is applied to the problem of angular stabilization of longitudinal multi-regime aircraft motion.

IS A MIXED DESIGN OF OBSERVER‐CONTROLLERS FOR TIME‐DELAY SYSTEMS INTERESTING?

ABSTRACTThis paper deals with H∞ observer‐based feedback control for linear time‐delay systems, in the framework of delay independent stability. We will propose a new LMI solution to observer‐controller design that ensures a disturbance attenuation level for the controlled output as well as for the state estimation error, which is an open problem. This will be compared with a well‐known solution and with a usual strategy in control which consists in designing the observer and the controller separately. Our aim is to try to bring a positive answer to the following question: is there an interest to solve the problem in a single (unique) formulation or should we design separately the observer and the controller? An application to a wind tunnel model is provided to emphasize the interest of the given results, particularly in comparison with existing results on H∞ observer‐based control.

OBSERVER-BASED H∞ CONTROL FOR TIME-DELAY SYSTEMS : A NEW LMI SOLUTION

We propose here a new LMI solution to H∞ observer-controller design that ensures a disturbance attenuation level for the controlled output and for the state estimation error, which is an open problem. This will be compared with a well-known solution. An application to a wind tunnel model is provided.

A REFERENCE MODEL BASED ROBUST ℋ∞ FILTERING APPROACH TO FAULT DETECTION IN UNCERTAIN SYSTEMS

Model-based robust fault diagnosis aims to attenuate influence from model uncertainties on the residual while maintaining fault detection and isolation performance. In this paper, we consider robust residual generation for integral quadratic constrained (IQC) uncertain systems. The design consists of two steps. A reference model, incorporated into a robust ℋ∞ filtering framework, is set up to represent desired detection performance such as disturbance attenuation. Then, the extended robust ℋ∞ filtering problem is solved by constructing a nonlinear matrix inequality (NLMI). Linearization of the NLMI results in an tractable LMI solution, where an illustrative example follows to verify the algorithm.

A simple derivation of ARE solutions to the standard [formula omitted] control problem based on LMI solution

In this note, a simple derivation of the Riccati equation based solutions to the standard H ∞ control problem, namely the well-known Glover–Doyle solution and DGKF solution is given based on LMI solution. It is hoped that this will be helpful in deepening the understanding of Riccati equation solutions.

An LMI solution to the robust synthesis problem for multi-rate sampled-data systems

In this paper we address the asynchronous multi-rate sampled-data H ∞ synthesis problem. Necessary and sufficient conditions are given for the existence of a controller achieving the desired performance, and the problem is shown to be equivalent to a convex optimization problem expressed in the form of linear operator inequalities. In the case where the sample and hold rates are synchronous, these operator inequalities reduce to linear matrix inequalities, for which standard numerical software is available.

Periodic H2 Synthesis for Spacecraft Attitude Determination and Control with a Vector Magnetometer and Magnetorquers

A control synthesis for a spacecraft equipped with a set of mutually perpendicular coils and a vector magnetometer is addressed in this. paper. The interaction between the Earth's magnetic field and an artificial magnetic field generated by the coils produces a control torque. Comparison between the expected magnetic field vector and the true magnetometer data is used for the attitude determination. The magnetic attitude control and determination is intrinsically periodic due to periodic nature of the geomagnetic field variation in orbit. The control performance is specified by the generalized H2 operator norm. The paper proposes an LMI solution to this problem.