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Learning from expert demonstrations to flexibly program an autonomous system with complex behaviors or to predict an agent's behavior is a powerful tool, especially in collaborative control settings. A common method to solve this problem is inverse reinforcement learning (IRL), where the observed agent, e.g., a human demonstrator, is assumed to behave according to the optimization of an intrinsic cost function that reflects its intent and informs its control actions. While the framework is expressive, the inferred control policies generally lack convergence guarantees, which are critical for safe deployment in real-world settings. We therefore propose a novel, stability-certified IRL approach by reformulating the cost function inference problem to learning control Lyapunov functions (CLF) from demonstrations data. By additionally exploiting closed-form expressions for associated control policies, we are able to efficiently search the space of CLFs by observing the attractor landscape of the induced dynamics. For the construction of the inverse optimal CLFs, we use a Sum of Squares and formulate a convex optimization problem. We present a theoretical analysis of the optimality properties provided by the CLF and evaluate our approach using both simulated and real-world, human-generated data.

Nowadays antiretroviral therapy is widely used to cut down the viral burden and cut off a few infection sources in clinical medicine for Human Immunodeficiency Virus (HIV) infected patients, and a lot of evidence have shown that a massive coverage with antiretroviral therapy has already acquired a series of contributions and successes to save life and popularize preventive knowledge. Based on the HIV dynamic model, this paper designs a feedback controller to adjust the concentration values of CD4+T cell, CD8+T cell and viral load in HIV dynamic model to a healthy condition asymptotically. The HIV dynamic model is expressed in the form of a polynomial system and then the control law, as the appropriate drug dosage usually applied in the medical therapy, is designed to suppress the reproduction of the HIV virus and improve the production rate of healthy cell in vivo, simultaneously. According to the polynomial Lyapunov theory and sum of squares (SOS) technique, the conditions for the controller synthesis are proposed. The simulation experimental results can be testified the availability of the proposed method.

Total transfer capability evaluation is an effective method to analyze the backbone transmission capability among regions. To address renewable energy uncertainties, an interval total transfer capability model based on the multi-dimensional holomorphic embedding method and sum of squares relaxation technique is proposed to solve the regional total transfer capability in meshed high voltage direct current systems. First, the multi-dimensional holomorphic embedding method is used to derive the analytical expressions of regional tie lines. Second, the interval total transfer capability model can be reformulated by two bi-level optimization models. Third, sum of squares relaxation is employed to solve the two optimization problems. Numerical results on a 40-bus European Synthetic System and the Chinese meshed high voltage direct current system validate the effectiveness of the proposed model and method. [ABSTRACT FROM AUTHOR]

Due to its inherent ability in reducing hardware cost and power consumption while maintaining high system capacity, hybrid precoding is deemed as one of the key technologies in the upcoming 5G/6G millimeter-wave (mmWave) massive multiple-input multiple-output (MIMO) systems. However, it is challenging to design high performance hybrid precoders/combiners with low computational complexity. In this paper, based on the singular value decomposition (SVD) technique and the concept of equivalent channel, joint hybrid precoding strategies with high spectral-efficiency and low complexity are proposed for both single-user and multi-user massive MIMO systems. Specifically, for single-user massive MIMO scenarios, after transforming the design of hybrid beamforming into the problem of maximizing the square of sum eigenvalues for an equivalent channel, a two-stage successive method is conceived to design the analog precoder and combiner jointly, and the corresponding equivalent channel is constructed. Then, the digital precoding and combining operations are realized directly by applying the SVD technique to the matrix of equivalent channel. Meanwhile, the hybrid precoding strategy is extended to the multi-user scenario for achieving high performance resultant from multi-user diversity. Extensive simulations are conducted to verify the effectiveness of the precoding/combing schemes. The results show that our proposed schemes can achieve superior performance with lower complexity compared to the existing ones. [ABSTRACT FROM AUTHOR]

