Linear Matrix Inequality Optimization Research Articles

Output Feedback T-S Fuzzy RMPC Applied to 3SSC Boost Converter

This article proposes a controller using Fuzzy Model Predictive Control (FMPC) and a fuzzy state observer applied to a three states switching cell (3SSC) boost converter. The proposed approach is an observer-based output feedback fuzzy MPC, which combines a state feedback FMPC controller with a fuzzy state observer. Moreover, a stability criterion is developed for the controller-observer procedure, considering a Takagi-Sugeno (T-S) fuzzy model, a PDC fuzzy control law, a fuzzy state observer and a state feedback FMPC, through the Linear Matrix Inequalities (LMI) optimization procedure. Furthermore, an Anti-Windup (AW) procedure is added to the control scheme. The proposed procedure is implemented for a boost converter through computer simulation, and the obtained results are compared with two MPC controllers. The analysis is done considering the time response and some performance indexes, moreover, the robust stability for the studied controller is explicit using stability ellipsoids.

A robust delay-dependent guaranteed cost PID multivariable output feedback controller design for time-varying delayed systems: An LMI optimization approach

This paper deals with the new formulated problem of designing a robust delay-dependent guaranteed optimal cost proportional-integral-derivative (PID) multivariable output feedback controller for linear uncertain time delay systems with nonlinear parameter perturbations using a linear matrix inequalities (LMI) approach. Several less conservative delay-dependent stability conditions are formulated for the time-delay system under consideration in terms of LMIs. Based on an augmented form of Lyapunov-Krasovskii functionals, the free weighting matrices and Wirtinger inequality techniques are employed to obtain improved performance. An optimal guaranteed cost PID controller which minimizes the upper bound of cost function is provided. The main advantage of the proposed approach is to decouple the input and the output gain matrices allowing to synthesize the controller gain matrices through a strict LMI technique. The synthesis conditions are thus formulated in LMI form which avoids the use of any iterative approach to resolve the feasibility problem. Two numerical examples selected from the literature are presented to illustrate the effectiveness of the developed methodology. The numerical results indicate that the proposed method performs efficiently in comparison to the approaches from the existing literature.

Robust [formula omitted] model predictive control for constrained Lipschitz non-linear systems

This paper is concerned with the robust H∞ model predictive control problem for a class of non-linear systems subject to state and input constraints and with norm bounded disturbances. It is well known that the disturbance degrades the control performance remarkably and can cause system instability. As well as, design the H∞ model predictive control based on the non-linear model is much more challenging, because the control problem changes to a non-convex non-linear problem. The main contribution is the introduction of the novel robust controller to stabilize the perturbed Lipschitz non-linear systems. The objective is to minimize the L2 gain between the disturbance input and the controlled output. The non-convex control problem is formulated as a linear matrix inequality optimization problem. The designed controller guarantees the closed-loop asymptotic stability with a prescribed H∞ disturbance attenuation level. In order to reduce conservatism, a sum of squares optimization problem is proposed to obtain the optimal value of Lipschitz coefficient. The proposed algorithm is applied to two non-linear systems, a laboratory tank and a DC/AC converter to evaluate its applicability and effectiveness.

Invariant-set design of observer-based robust control for power systems under stochastic topology and parameters changes

Power systems are subject to stochastic fluctuations which can be classified as topological or parametric. This paper models the random topological changes due to a series of lightning strokes hitting a transmission line (associated with open/reclose of circuit breakers) in a power system as a Markov jump system. Whereas the line reactance (depending on the phase conductors spacing) changes due to the random wind speed fluctuations, are represented as a stochastic external disturbances. A novel excitation control for a stochastic power system is developed. The optimal two-controller and observer gains are designed based on the attracting ellipsoid method and the linear matrix inequalities (LMI) optimization. The effectiveness of the proposed control is tested on a multimachine system.

