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As a category of the recurrent neural network (RNN), zeroing neural network (ZNN) can effectively handle time-variant optimization issues. Compared with the fixed-parameter ZNN that needs to be adjusted frequently to achieve good performance, the conventional variable-parameter ZNN (VPZNN) does not require frequent adjustment, but its variable parameter will tend to infinity as time grows. Besides, the existing noise-tolerant ZNN model is not good enough to deal with time-varying noise. Therefore, a new-type segmented VPZNN (SVPZNN) for handling the dynamic quadratic minimization issue (DQMI) is presented in this work. Unlike the previous ZNNs, the SVPZNN includes an integral term and a nonlinear activation function, in addition to two specially constructed time-varying piecewise parameters. This structure keeps the time-varying parameters stable and makes the model have strong noise tolerance capability. Besides, theoretical analysis on SVPZNN is proposed to determine the upper bound of convergence time in the absence or presence of noise interference. Numerical simulations verify that SVPZNN has shorter convergence time and better robustness than existing ZNN models when handling DQMI.

The stability analysis problem is considered for multiarea load frequency control (LFC) systems with electric vehicles (EVs) and time delays. The novel linear operator inequality approach is proposed and a less conservative delay-dependent stability condition is achieved. First, the model of the multiarea LFC system with EVs and delays is expressed by the partial integral equation (PIE) at the first time. Then, a complete quadratic Lyapunov-Krasovskii functional is built in the form of an inner product of the linear partial integral (PI) operator. The novel stability criteria with less conservatism are proposed in the form of linear operator inequality. Moreover, the relationships between the delay margins and the controller parameters are shown. Finally, the simulations are conducted on both one-area and two-area LFC systems to show the effectiveness of the proposed approach.

This paper deals with the sliding mode stabilization for chaotic systems. In the system under consideration, the nonlinear function is one-sided Lipschitz with quadratic inner-boundedness. Specifically, a non-fragile sliding mode surface is constructed, and the sufficient condition for the convergence is derived. Then, a new feedback law is proposed to enable the state trajectories of the closed-loop system to reach the sliding mode surface in finite time. Finally, an example in the background of the unified chaos system is simulated to show the validation of the designed controller.

This paper presents design and evaluation of a Quadratic Buck Converter (QBC). A step-by-step procedure to select the converter’s component values and semiconductor device ratings is demonstrated. A prototype QBC with a simple closed loop output voltage control is constructed and experimentally evaluated. It is shown that the converter performs well within the design specification, has good output voltage regulation and fast transient response, and achieves the highest efficiency of 82%.

A control design framework for the coupled stability problem in robotics is presented. The proposed framework fundamentally generalizes the conventional passivity-based approaches to the coupled stability problem. In particular, it allows for stabilization of not necessarily passive robot-environment interaction where both the manipulator and the environment are dissipative systems with quadratic supply rates. In contrast with existing results, the proposed framework can be used in combination with an arbitrary robot’s tracking control algorithm, and its stabilizing action when in contact with environment does not affect the robot’s trajectory tracking performance in free space. The framework is based on the recently developed nonplanar conic systems formalism and generalized scattering-based stabilization methods. A detailed design example is presented which illustrates the capabilities of the proposed method.

In this paper, for a class of continuous-time multivariable linear systems with strong coupling property, a new optimal tracking controller is proposed, which can simultaneously decouple the closed-loop system in its dynamic, and provide optimal performance. Firstly, a new quadratic performance index considering decoupling design is introduced, and then the optimal tracking controller is derived by minimizing the new index according to the minimum principle. Finally, the weighting matrices are provided, by using which decoupling and tracking can both be realized. Experiments on a Coupled-Tank are conducted, whose results show the superiority of the proposed method comparing with the conventional linear quadratic tracking (LQT) controller.

This brief mainly deals with the issue of guaranteed cost impulsive synchronization of uncertain multi-agent systems from the multiplex network prospective, where the uncertain time-varying system parameters are supposed to be norm-bounded. By means of a group of linear matrix inequalities, the effective guaranteed cost impulsive control is designed to not only ensure that the trajectories of all followers synchronize with the leader, but also guarantee that the control cost is no higher than an upper bound of the quadratic guaranteed cost function. Numerical example demonstrates the feasibility of theoretical results.

This article focuses on the sampled-data output-feedback control problem for nonlinear systems represented by Takagi-Sugeno fuzzy affine models. An input delay approach is adopted to describe the sample-and-hold behavior of the measurement output. Via augmenting the system states with the control input, the resulting closed-loop system is converted into a singular system first. Based on the piecewise quadratic Lyapunov-Krasovskii functionals, some novel results on the sampled-data piecewise affine output-feedback controller design are attained by employing some convexification techniques. The simulation studies are presented to illustrate the effectiveness of the proposed scheme.