Computation over multiple access channels (CoMAC) has been proposed to solve the problem of spectrum scarcity in wireless networks, which combines communication and computation efficiently using the superposition property of wireless channels. In this paper, we consider a multi-cluster CoMAC network, whose performance is affected by the inter-cluster interference and the non-uniform fading. To minimize the sum mean squared error of signals aggregated at different fusion centers (FCs), we propose a transceiver design for multi-cluster CoMAC. Specifically, we adopt a uniform-forcing transmitter design to formulate the receiver design as a quadratic sum-of-ratios problem with nonconvex quadratic constraints. Then, we propose a branch-and-bound algorithm to find its optimal solution with a given error tolerance. To solve the problem in a decentralized way, we develop a distributed algorithm based on the primal decomposition theory. Each subproblem is solved by using the successive convex approximation method. Further combining Lagrange duality, we derive the optimal solution structure of each subproblem, based on which we can find the solution with lower complexity. Simulation results demonstrate the effectiveness of the proposed distributed transceiver design. [ABSTRACT FROM AUTHOR]

In this article, a collection of conditions to achieve asymptotic stability of switched nonlinear systems with guaranteed safety via a state-dependent switching law are provided, where the asymptotic stability of individual subsystem is not assumed. Multiple barrier functions and multiple Lyapunov functions (MLFs) are merged as a tool for analyzing the asymptotic stability with guaranteed safety control problem of switched nonlinear systems. Meanwhile, the state-dependent switching law is designed to refrain zeno phenomenon. Moreover, bilinear sum of squares methodologies are employed to construct corresponding MLFs for switched nonlinear systems. Finally, three simulation examples are introduced to prove the effectiveness of the provided method. [ABSTRACT FROM AUTHOR]

This article studies the integrated fault-tolerant control (FTC) and fault estimation (FE) problem using polynomial fuzzy model (PFM) based on the sum of squares (SOS) approach. The integrated approach not only considers the bidirectional interaction between fault diagnosis and control units but also ensures an optimal response. The transient management in the fault occurrence situation and the alleviation of bidirectional interaction between FE and FTC are the motivational challenges. However, the integrated approach increases the complexity and problem's dimension. In this situation, PFM can reduce the problem's dimensions and increase modeling accuracy. The additive actuator faults, input disturbance, and structured uncertainty are considered to bring the problem closer to practical applications. A polynomial fuzzy observer with unknown input is designed to estimate the time-varying faults that is used to remove the effects of faults on the control input. Thus, the proposed approach benefits from PFM in FE and FTC synthesis to reduce the design dimensions, have a more precise model, and make the synthesis less conservative. Moreover, the PFM is more robust against intense model uncertainties and faults. To evaluate the proposed approach, the FTC of an inverted-pendulum system is simulated. The fault-tolerant and fault estimation performances of the proposed approach are compared with those of the linear matrix inequality (LMI) approach. The simulated results show that the proposed SOS approach outperforms the LMI approach. [ABSTRACT FROM AUTHOR]

This article investigates the polynomial fuzzy output feedback (PFOF) control synthesis problem for positive polynomial fuzzy systems. When the states of a positive system cannot be fully obtained, the output feedback control strategy is a good method to stabilize the control system. From fuzzy control point of view, we employ the polynomial fuzzy model rather than the Takagi–Sugeno fuzzy model, and this kind of models can express a wider range of nonlinear positive systems. However, the polynomials in the system matrices and the feedback control gain matrices will make the nonconvex stability conditions more difficult to deal with. Thereby, in order to crack the hard nut, a nonzero transformation vector is introduced in this article to deal with the nonconvex problem skillfully. Furthermore, the imperfect premise matching technique is taken into account so that the implement of the controller is more simple and money-saving. In addition, the augmented dynamic of the positive polynomial fuzzy-model-based (PPFMB) control system is investigated to facilitate the stability and positivity analysis, and the basic conditions in the light of sum of squares (SOSs) are derived. Besides, the advanced membership function dependent (MFD) technique is used so that a great of useful information of MFs is extracted to improve the relaxation of the results. Finally, the effectiveness of the theoretical findings is illustrated by a simulation example. [ABSTRACT FROM AUTHOR]