Dynamic Output Feedback MPC of Polytopic Uncertain Systems: Efficient LMI Conditions

We focus on the design of an efficient dynamic output feedback model predictive control (DOFMPC) for linear systems with both polytopic and additive uncertainties. We tackle the problem of bilinear matrix inequality formulation which is often encountered in this type of work. In order to formulate a numerically traceable optimization problem, expressed in terms of linear matrix inequalities (LMIs), we propose a new convex stability condition by the utilization of a relaxation formula. Moreover, other inequality conditions in the optimization problem are tailored so that an efficient LMI optimization problem is formulated. Unlike in previous works, the proposed approach does not require any special structure of system matrices, which results in more flexibility. The effectiveness of the proposed approach is verified through a numerical example.

A new actuator fault‐tolerant control for Lipschitz nonlinear system using adaptive sliding mode control strategy

AbstractThis article proposed a new adaptive integral sliding mode (ISM) based fault‐tolerant control (FTC) strategy to solve the actuator's faults and failures compensation problem for the class of Lipschitz nonlinear systems. A nominal state feedback virtual control law is designed first to stabilize the Lipschitz nonlinear system and to attain the desired nominal performance. To cater for the effect of faults and failures, the control allocation (CA) scheme reorganizes the virtual input signals among the healthy redundant actuators based on actuator's effectiveness level. Then, a nonlinear adaptive integral sliding mode controller (ISMC) is incorporated with the CA scheme to compensate for unknown disturbance and uncertainties effect that arises in the system by virtue of actuator faults/failures and error in fault estimation . An effective synthesis procedure is adopted to ensure the closed‐loop stability condition using linear matrix inequality (LMI) optimization. Finally, the FTC scheme is tested to achieve maneuvering control of coaxial octorotor unmanned aerial vehicle (UAV) system. Simulations are performed on the nonlinear system at different actuator faults/failures combinations. Moreover, the effect of wind‐gust, parameter variations, estimated state feedback and sensor noise are considered in nonlinear simulations. Finally, the results obtained during faults/failures are compared with the nominal condition and fixed ISMC based CA scheme.

Voltage Sensorless Model Predictive Control for a Grid-Connected Inverter With LCL Filter

This article introduces a sensorless model predictive control (MPC) scheme for a grid-connected inverter with an inductive–capacitive–inductive ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">LCL</i> ) filter using only the grid-side current measurement. A state estimator and a disturbance observer are designed based on the Lyapunov stability theory to reduce the number of sensors and to eliminate the steady-state error. A cost function penalizing the state tracking error is used for the MPC design, and the optimal weights of the cost function are systematically obtained by solving a linear matrix inequality (LMI)-based optimization problem. The variation in grid impedance is taken into account in the LMI optimization. The stability analysis of the overall system is presented, and the frequency responses of the closed-loop and open-loop systems are presented to verify suppression of the filter resonance frequency component. The effectiveness and feasibility of the proposed controller are validated through frequency response analysis and comparative simulation results. Experimental results are also presented to demonstrate the efficacy of the proposed control scheme compared to the linear quadratic regulator method.

Ellipsoidal-Set Design of the Decentralized Plug and Play Control for Direct Current Microgrids

Recently the integration of renewable energy resources to direct-current microgrids has become a hot research topic. The voltage stability problem is of paramount importance when the system is subject to external disturbances, parameters uncertainties, and plug-and-play regimes. This paper introduces a novel decentralized voltage tracking for a direct-current islanded microgrid. It consists of numerous Distributed Generation units. The decentralized controller of each distributed generator adjusts the voltage at the point of common coupling to track the desired reference. The proposed control copes with the plug-and-play operation of the microgrid. This means that the possibility of connection/disconnection distributed generators without deteriorating the stability of the overall microgrid is done through the invariant ellipsoid set and the linear matrix inequality optimization. Another merit of the proposed control is that updating the rest of the controllers is not required when a distributed generator is plugged in or out. Moreover, the proposed decentralized controller just uses local states (information) of its distributed generator only. Many simulations and practical studies with different scenarios have been conducted in this paper to verify the performance of the proposed controllers. Comparison with the existing schemes is included.