Recent decades have witnessed a trend that control-theoretical techniques are widely leveraged in various areas, e.g., design and analysis of computational models. Computational methods can be modeled as a controller and searching the equilibrium point of a dynamical system is identical to solving an algebraic equation. Thus, absorbing mature technologies in control theory and integrating it with neural dynamics models can lead to new achievements. This work makes progress along this direction by applying control-theoretical techniques to construct new recurrent neural dynamics for manipulating a perturbed nonstationary quadratic program (QP) with time-varying parameters considered. Specifically, to break the limitations of existing continuous-time models in handling nonstationary problems, a discrete recurrent neural dynamics model is proposed to robustly deal with noise. This work shows how iterative computational methods for solving nonstationary QP can be revisited, designed, and analyzed in a control framework. A modified Newton iteration model and an improved gradient-based neural dynamics are established by referring to the superior structural technology of the presented recurrent neural dynamics, where the chief breakthrough is their excellent convergence and robustness over the traditional models. Numerical experiments are conducted to show the eminence of the proposed models in solving perturbed nonstationary QP.

For the conservatism issue of state-feedback control for Takagi-Sugeno (T-S) fuzzy systems, a novel local controller design method and stability analysis approach are proposed in this article. First, based on a membership function piecewise linearization technique, a local linear controller is proposed to form a closed-loop system. Then, a series of system stability conditions are derived using quadratic and piecewise function approaches. Further, with a designed fuzzy local controller and fuzzy Lyapunov function, less conservative stability conditions are obtained. Finally, a simulation example is adopted to make comparisons with existing and proposed methods. The results clearly show the conservatism reduction and excellent performance of the proposed approach.

To address the low computational efficiency and accuracy for reliability optimization of flexible mechanisms, the mean-probability decomposition-coordination-based extreme support vector machine regression (MPDC-ESVR) method based on the dynamics and uncertainty is proposed. Firstly, a dynamical model is built to calculate the maximum deformation. Then, the ESVR is used as a surrogate model to study the reliability of the flexible mechanisms. Finally, the MPDC are adopted to optimize the weight of the flexible mechanisms considering multiple failure modes. It is proved that the computational efficiency and accuracy of the present methodology are superior to those of Monte Carlo simulation (MCS) and quadratic polynomial-Monte Carlo simulation (QP-MCS) through exemplification with a two-link flexible manipulator. The results indicate the two-link flexible manipulator optimized by current MPDC is lighter than that by the equal distribution probabilistic method and the original manipulator, which is essential for low cost-effectiveness without compromise to safety.

In this article, we propose a new method to ob-tain feedback controllers of an unknown dynamical systemdirectly from noisy input/state data. The key ingredient ofour design is a new matrix S-lemma that will be proven inthis article. We provide both strict and nonstrict versionsof this S-lemma, which are of interest in their own right.Thereafter, we will apply these results to data-driven con-trol. In particular, we will derive nonconservative designmethods for quadratic stabilization, H2 and H∞ control, allin terms of data-based linear matrix inequalities. In contrastto previous work, the dimensions of our decision variablesare independent of the time horizon of the experiment. Ourapproach, thus, enables control design from large datasets.

This article deals with the robust control design for linear systems with input and state delays, subject to nonvanishing matched disturbances. The controller is synthesized with the Lyapunov redesign technique in two stages: first, an optimal predictor compensates the input delay of the nominal system while a quadratic performance index is minimized. Then, the robust component guarantees that the solutions are ultimately bounded. The theoretical results are experimentally validated through a dehydration process, with the controller digital implementation on an industrial programmable automation controller cDAQ-9132.

This article proposes a systematic synthesis method to identify the optimum converter topology for a specified voltage conversion ratio. This gain-oriented converter synthesis is formulated as an inverse problem around the inductor flux balance equations. The proposed synthesis method consists of two processes. A set of distinct converter topologies is first synthesized from the specified voltage conversion ratio by obtaining the solutions for a set of six inverse equations in twelve unknowns. The optimal topology for any intended application can be identified based on the desired performance metrics. The complete synthesis method is illustrated with quadratic buck–boost gain as an example. In total, 25 distinct topologies are synthesized using the first process, and their feasibility is validated by PLECS simulation. In total, three case studies are reported to explain the second process. Ground-referenced output and the minimum number of switches are used as the first two selection criteria in all the case studies. Minimum peak inductor current, minimum component stress factor, and minimum voltage and current stress are the third selection criterion in Case Studies-1, 2, and 3, respectively. The steady-state operations of two optimal converters selected in Case Study-1 were verified experimentally.