In this article, we investigate the inner estimations of the minimal domains of attraction (MDA) for uncertain nonlinear systems, whose uncertainties are modeled by parameters defined in a semialgebraic set. We begin from an initial inner estimation of MDA and then enlarge this initial inner estimation by iterative calculating common Lyapunov-like functions with a linear sum of squares programming-based approach. Afterwards, this enlarged inner estimation of MDA is further improved by iterative computations of parameter-dependent Lyapunov-like functions. Especially, we use a simple semialgebraic set, described by a polynomial level-set function, to under-approximate this improved estimation. In the end, our methods are implemented and tested on several uncertain examples with comparisons to existing methods in the literatures. [ABSTRACT FROM AUTHOR]

This article proposes a novel membership-function dependent approach for the stability/positivity investigation and controller design of a nonlinear, discrete-time system with time delay which is represented by a polynomial fuzzy model to enhance the accuracy of the approximation. The polynomial fuzzy controller is designed based on imperfect premise matching design concept and a set of sum of square (SOS)-based conditions is formulated to check the positivity and stability of the control system. To relax the conservative SOS-based conditions, we employ piecewise Taylor series membership functions (PTSMFs) and introduce the membership function knowledge into the stability conditions. Slack matrices are used to represent the membership function and premise variable knowledge, which contains: 1) regional approximation error between PTSMFs and original membership functions; 2) regional bounds of PTSMFs; and 3) the property knowledge of interpolation membership function of PTSMFs and regional bounds of premise variables. A simulation example is finally given to verify our novel stability/positivity conditions and discrete-time polynomial fuzzy (DPF) controller design. [ABSTRACT FROM AUTHOR]

The Perspective-n-Point-and-Line (PnPL) problem, as a cornerstone in geometric computer vision, seeks to estimate the absolute pose of a calibrated camera from 3D-to-2D point and line correspondences. In this paper, we present a certifiably globally optimal and robust solution to the PnPL problem with a large number of outliers among the correspondences. Our first contribution is to reformulate the general PnPL problem as a novel constrained global optimization problem of Sum-of-Squares (SOS) polynomials using generalized geometric distances for both points and lines. Our second contribution is to efficiently solve this non-convex optimization problem by reducing it to an equivalent convex Linear Matrix Inequality (LMI) problem via a series of SOS relaxations. With these two contributions, we can develop a non-minimal solver, named SPnPL, for the outlier-free cases. The third contribution is to further add a Graduated Non-Convexity (GNC) cost function to SPnPL so as to remove outliers through closed-form iterations, which leads to a robust solver, named GNC-SPnPL. Both synthetic and real-data experiments confirm that SPnPL can mostly outperform the existing state-of-the-art PnPL algorithms and GNC-SPnPL can render accurate results even when 85% of the correspondences are outliers.

We present a sum of squares (SOS) method for the synthesis of nonlinear polynomial control systems. As an emerging numerical solution method in recent years, SOS targets polynomials as the research object. It guarantees that the polynomial we solve for is always nonnegative. In this paper, we give a generalized S-procedure to solve the SOS problem. As an illustration of how the SOS method can be used, the region of attraction (ROA) in a nonlinear polynomial system is analyzed in detail. The method of determining decision variables is given in the SOS problem. We discuss the determination and solution of set-containment constraints and the conservatism problem in solving the SOS problem. SOS provides a convenient numerical method to solve nonlinear problems that are not easy to solve analytically.

A new method to detect the initial rotor position of switched reluctance machine (SRM) is presented in this article. Unlike most conventional position estimation methods, the proposed method does not need any extra premeasurement and only the data with finite element method (FEM) are required. First, a linear regression model (LRM) is presented to describe the relationship between FEM and measured inductance characteristics. Then, to detect the position, the residual sum of squares of the proposed LRM is considered as an objective function, which is a convex function with rotor position. The rotor position can be estimated by minimizing the objective function with the golden-section search method. Finally, the accuracy of the proposed estimation algorithm is validated by the experimental results on a three-phase 12/8 pole SRM prototype. Compared with the existing position estimation methods, the proposed method has higher accuracy and less measurement effort. The proposed method can serve as a supplement to provide accurate initial position information for incremental position sensors. [ABSTRACT FROM AUTHOR]