Robust linear parameter-varying output-feedback control of permanent magnet synchronous motors

This paper investigates the design of a robust linear parameter-varying (LPV) controller for speed regulation of surface permanent magnet synchronous motors (SPMSMs). Motor dynamics is defined in the α–β stationary frame and a parameter-varying model formulation is provided to describe its nonlinear dynamics. A robust gain-scheduled LPV dynamic output-feedback controller is designed to guarantee the asymptotic stability and performance requirements, as well as, guarantee robustness against parameter perturbations and torque load disturbances. As a novel aspect in the SPMSM control, the real-time impact of temperature variation on the winding resistance and magnet flux during motor operation is explicitly considered in the LPV modeling as a scheduling parameter and the subsequent LPV control design compensating for demagnetization effects in the motor response. The controller synthesis conditions guaranteeing stability and robust performance to norm-bounded uncertainty in the system matrices are formulated in a convex linear matrix inequality (LMI) optimization framework. Finally, the validity of the proposed method is assessed in simulation studies. The closed-loop simulation studies demonstrate that the proposed LPV controller provides improved transient response with respect to settling time, overshoot, and disturbance rejection in tracking the velocity profile under the influence of parameter perturbation, temperature variations, and load disturbances.

Average Dwell Time Based Smooth Switching Linear Parameter-Varying Proportional-Integral-Derivative Control for an F-16 Aircraft

Switching control methods have great potential applications in flight control system design. However, nonsmooth control commands at switching instants could lead to performance degradations or bring in safety risks. This paper presents a smooth switching proportional-integral-derivative (PID) control method for linear parameter-varying (LPV) systems to solve this issue. By introducing a transition parameter subspace between any two neighboring LPV subsystems, the switched controller gains are designed to be smoothly varied when the parameter trajectory passes through these subspaces, and the Lyapunov function in the transition subspace is designed independently to make the algorithm less conservatism. The controller synthesis condition is formulated as a linear matrix inequality (LMI) optimization problem using Finsler’s lemma. The concept of average dwell-time (ADT) is employed to analyze the performance of the resulting closed-loop system. The effectiveness of the ADT-based smooth switching control strategy is demonstrated by applying it to the nonlinear longitudinal model of the F-16 aircraft, and the simulation results are compared with the traditional ADT switching control method. The results show that the proposed method can achieve a better transition performance with a simpler control structure.

Extended hybrid control scheme for asynchronous switching

This paper is devoted to the problem of extended hybrid control for asynchronous switching between system modes (we call each subsystem a mode) and controller candidates. Such undesirable behavior is caused by mismatch delay. Since asynchronous switching is relevant in many switched systems, this paper presents highly impressive results in stabilizing and controlling a switched linear system infected by mismatch delay. In this technical note, an asynchronous switched system is considered as a switched system with new stable and unstable subsystems.Through piecewise Lyapunov-like function (LLF) approach, two different mode-dependent dwell time (MDT) structures are designed. These dwell time structures satisfy a lower bound and an upper bound for stable and unstable part of each controlled subsystem respectively. In this regard, a hybrid control scheme with L2-gain stability analysis is provided for the mentioned system to cover the mismatch defect. The obtained boundary conditions can be incorporated with the synthesis problem in convex formation. Besides, to have more satisfying results, a rest supervisor is also considered to enforce the reset rules to the controller candidates. By determining acceptable dwell time parameters, the controller gain matrices of the new approach will be calculated to solve linear matrix inequality (LMI) optimization. Finally, the effectiveness of the obtained theoretical results is demonstrated via a numerical example.

Model-Based Fault Detection and Isolation in DC Microgrids Using Optimal Observers

DC microgrids require advanced protection techniques for fault detection and isolation (FDI). In this work, an FDI method able to respond to different types of component faults is developed based on system modeling. First, the state-space representation of a multiterminal dc microgrid with component faults is derived. Then, an FDI function based on <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${\mathcal {H}}_{-}/{\mathcal {H}}_{\infty }$ </tex-math></inline-formula> observers is designed. To achieve the desired selectivity in fault isolation, the linear matrix inequality (LMI) optimization approach is adopted in the observer design. The performance of the proposed FDI method is verified under the real-time (RT) simulation of a three-terminal low-voltage dc microgrid and with a small-scale laboratory dc grid. The proposed FDI method is proved to be effective to detect and isolate different faults in dc microgrids with a response time of 1 ms.