This paper is concerned with event-triggered and guaranteed cost finite-time control for switched systems with dynamic quantized output feedback and exogenous disturbances. First, one common strategy is superseded by one mode-dependent event-triggered strategy, which means each subsystem possesses its own event-triggered substrategy. Second, considering the hardship of obtained system state information, a dynamic quantized output feedback controller is used to stabilize the switched system. Third, by using the methods of multiple Lyapunov functionals, free-weighting matrices and the average dwell time for the switched system, the sufficient condition of finite-time boundedness (FTB) is obtained for the switched system; and a synthesis procedure is provided to obtain the dynamic output feedback controller gain, event-triggered strategy parameters and an upper bound of the quadratic performance function. Finally, a numerical simulation is given to demonstrate the effectiveness of the proposed method.

The distributed fault detection and isolation of linear discrete time-varying multi-agent systems subject to heterogeneous dynamics and norm bounded model uncertainties is investigated. By combining the model uncertainties and external disturbances into a new generalized disturbance, a distributed closed-loop residual generator is constructed based on the estimate of the generalized disturbance. Then, the concerned fault detection is transformed into an indefinite quadratic minimum problem by using the finite-horizon robust H ∞ filtering method, for which necessary and sufficient minimum conditions are provided by the Krein-space theory. Afterwards, a computationally efficient recursive algorithm is further developed to determine the residual for individual agent. Based on the resulting residuals, the fault occurrence can be alerted by devising a novel distributed fault detection scheme , which is then applied for the fault isolation by some appropriate transformation of the output measurements. Finally, both numerical and practical simulations are proposed to verify the effectiveness of the proposed algorithm.

PURPOSE Thermal dose delivery in microwave hyperthermia for cancer treatment is expected to benefit from the introduction of ultra-wideband (UWB)-phased array applicators. A full exploitation of the combination of different frequencies to improve the deposition pattern is, however, a nontrivial problem. It is unclear whether the cost functions used for hyperthermia treatment planning (HTP) optimization in the single-frequency setting can be meaningfully extended to the UWB case. METHOD We discuss the ability of the eigenvalue (EV) and a novel implementation of iterative-EV (i-EV) beam-forming methods to fully exploit the available frequency spectrum when a discrete set of simultaneous operating frequencies is available for treatment. We show that the quadratic power deposition ratio solved by the methods can be maximized by only one frequency in the set, therefore rendering EV inadequate for UWB treatment planning. We further investigate whether this represents a limitation in two realistic test cases, comparing the thermal distributions resulting from EV and i-EV to those obtained by optimizing for other nonlinear cost functions that allow for multi-frequency. RESULTS The classical EV-based single-frequency HTP yields systematically lower target SAR deposition and temperature values than nonlinear HTP. In a larynx target, the proposed single-frequency i-EV scheme is able to compensate for this and reach temperatures comparable to those given by global nonlinear optimization. In a meninges target, the multi-frequency setting outperforms the single-frequency one, achieving better target coverage and 0.5∘C higher T90 in the tumor than single-frequency-based HTP. CONCLUSIONS Classical EV performs poorly in terms of resulting target temperatures. The proposed single-frequency i-EV scheme can be a viable option depending on the patient and tumor to be treated, as long as the proper operating frequency can be selected across a UWB range. Multi-frequency HTP can bring a considerable benefit in regions typically difficult to treat such as the brain.

This article proposes a robust model predictive control (MPC) algorithm for the tracking problem of wheeled mobile robots. The robots are subject to bounded disturbances and various practical constraints. Particularly, the incremental input constraint is introduced in the consideration of the safety and comfortability needs in real life. Conditions on the acceleration of the leader robot are derived to guarantee the satisfaction of the incremental input constraint of follower robot. To compensate for the effect of disturbances, a disturbance observer is designed to obtain the estimation of the disturbances, which together with the optimal control input of MPC optimization is contained in the actual control input. Also, a novel quadratic robustness constraint is developed to handle the disturbance estimation error, which allows the designer to balance the initial feasible region and control performance. The proposed algorithm can ensure recursive feasibility, robust constraint satisfaction, and closed-loop stability. Finally, both simulation and experiment results are provided to verify the theoretical properties.

In this paper, the output reachable set synthesis problem for periodic piecewise time-varying systems has been addressed for the first time. Generalized periodic time-varying conditions of the closed-loop system to guarantee the system output bounded by a collection of finite ellipsoids are developed. The decoupling of time-varying observer and controller gains is achieved by a technical lemma . Moreover, by using time-varying matrix functions in multiple linear-interpolative forms and the relaxed quadratic matrix polynomial definiteness results, sufficient condition is developed to determine the periodic time-varying observer and controller with reduced conservatism. A tractable iterative algorithm is proposed to obtain the periodic time-varying observer and controller gains. A numerical example is presented to illustrate the validity of proposed methods.