The volatility of renewable energy causes mismatch between real-time generation and demand, calling for sufficient backup to compensate such discrepancy. This paper studies the uncertainty mitigation problem at a given operating point, which entails correctively dispatching obligate generators to maintain power balancing and network power flow constraints. The redispatch problem is modeled via a convex quadratic program parameterized in the real-time renewable output, aiming at minimizing the weighted sum of square of generator incremental output. Such an objective leads to a proper allocation of unbalanced power among generators and ensures a unique optimal solution, therefore circumvents model degeneracy. Based on the first-order optimality condition, the analytical expression of the optimal redispatch policy is proven to be piecewise affine: the renewable output set is partitioned into polyhedral regions; in each region, the optimal redispatch policy of generator is an affine function in the incremental output of renewable plants. Provided with the optimal redispatch policy in the analytical form, the nodal-wise flexibility requirements on obligate generators, including the spinning reserve capacity and the ramping capability, can be easily assessed, which is useful in generation scheduling. Case studies on the PJM 5-bus system and the modified IEEE 118-bus system demonstrate the outcome and validate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

In this article, the problem of dissipativity-based consensus is considered for polynomial fuzzy multiagent systems (MASs) with switching directed topologies. First, a novel polynomial fuzzy modeling approach is proposed to describe the error dynamic system which is formulated by a virtual leader and follower agents. Then, consensus control protocol is designed to guarantee that the MASs under switching topologies can reach an agreement. By the polynomial Lyapunov function technique, relaxed sufficient conditions are presented to ensure exponential consensus with a strictly dissipative performance for the underlying systems subject to external disturbances. The derived conditions are converted into sum of squares and can be numerically solved. Finally, an illustrative example is provided to demonstrate the effectiveness of the new design scheme developed. [ABSTRACT FROM AUTHOR]

This study presents an optimization-based controller state initialization method for improving the initial transient response. Uncertainties in the uncontrolled periods around transition events or a large change in the reference may result in unexpected growth of initial tracking error. The proposed method mainly aims to regulate out the initial error at the instance of feedback control initiation with a small amount of control effort and a short settling time. The proposed method minimizes a cost function given by a weighted sum of infinite-horizon square integrals, provided that the other controller parameters are fixed a priori to yield closed-loop stability. The performance-oriented initial controller state optimization is desirable for efficient and rapid initial error convergence in systems such as missiles where agility is of major concern. This study suggests performance-related optimization as an alternative for controller state setting besides zero filling or solving for bump-less transfer in switching systems. The concept and the effectiveness of the proposed method is demonstrated by numerical simulation considering the three-loop missile acceleration autopilot as an example application. [ABSTRACT FROM AUTHOR]

The present article proposes two construction ways to study the general forms of ordinal sums of fuzzy implications with the intent of unifying the ordinal sums existing in the literature. The first ordinal sum construction way, which we call “Implication Complementing,” is to study how to complement a specific fuzzy implication to the linear transformations of given fuzzy implications defined on respective disjoint subsquares whose principal diagonals are segments of the principal diagonal of the unit square, in order that the resulting ordinal sum on the unit square is a fuzzy implication. The second way, which we call “Implication Reconstructing,” is to study how to reconstruct an initial fuzzy implication through replacing its some values on given rectangular regions of the unit square with the linear transformations of respective given fuzzy implications such that the redefined function is a new fuzzy implication. In both ways, necessary and sufficient conditions for the final reconstructed functions to be fuzzy implications are given and several new constructions of ordinal sums of fuzzy implications are obtained, which would generalize the existing ordinal sums from several aspects. In particular, by adopting the idea behind the second way, the generalized ordinal sums of fuzzy implications are proposed, in which the regions where the linear transformations of given fuzzy implications are defined are neither necessarily subsquares nor necessarily along the principal or minor diagonal of the unit square. [ABSTRACT FROM AUTHOR]