Robust Actuator Fault Reconstruction for Takagi-Sugeno Fuzzy Systems with Time-varying Delays via a Synthesized Learning and Luenberger Observer

This paper addresses the problem of robust actuator fault reconstruction for Takagi-Sugeno (T-S) fuzzy systems subjects to actuator faults, unknown inputs and time-varying delays via a Fuzzy Synthesized Learning and Luenberger Observer (FSL2O). Through a coordinate transformation, the original T-S fuzzy system is decomposed into two subsystems: subsystem-1 effected by actuator faults and subsystem-2 effected by unknown inputs. In the presented FSL2O methodology, a Reduced-Order Fuzzy Learning Observer (ROFLO) is explored for the subsystem-1 to reconstruct actuator faults accurately while a Reduced-Order Fuzzy State (Luenberger) Observer (ROFSO) is designed for the subsystem-2 based on the H∞ control technique such that it has strong robustness against the unknown inputs. The synthesized design of the ROFLO and the ROFSO is formulated in a unified manner in terms of Linear Matrix Inequalities (LMIs) that can be conveniently solved using LMI optimization technique. In addition, as a comparison, a full-order FLO is suggested for robust actuator fault reconstruction. Finally, a numerical example and simulation are provided to demonstrate the effectiveness of the proposed approaches.

A novel active fault-tolerant control for spacecrafts with full state constraints and input saturation

This paper proposes an active fault-tolerant control (AFTC) system for spacecrafts subject to model uncertainty, external disturbance and actuator fault simultaneously. Fault diagnosis is implemented by a robust fault observer with a simple structure. The observer can separately estimate the fault in the existence of disturbance and uncertainty. The influence on observation performance from disturbance and uncertainty is attenuated by linear matrix inequality (LMI) optimization. For the fault-tolerant controller, asymmetric barrier Lyapunov function and backstepping method are used to constrain all the states. Meanwhile, the control input is restricted by a saturation function. Validation and comparative simulations are implemented to demonstrate the proposed AFTC method.

Simultaneous actuator and sensor faults estimation design for LPV systems using adaptive sliding mode observers

This paper considers the problem of simultaneous actuator and sensor faults estimation for linear parameter varying system expressed in the polytopic representation based on robust adaptive sliding mode observer technique. We start by constructing two polytopic sub-systems using transformed coordinate system design. The first sub-system includes only actuator faults. Hence, the second one is potentially faulty sensor and it is free from actuator faults. Assuming that sensor faults distribution matrix verifies the observer matching condition, we propose to conceive two adaptive sliding mode observers for estimating system states, as well as actuator and sensor faults in the presence of external disturbances. Anyway, in practise, the so-called observer matching condition is usually hard to satisfy due to the complexity and unpredictability of the system faults. Subject to relaxing this conservative condition, a new simultaneous fault estimation scheme is investigated by introducing an adaptive sliding mode observer with intermediate variable in order to estimate sensor faults. In formalism of linear matrix inequalities optimisation methods, sufficient conditions are developed with H∞ optimal performances to guarantee the stability of the proposed observers. Finally, simulation results on VTOL aircraft defence system are highlighted to illustrate the effectiveness of the proposed simultaneous fault estimation.

Pareto-Optimal Pilot Design for Cellular Massive MIMO Systems

We introduce a non-orthogonal pilot design scheme that simultaneously minimizes two contradicting targets of channel estimation errors of all base stations (BSs) and the total pilot power consumption of all users in a multi-cell massive MIMO system, subject to the transmit power constraints of the users in the network. We formulate a multi-objective optimization problem (MOP) with two objective functions capturing the contradicting targets and find the Pareto optimal solutions for the pilot signals. Using weighted-sum-scalarization technique, we first convert the MOP to an equivalent single-objective optimization problem (SOP), which is not convex. Assuming that each BS is provided with the most recent knowledge of the pilot signals of the other BSs, we then decompose the SOP into a set of distributed non-convex optimization problems to be solved at individual BSs. Finally, we introduce an alternating optimization approach to cast each one of the resulting distributed optimization problems into a convex linear matrix inequality (LMI) form. We provide a mathematical proof for the convergence of the proposed alternating approach and a complexity analysis for the LMI optimization problem. Simulation results confirm that the proposed approach can significantly reduce pilot power, whilst maintaining the same level of channel estimation error as in a baseline.