This paper is concerned with the forecasting aided state estimation (FASE) problem for power distribution networks (PDNs) subject to nonlinear measurements and limited communication resources. For the sake of using bandwidth more effectively, a special closed-loop event triggering condition is first designed with the hope to reduce unnecessary data transmission from the measurement side to the remote estimator. And an event-based robust filtering algorithm is proposed to improve the estimation performance of estimator with the nonlinear intermittent observations. In this algorithm, the measurement output function with high-order nonlinearity is reasonably reduced to a quadratic alternative form, in order to avoid the computation burden caused by the use of the second-order extended Kalman filter (SOEKF), the quadratic nonlinear function is further linearized by Taylor series with quadratic norm bound. Furthermore, an upper bound of the filtering error covariance containing some uncertainties (includes quadratic term and non-triggering errors) is derived and subsequently minimized at each time step. The desired filter gain is obtained by recursively solving a set of Riccati-like matrix equations, which is easy to implement via online computation. Finally, the effectiveness of the proposed algorithm is demonstrated using the standard IEEE 13-bus and 123-bus distribution test feeders with both phasor measurement unit (PMU) and conventional measurements.

This paper investigates an ${H}_{{\infty }}$ static output feedback for a low-frequency (LF) networked control system (NCS). A decentralized event-triggered scheme (DETS) is proposed to reduce the network communication loads. The LF NCS with the DETS is modeled as a time-delay system with an LF constraint. With this model, ${H}_{{\infty }}$ performance analysis is developed via an LF integral quadratic constraint method and a generalized Kalman–Yakubovich–Popov lemma. Furthermore, a detailed controller design algorithm is presented to obtain an ${H}_{{\infty }}$ static output feedback controller for the LF NCS with the DETS via a two-stage approach. The numerical results are provided to demonstrate the effectiveness and superiority of the proposed techniques.

This article introduces a control design framework for modern dc–dc topologies with high-order dynamics. In particular, model-based and model-free approaches using high-order controllers are introduced. The model-based approach permits the use of a minimum number of sensors, even for converters with a high number of components (e.g., multilevel, quadratic, input/output $LC$ filter-based converters, etc.). This setting does not require estimation of state variables and its gain tuning can be achieved by selecting time-response specifications. The proposed model-free approach control exhibits the same, as well as some additional characteristics. Namely, controllers can be synthesized without the requirement of an explicit dynamic model, and gain tuning with guaranteed stability is directly achieved from measurement data. The latter controller is implemented in discrete time, which facilitates a digital implementation. The proposed approaches are validated through the control design and closed-loop implementation of a sixth-order topology.

This article studies full-state constrained control for high-order nonlinear systems with unknown multiple time-varying powers and serious parameter unknowns. Due to the simultaneous existence of unknown powers and full-state constraints, we construct a log-type quadratic barrier Lyapunov function (BLF) rather than a quadratic Lyapunov function. By skillfully combining the log-type BLF, adding a power integrator technique and adaptive technique, an adaptive state feedback controller is developed. Under feasibility conditions, which are provided as sufficient conditions for the existence of proposed full-state constrained control, it is proved that all the signals of the closed-loop system are bounded, original system states converge to zero and full-state constraints are not violated.

The actual problem of synthesizing the optimal control law for the intermittent heating mode of office buildings is considered, which consists in the programmed reduction of the room temperature during off-hours. The analysis of information sources showed the absence of sufficiently justified methods for solving the problem of optimizing the thermal processes of buildings, which provide comfortable conditions for the functioning of personnel, on the one hand, and save costs for buildings maintenance, on the other hand. The statement of the building thermal state optimal control problem is formulated, which contains a mathematical model of the process, a control goal, constraints on control actions and an integral quadratic quality criterion, including deviations of the room temperature from a given program and heat consumption. The limitation on the control action is taken into account by the method of penalty functions. As a mathematical model of the optimized thermal process, a two-dimensional controlled system of differential equations with constant coefficients is applied. The values of these coefficients are determined on the basis of building similarity criteria, which allows solving the optimization problem in a dimensionless form. The model includes a control action - the supplied heat flux, and a disturbing action - the ambient temperature, changing according to a given harmonious law. The numerical solution of the optimal control problem is implemented by the Chernous'ko method of successive approximations. A description of the user interface is given, as well as examples of the implementation of the thermal state optimal control. The proposed software allows on the stage of designing the heating system to obtain express assessments of various thermal modes of the building, and can also be used as computer support for automated individual heating points. Keywords: intermittent heating mode, optimal control, mathematical model, control quality criterion, control constraints, penalty function, successive approximations, program interface, automated individual heating point.

This paper presents a novel technique for optimum load shedding in a power system based on under voltage considerations. A quadratic performance index based on voltage deviation has been adopted. T...