Massive access for Internet-of-Things (IoT) in beyond 5G networks represents a daunting challenge for conventional bandwidth-limited technologies. Millimeter-wave technologies (mmWave)—which provide large chunks of bandwidth at the cost of more complex wireless processors in harsher radio environments—is a promising alternative to accommodate massive IoT but its cost and power requirements are an obstacle for wide adoption in practice. In this context, meta-materials arise as a key innovation enabler to address this challenge by Re-configurable Intelligent Surfaces (RISs). In this article we take on the challenge and study a beyond 5G scenario consisting of a multi-antenna base station (BS) serving a large set of single-antenna user equipments (UEs) with the aid of RISs to cope with non-line-of-sight paths. Specifically, we build a mathematical framework to jointly optimize the precoding strategy of the BS and the RIS parameters in order to minimize the system sum mean squared error (SMSE). This novel approach reveals convenient properties used to design two algorithms, RISMA and Lo- RISMA, which are able to either find simple and efficient solutions to our problem (the former) or accommodate practical constraints with low-resolution RISs (the latter). Numerical results show that our algorithms outperform conventional benchmarks that do not employ RIS (even with low-resolution meta-surfaces) with gains that span from 20% to 120% in sum rate performance. [ABSTRACT FROM AUTHOR]

In this article, the stability analysis and control synthesis of interval type-2 (IT2) polynomial-fuzzy-model-based networked control systems are investigated under the event-triggered control framework. The nonlinear dynamics in the plant is efficiently represented by an IT2 polynomial fuzzy model that the IT2 membership functions are utilized to capture the uncertainties in the plant. An event-triggered IT2 polynomial fuzzy controller is then designed to stabilize the nonlinear model subject to uncertainties. The stability conditions of the closed-loop control system are summarized in the form of sum-of-squares. Under the imperfectly premise matching (IPM) concept, the membership-function-dependent (MFD) approach is applied to endow the polynomial fuzzy controllers with more flexibility in terms of number of rules and premise membership functions. In the MFD approach under the IPM concept, both the number of rules and the shape of membership functions in the fuzzy models and controllers can be different. Also, the information of IT2 membership functions of the polynomial fuzzy model and controller is considered and adopted to further relax the stability conditions. Furthermore, the intrinsic mismatched issue of the premise variables of the fuzzy model and controllers due to the event-triggering mechanism is handled by the MFD approach. A detailed simulation example is provided to verify the effectiveness of the proposed event-based control strategy. [ABSTRACT FROM AUTHOR]

For systems that can only be locally stabilized, control laws and their effective regions are both important. In this paper, invariant policy iteration is proposed to solve the optimal control of discrete-time systems. At each iteration, a given policy is evaluated in its invariantly admissible region, and a new policy and a new region are updated for the next iteration. Theoretical analysis shows the method is regionally convergent to the optimal value and the optimal policy. Combined with sum-of-squares polynomials, the method is able to achieve the near-optimal control of a class of discrete-time systems. An invariant adaptive dynamic programming algorithm is developed to extend the method to scenarios where system dynamics is not available. Online data are utilized to learn the near-optimal policy and the invariantly admissible region. Simulated experiments verify the effectiveness of our method. [ABSTRACT FROM AUTHOR]

Despite it is essential to distribution network economics, computing energy loss for most major networks is still a tough task due to the absence of full monitoring. Assume the line current follows a normal distribution, the sum of its square is a linear combination of independent chi-square variables, which follows a generalized noncentral chi-square distribution. Based on this finding, we develop a new probability-based analytical method to estimate distribution network energy losses efficiently. The proposed analytical method requires merely the knowledge of mean and variance of line current as well as the line resistance while provides a closed-form formula of the probability characteristics of energy loss. The method is demonstrated on a three-feeder radial network. [ABSTRACT FROM AUTHOR]