Robust model predictive control for nonlinear parameter varying systems without computational delay

SummaryThis article proposes a one‐step ahead robust model predictive control (MPC) for discrete‐time Lipschitz nonlinear parameter varying (NLPV) systems subject to disturbances. Within the proposed design framework, the optimization that generates the MPC policy to be implemented at next time instant is executed in advance during the current sampling period based on future state prediction. This new feature allows avoidance of the online computational delay existing in the traditional MPC settings and improves the control performance. The proposed MPC is proved to be recursively feasible with the guarantee for robust closed‐loop system stability and satisfaction of input and output constraints. A tractable linear matrix inequality (LMI) optimization problem is formulated to compute the control gains at each time instant. The computational complexity of the obtained LMI problem is also analyzed. The one‐step ahead robust MPC is further developed to cover discrete‐time Lipschitz NLPV systems with disturbance compensation. Efficacy and performance improvement of the design are demonstrated through a numerical example and an application to adaptive cooperative cruise control for automated vehicles under variable road geometry.

Lyapunov-based Methods for Maximizing the Domain of Attraction

This paper investigates Lyapunov approaches to expand the domain of attraction (DA) of nonlinear autonomous models. These techniques had been examined for creating generic numerical procedures centred on the search of rational and quadratic Lyapunov functions. The outcomes are derived from all investigated methods: the method of estimation via Threshold Accepted Algorithm (TAA), the method of estimation via a Zubov technique and the method of estimation via a linear matrix inequality (LMI) optimization and genetic algorithms (GA). These methods are effective for a large group of nonlinear models, they have a significant ability of improvement of the attraction domain area and they are distinguished by an apparent propriety of direct application for compact and nonlinear models of high degree. The validity and the effectiveness of the examined techniques are established based on a simulation case analysis. The effectiveness of the presented methods is evaluated and discussed through the study of the renowned Van der Pol model.

Optimizing the performance of the feedback controller for state‐based switching bilinear systems

SummaryThis article is concerned with the design and performance optimization of feedback controllers for state‐based switching bilinear systems (SBLSs), where subsystems take the form of bilinear systems in different state space polyhedra. First, by further dividing the subregions into smaller regions and designing region‐dependent feedback controllers in the resulting regions, the SBLSs can be transformed into corresponding switching linear systems (SLSs). Then, for these SLSs, by imposing contractility conditions on the Lyapunov functions, an upper bound on the infinite horizon quadratic cost can be obtained. Optimizing this upper bound yields the controller design. The optimization problem is formulated as a linear matrix inequalities optimization problem, which can be solved efficiently. Finally, the stability of the close‐loop system under the proposed controller is established step by step through a decreasing overall Lyapunov function.

Secure communication system in maritime navigation using state observer with linear matrix inequality

ABSTRACT With emerge of smart navigation, the secure communication issues have drawn extensive attention on maritime agendas between ships or with the shore. This paper presents a chaotic secure communication scheme by using observer design for maritime navigation and transportation systems. The proposed scheme involves three key factors: chaotic encryption, state observer, and chaotic decryption. The chaotic system, as the encryption keys carrying confidential information, will be sent from transmitter to the receiver through a public channel. It is obvious that the fewer signals are transmitted on the public channel, the higher security of the communication system is possible. A state observer is designed to estimate all system states when only partial states are detectable on the public channel. The robust observer gain is implemented in terms of linear matrix inequality (LMI) for convex optimization. The process of information encryption and recovery has been discussed in detail. From the simulation results, it is found that the observer-based method can robustly estimate full state variables by using system output signals with LMI optimization. Based on these updated states with the the state observer, the original information is accurately recovered for safe navigation of vessels with reliability and efficiency.