DC/DC converters, which have a quadratic term of the duty cycle, are useful, when wide voltage transformation ratios have to be obtained. Taking a d-square step-down converter as an example, the function of the converter, the generation of the large and small signal models is explained. From the voltage transformation ratio, a control law is derived and the behavior of the feed-forward converter is shown by simulations. Results of two other quadratic converters are also shown.

This paper considers the problem of designing a shifting state-feedback controller via quadratic parameter-dependent Lyapunov functions (QPDLFs) for systems subject to symmetric time-varying saturations. By means of the linear parameter varying (LPV) framework and the use of the shifting paradigm and the ellipsoidal invariant theory, it is shown that the solution to this problem can be expressed with linear matrix inequalities (LMIs) which can efficiently be solved via available solvers. Specifically, three hyper-ellipsoidal regions are defined in the state-space domain for ensuring that the control action remains in the linearity region of the actuators where saturation does not occur. Furthermore, the closed-loop convergence speed is regulated online according to the instantaneous saturation limit values through the shifting paradigm concept. The main characteristics of the proposed approach are validated by means of two illustrative examples. This work has been partially funded by the Spanish State Research Agency (AEI) and the European Regional Development Fund (ERFD) through the project SaCoAV (ref. PID2020-114244RB-I00). This work has also been partially funded by AGAUR of Generalitat de Catalunya, Spain through the Advanced Control Systems (SAC) group grant (2017 SGR 482) and by the University of Stavanger, Norway through the project IN-12267. A. Ruiz is also supported by the Secretaria d’Universitats i Recerca de la Generalitat de Catalunya, Spain, the European Social Fund (ESF) and AGAUR under a FI SDUR grant (ref. 2020 FI-SDUR 00097).

A protection scheme is proposed using alienation method derived from coherence model which is a backup protection method for the differential overcurrent protection of synchronous generators. This scheme which is realized by the computational technique based on the alienation coefficients estimated for generator voltage and current signals is considered to be mounted beside the main differential protection system, which operates in the cases that differential protection is unable to detect the internal faults. This novel protection algorithm operates by adjusting the alienation settings of the suggested relay that sends the trip signal to the three‐phase circuit breaker of the protected generator. In the proposed method, fault occurrences can be determined regardless of variations of terminal voltage and current in different working states of synchronous generator. This is done by designing new quadratic‐tripping characteristics based on alienation limits for the electrical signals. To demonstrate the proposed method, a motor‐synchronous generator set with built instrument transformers, for measuring voltage and current data at the generator terminals, are used. Extensive experimental investigations validate the functionality of this novel protection scheme under different abnormal, unbalance and operating conditions for the generator under test.

This article mainly focuses on the problem of synchronization in finite and fixed time for fully complex-variable delayed neural networks involving discontinuous activations and time-varying delays without dividing the original complex-variable neural networks into two subsystems in the real domain. To avoid the separation method, a complex-valued sign function is proposed and its properties are established. By means of the introduced sign function, two discontinuous control strategies are developed under the quadratic norm and a new norm based on absolute values of real and imaginary parts. By applying nonsmooth analysis and some novel inequality techniques in the complex field, several synchronization criteria and the estimates of the settling time are derived. In particular, under the new norm framework, a unified control strategy is designed and it is revealed that a parameter value in the controller completely decides the networks are synchronized whether in finite time or in fixed time. Finally, some numerical results for an example are provided to support the established theoretical results.

Periodic event-triggered control (PETC) evaluates the triggering rule periodically and is well-suited for implementation on digital platforms. This paper investigates PETC design for nonlinear systems affected by external disturbances under the impulsive system formulation. Sufficient conditions are provided to ensure the input-to-state stability of the resulting closed-loop system for the state feedback and the observer-based output feedback configurations separately. For each configuration, the sampling period and the triggering functions are provided explicitly. Sufficient conditions in the form of linear matrix inequalities are provided for the PETC design of incrementally quadratic nonlinear systems. Two examples are given to illustrate the effectiveness of the proposed method.

We present an advanced and novel control method to enable actuated Spring Loaded Inverted Pendulum model to walk over rough and challenging terrains. The high-level philosophy is the decoupling of the controls of the vertical and horizontal states. The vertical state is controlled via Backstepping-Barrier Function (BBF) based quadratic programs: a combination of control Lyapunov backstepping and control barrier function, both of which provide inequality constraints on the inputs. The horizontal state is stabilized via Hybrid-Linear Inverted Pendulum (H-LIP) based stepping, which has a closed-form formulation. Therefore, the implementation is computationally-efficient. We evaluate our method in simulation, which demonstrates the aSLIP walking over various terrains, including slopes, stairs, and general rough terrains with uncertainties., Comment: 8 pages, 7 figures. To Appear in IEEE Robotics and Automation Letters, 2021

Conditions for robust input–output stability of barrier-based model predictive control of linear systems with linear and convex nonlinear (hard or soft) constraints are established through the construction of integral quadratic constraints (IQCs). The IQCs can be used to determine sufficient conditions for global closed-loop stability. In particular, conditions for robust stability can be obtained in the presence of unstructured model uncertainty. IQCs with both static and dynamic multipliers are developed and appropriate convex searches for the multipliers are presented. The effectiveness of the robust stability analysis is demonstrated through an illustrative numerical example.