An indirect measurement method based on an analytical formula is presented to estimate the effective inductance which is associated with the winding resonances of an iron core transformer winding. It is applicable to any 1-Φ or 3-Φ (Y, Δ) winding, with any condition of the neutral. A new analytical method is developed using authors’ recent work (which linked the harmonic sum of squares of natural frequencies of a winding to its inductances and capacitances). Data about the trough (SCNFs) or peak (OCNFs) frequencies corresponding to two FRAs is the only required input; one FRA corresponding to the nominal condition and another measured after connecting a known lumped capacitor across the winding. Details of derivations for each 1-Φ and 3-Φ configuration is initially presented. Thereafter, experimental results are discussed on 1-Φ and 3-Φ, 33 kV, 3.5 MVA winding setup, where any desired winding connection can be configured and examined. Then, results on two actual transformers are discussed to prove method's practical implementability. Finally, some preliminary thoughts on using this newly defined quantity for assessing mechanical integrity of winding is briefly examined. [ABSTRACT FROM AUTHOR]

In this paper, the stability and positivity of positive polynomial fuzzy model based (PPFMB) control system are investigated, in which the positive polynomial fuzzy model and positive polynomial fuzzy controller are allowed to have different premise membership functions from each other. These mismatched premise membership functions can increase the flexibility of controller design; however, it will lead to the conservative results when the stability is analyzed based on the Lyapunov stability theory. To relax the positivity/stability conditions, the improved Taylor-series-membership-functions-dependent (ITSMFD) method is introduced by introducing the sample points information of Taylor-series approximate membership functions, local error information and boundary information of substate space of premise variables into the stability/positivity conditions. Meanwhile, the ITSMFD method is extended to the PPFMB control system with input saturation to relax the estimation of domain of attraction. Finally, simulation examples are presented to verify the feasibility of this method. [ABSTRACT FROM AUTHOR]

The Cole model is widely used in bioimpedance spectroscopy (BIS) applications for evaluating the contents and status of biological tissues. Traditional frequency-domain fitting methods for Cole parameter estimation (CPE) often need wideband direct or indirect BIS measurements. The newly emerged time-domain fitting methods do not require BIS measurement, but they usually have unsatisfactory estimation accuracy and heavily rely on some specific excitations. This paper proposes a novel time-domain fitting method based on the fractional operational matrix (FOM) for CPE. First, the Cole model is represented as a FOM-based algebraic equation. Then, the model-based voltage response can be calculated as the product of the sampled current excitation and the FOM-based Cole equation. Finally, the Cole parameter can be estimated by minimizing the sum of squares error between the sampled voltage response and the model-based voltage response using an iterative nonlinear least-squares fitting algorithm. Experimental measurements are verified on three 2R1C circuits and in vivo leg muscle of a healthy volunteer. The results show that the Cole parameter can be accurately estimated by the proposed FOM-based fitting method directly using the sampled current and voltage signals. This paper establishes an effective time-domain fitting method for CPE, which could greatly simplify the hardware and software designs without the need for the BIS measurement. [ABSTRACT FROM AUTHOR]

Time-varying (TV) nonlinear systems widely exist in various fields of engineering and science. Effective identification and modeling of TV systems is a challenging problem due to the nonstationarity and nonlinearity of the associated processes. In this paper, a novel parametric modeling algorithm is proposed to deal with this problem based on a TV nonlinear autoregressive with exogenous input (TV-NARX) model. A new class of multiple beta wavelet (MBW) basis functions is introduced to represent the TV coefficients of the TV-NARX model to enable the tracking of both smooth trends and sharp changes of the system behavior. To produce a parsimonious model structure, a locally regularized ultraorthogonal forward regression (LRUOFR) algorithm aided by the adjustable prediction error sum of squares (APRESS) criterion is investigated for sparse model term selection and parameter estimation. Simulation studies and a real application to EEG data show that the proposed MBW-LRUOFR algorithm can effectively capture the global and local features of nonstationary systems and obtain an optimal model, even for signals contaminated with severe colored noise. [ABSTRACT FROM AUTHOR]