Control Lyapunov functions (CLFs) and control barrier functions (CBFs) have been used to develop provably safe controllers by means of quadratic programs (QPs), guaranteeing safety in the form of trajectory invariance with respect to a given set. In this letter, we show that this framework can introduce equilibrium points (particularly at the boundary of the safe set) other than the minimum of the Lyapunov function into the closed-loop system. We derive explicit conditions under which these undesired equilibria (which can even appear in the simple case of linear systems with just one convex unsafe set) are asymptotically stable. To address this issue, we propose an extension to the QP-based controller unifying CLFs and CBFs such that the resulting system trajectories avoid the undesirable equilibria problem on the boundary of the safe set. The solution is illustrated in the design of a collision-free controller.

The integrated energy system (IES) is the physical carrier of the Energy Internet, whose optimal operation has become a hot topic because of its effectiveness in improving energy utilization efficiency. This paper proposes an optimal operation model of integrated energy system, where the internal energy flow transmission characteristic of the heating network is modeled as virtual heating energy storage by the node method to enhance the operating flexibility of IES. The second-order cone relaxation method and the incremental formulation for the piecewise linearization method are utilized to transform the proposed nonlinear model into mixed integer quadratic constraint programming model, which can be effectively solved by the commercial solver. Case studies show that the proposed model effectively reduces the operating costs and improves the renewable energy penetration level of IES.

This article presents a general-purpose full-speed sensorless control scheme for interior permanent magnet synchronous motors (IPMSMs). By applying a quadratic extended back electromotive force (QBEMF) model, the injection-based and model-based position estimations can be combined into a universal sensorless control strategy for the full-speed operation. At low speed, the QBEMF model acts as a self-demodulator that can extract position information from arbitrary high-frequency currents without using digital filters. Therefore, it is suitable for any type of injection signals and can eliminate the adverse effect of filters. When the injection is removed at high speed, the same QBEMF model can still be used for position estimation, thereby solving the conventional transition issue from low-speed to high-speed sensorless control. In consequence, a unified algorithm is designed to achieve arbitrary injection for low-speed sensorless control and seamless transition across full-speed region. The proposed scheme is hence simpler and more effective compared to conventional full-speed sensorless methods. Finally, the feasibility of the proposed estimation algorithm is verified for a 15-kW IPMSM drive.

International audience; This paper deals with the design of quadratic and linear dynamic output feedback controllers for quadratic systems to ensure, on the one hand, local exponential stability of the origin in the closed-loop form and, on the other hand, to increase an estimate of the basin of attraction of the origin as large as possible. The introduction of a quadratic term in the controller permits to consider a controller in the same class of dynamics as the studied system. Here, our approach is to consider a Lyapunov function with respect to the extended state gathering the states of the system and the controller. The induced nonlinear inequalities are treated thanks to an auxiliary vector repeating adequately the extended state and by combining distinct linearization techniques to finally obtain Linear Matrix Inequalities (LMIs). For comparison purposes, we provide also an other approach characterizing the extended state as belonging to a polytope in the state space. The results are illustrated by numerical examples.

This work addresses stability of interfered digital filters with state-delay and saturation arithmetic. By utilizing a quadratic Lyapunov functional and properties of saturation overflow, a new condition is established to ensure stability of interfered digital filters under the influence of saturation arithmetic and state-delay. The criterion is capable of finding minimum $$H_\infty $$ norm in the existence of external disturbance and ensures exponential stability in the nonexistence of disturbance. Further, an improved condition is obtained to ensure asymptotic stability of digital filters with saturation arithmetic. The established conditions are in linear matrix inequality framework and therefore computationally less demanding. It is shown that the stability criteria presented in this study are less stringent than few existing stability results. With the help of numerical examples, superiority of the presented approach is demonstrated.

We state an optimal control problem for a class of dynamical systems whose nonlinear objects can be represented as objects with linear structure and state-dependent parameters. The linearity of the structure of the transformed nonlinear system and the quadratic performance functional allow one to move from the need to search for solutions of the Hamilton–Jacobi equation to an equation of the Riccati type with state-dependent parameters when synthesizing the optimal control, i.e., the controller parameters. The main problem of implementing the optimal control is related to the problem of being capable of finding solutions of such an equation online, at the object operation rate. An algorithmic method for the parametric optimization of the controller is proposed. The method is based on using the necessary optimality conditions for the control system in question. Our algorithms can be used both to optimize the time-varying objects themselves given an appropriate choice of the parameters for this purpose and to optimize the entire control system using an appropriate parametric adjustment of the controllers. The efficiency of the algorithms is demonstrated by the example of drug treatment of patients with HIV.

This paper is concerned with the optimal output synchronization control problem for a class of heterogeneous complex dynamical networks (CDNs) with partially unknown system dynamics. By defining a new quadratic performance index including the information of state couplings, an optimal controller consisting of a feedback control and a compensated feedforward control is then designed. A necessary and sufficient condition for the optimal control minimizing the quadratic performance index is established. Especially, an algebraic Riccati equation (ARE) associated with a discount factor is obtained, and a novel online iteration algorithm by iteratively solving the ARE is proposed to compute the optimal controller gain for the case that the CDNs are with partially unknown system dynamics. Moreover, it is proved that the output synchronization errors converge to zero asymptotically by applying the optimal control laws. Finally, two simulation examples are provided to verify the effectiveness of the proposed control method.

This article considers security control under the network environment for a system with deception attacks, polytopic uncertainty, and persistent bounded disturbance. Since the state is immeasurable and the physical constraint is considered, the output feedback robust model predictive control (MPC) is utilized. The previous results on the output feedback robust MPC are extended to address the deception attacks. The mean-square quadratic boundedness is defined in order to characterize the closed-loop stability. An optimization problem is proposed, which can be solved by linear matrix inequality techniques. By a simple refreshment of the state estimation error set, the optimization problem is shown to be recursively feasible, and the augmented state converges to the neighborhood of equilibrium point. The effectiveness of the proposed theoretical approach is demonstrated by a numerical simulation example.

This article undertakes the problem of simultaneous estimation of state and process faults in linear parameter varying systems. For this purpose, a novel strategy that exploits recent results on the design of observers for quadratic parameter varying systems is developed, and a complete design procedure is described. First, it is shown that by treating the process faults as additional states to be estimated, the arising augmented state-space model is indeed expressed as a quadratic parameter varying system. Hence, the estimates provided by a quadratic parameter varying observer based on the so-called linear output error injection principle would comprise both the actual state and the process faults estimates. Robust design conditions that minimize the effect of disturbances and measurement noise on some linear, and possibly parameter-varying, combina- tion of error variables are obtained using a Lyapunov-based approach. Then, it is shown that the design problem can be reduced to a finite set of linear matrix inequalities that can be solved using available computational tools. The final part of the article exhibits an illustrative example, which clearly exposes the potential applicability and performance of the developed approach.

Blade tip timing (BTT) vibration measurement is a promising on-line blade monitoring method, but various uncertainties bring great challenge in engineering applications. Most existing works are based on the assumption of constant rotating speeds. However, rotating speed is hardly fixed under variable conditions. In this case, these uncertainties always become more serious. To deal with this problem, this paper proposes to investigate BTT measurement derivations in angular domain, instead of time domain. Firstly, this paper systematically analyzes the effects of variable rotating speed, static angle errors and translational blade motions on the accuracy of BTT vibration measurement. Then the corresponding calibration methods are presented by only using times of arrival (TOAs). In the end, Matlab/Simulink simulations are done to validate the proposed method under linear and quadratic variations of rotating speeds. The results demonstrate that BTT measurement deviation under low rotating speeds is more than those under high rotating speeds and BTT measurement deviation due to static angle errors is independent of rotating speeds. And the proposed TOAs-based calibration method can reduce BTT measurement deviation greatly under variable rotating speeds, compared with traditional methods. BTT measurement deviation due to static angle errors can be calibrated by using low rotating speeds and those due to translational blade motions are difficult to be calibrated under variable rotating speeds. Thus simulation results indicate great potential of the proposed method for practical applications of the BTT method.

This paper focuses on the stochastically exponential synchronization problem for one class of neural networks with time-varying delays (TDs) and Markov jump parameters (MJPs). To derive a tighter bound of reciprocally convex quadratic terms, we provide an improved reciprocally convex combination inequality (RCCI), which includes some existing ones as its particular cases. We construct an eligible stochastic Lyapunov–Krasovskii functional to capture more information about TDs, triggering signals, and MJPs. Based on a well-designed event-triggered control scheme, we derive several novel stability criteria for the underlying systems by employing the new RCCI and other analytical techniques. Finally, we present two numerical examples to show the validity of our methods.

Model predictive control (MPC) is based on the systematic resolution of an online optimization problem at each time step. In practice, the computation cost is often very high, especially for the non-linear case under constraints, thus complicating the application of MPC to real-time systems. This paper proposes to improve the non-linear quadratic dynamic matrix control (NLQDMC) algorithm for MPC by solving constrained optimization problems only when necessary, and defaulting to the unconstrained solution whenever possible. The new algorithm is called fast NLQDMC (FNLQDMC) and is applied to the control of a nonlinear system comprised of converter and a DC machine, and implemented in a microcontroller board. The results obtained show that, depending to the setpoint profiles, this algorithm saves more than 64% computation of the constrained problem compared to the conventional NLQDMC, while keeping identical performance in terms of setpoint tracking and constraint satisfactions.

The Cascaded Connected Single Switch Quadratic Boost (C2S2-QB) is studied first from its ideal model, then with semi-real model taking into account resistive losses through the inductors and the capacitor. The continuous conduction mode equations, describing these different models are established, taking into account losses through passive components. From these equations, the voltage gain and the efficiency are determined for the semi-real model. The voltage gain and the efficiency are then analyzed versus duty cycle and the influence of passive component losses on the performance of the quadratic boost converter is carried out for the semi-real model. It has been showed that the quality of the passive components of a converter plays an important role in the quality of the conversion. However, not all passives components affect the converter in the same way.

This paper proposes augmenting the traditional quadratic event-triggered conditions for Takagi-Sugeno (TS) fuzzy models, by also considering triggering conditions defined by a variation of the membership function values. Suitable Linear Matrix Inequality (LMI) conditions are presented that make full use of the proposed modified triggering conditions to co-design the control law and triggering conditions. Under some mild assumptions, the closed loop system is guaranteed to avoid the Zeno behavior for its triggering instants. A numerical example is presented to illustrate the proposed conditions.

Intentional controlled islanding (ICI) is the last resort to split an endangered power system into smaller islands to prevent blackout. New lines that are planned by transmission expansion planning (TEP) can affect the stability of islands during ICI. In this paper, an ICI-TEP method is proposed to improve the stability of islands by more efficient planning of transmission assets. Moreover, by developing a criterion for the frequency of center of inertia (COI) in each island, the frequency deviations of generators from the COI frequency are minimized to result in more stable islands. The proposed ICI-TEP, incorporating AC network representation, is modeled as mixed-integer linear programming and quadratic convex problems ensuring tractability. A Benders decomposition strategy is also proposed to solve the problem. Results of testing the proposed ICI-TEP method on IEEE 39-bus and 300-bus test systems confirm its effectiveness, compared to conventional TEP, in terms of coping with sever disturbances by creating more stable islands with a lower load shedding.

Today, advanced driver-assistance systems (ADAS) come up with different abilities. One of them is the adaptive cruise control (ACC) system. The ACC system is a continuation of research on cruise control (CC) system, which integrates spacing control with the existing velocity control on the CC system. The vehicles with an ACC system guarantee traffic safety while at the same time ensure a well-driving sense. Many studies have demonstrated numerous control techniques applied as ACC controllers to accomplish uncertainty and perturbation issues. Nevertheless, most of the existing papers assumed the model vehicle dynamics as a linear time-invariant (LTI) system while designing the ACC controller. This paper proposed an ACC controller using the gain scheduling technique to deal with the model vehicle dynamics as a linear parameter varying (LPV) system. The passenger vehicle’s mass varies during ACC operation depending on how many passengers or loads on the vehicle’s trunks. Later, the vehicle’s mass is estimated by recursive least square (RLS) with a forgetting factor. Then, the disk margin is utilized to provide the high-level robustness at each operating or “frozen” point. The robustness performance will be analyzed using the worst-case gain metric while the uncertainty is modeled by integral quadratic constraints (IQC). The LPV system behavior, such as the rate vehicle’s mass, is also considered in the analysis. The effectiveness algorithm is validated through joint simulation between Matlab/Simulink and PreScan. The last, the comparison performance between gain scheduling and fixed gain ACC controller is evaluated.

The paper presents a worst-case touchdown condition analysis of an autolanded aircraft under crosswind. Aircraft dynamics are generally considered altitude- and speed-dependent and, thus, well covered inside the linear parameter-varying framework. Following a specific parameter trajectory tracking the instrument landing system’s guidance signal, its dynamics amount to a finite horizon linear time-varying (LTV) system. This allows to explicitly respect the varying dynamics during the flare maneuver, changing control laws, and the finite horizon of the approach using a finite horizon LTV analysis. A time-varying trajectory uncertainty is proposed to respect the effects of different environmental conditions and aircraft parameters in the analysis. By representing the uncertainty as an integral quadratic constraint (IQC), recent advances in the worst-case gain analysis of finite horizon LTV systems can be utilized. The analysis condition is based on a parameterized Riccati differential equation, which leads to an efficiently solvable nonlinear optimization problem. Applying the robust LTV framework, worst-case touchdown conditions of an autolanded large airliner under crosswind wind are calculated. The obtained results are evaluated against Monte Carlo analyses of the nonlinear model.