This article describes a fast calculation method for harmonic losses caused by inverter carrier in interior permanent-magnet synchronous motors (IPMSMs) under a large number of driving conditions. In the proposed method, the harmonic loss caused by the largest component of the harmonic voltages is calculated by the linear frequency-domain finite-element analysis (FEA) with the differential permeability distribution obtained by the time-domain FEA. The total carrier loss is predicted by the variation in this largest harmonic component and sum of the square of harmonic voltages. The proposed method is applied to the efficiency-map calculation of an IPMSM. It is clarified that the total computational time is reduced to be 1/20th when compared with the conventional method. [ABSTRACT FROM AUTHOR]

Objective: This study proposes a new parametric time-frequency conditional Granger causality (TF-CGC) method for high-precision connectivity analysis over time and frequency domain in multivariate coupling nonstationary systems, and applies it to source electroencephalogram (EEG) signals to reveal dynamic interaction patterns in oscillatory neocortical sensorimotor networks. Methods: The Geweke's spectral measure is combined with the time-varying autoregressive with exogenous input (TVARX) modeling approach, which uses multiwavelet-based ultra-regularized orthogonal least squares (UROLS) algorithm, aided by adjustable prediction error sum of squares (APRESS), to obtain high-resolution time-varying CGC representations. The UROLS-APRESS algorithm, which adopts both the regularization technique and the ultra-least squares criterion to measure not only the signal themselves, but also the weak derivatives of them, is a novel powerful method in constructing time-varying models with good generalization performance, and can accurately track smooth and fast changing causalities. The generalized measurement based on CGC decomposition is able to eliminate indirect influences in multivariate systems. Results: The proposed method is validated on two simulations, and then applied to source level motor imagery (MI) EEGs, where the predicted distributions are well recovered with high TF precision, and the detected connectivity patterns of MI-EEGs are physiologically interpretable and yield new insights into the dynamical organization of oscillatory cortical networks. Conclusion: Experimental results confirm the effectiveness of the TF-CGC method in tracking rapidly varying causalities of EEG-based oscillatory networks. Significance: The novel TF-CGC method is expected to provide important information of neural mechanisms of perception and cognition. [ABSTRACT FROM AUTHOR]

This paper presents a relaxed stabilization condition for polynomial-fuzzy-model-based control system by using sum-of-squares (SOS) approach. Full-block S-procedure is utilized to equivalently decouple the fuzzy weighting constraint into two constraints, which can be computed directly with the SOS approach. Besides, a free full-block multiplier imposed by this procedure also contributes to reducing the conservativeness of stability analysis. The copositivity verification relaxation performed on the membership-functions-related constraint can both obtain more relaxed results and reduce the computation complexity. The concept of polynomial Lyapunov function (PLF) with square matrical representation, which simplifies the stabilization condition by avoiding partial derivatives of a polynomial matrix, is also introduced to generalize the existing expression of PLFs. Then, the derived stabilization condition, which is represented in terms of SOS can be numerically solved. Three simulation examples are conducted to illustrate the effectiveness and applicability of the proposed method. These examples also demonstrate the advantages of the proposed method over the existing convex SOS approach. [ABSTRACT FROM AUTHOR]

Recently, the present authors’ research group derived an analytical expression to link the harmonic sum of the squares of short circuit natural frequencies (SCNFs) of a single, isolated winding to its elementary inductances and capacitances. Also, it was demonstrated how this expression could be practically used for locating radial and axial displacements, along with assessing its severity on a single, isolated, actual transformer winding. The next logical task was to extend the derived expression to multi-phase windings, viz., star/delta connections and for any terminal condition of the neutral. Actually, it would be desirable to have a similar expression for open circuit natural frequency (OCNF) as well. A major highlight of this paper is that it presents a single, unified approach (using salient features of coefficients of the numerator and denominator polynomial of driving-point impedance) by which compact analytical expressions can be simultaneously derived for both SCNF and OCNF, for any multi-phase transformer configuration, and for any condition of the neutral terminal. Complete derivation details of the proposed method are presented, and then, the expressions for SCNF and OCNF are derived for 1- $\Phi$ isolated windings as well as 3- $\Phi$ (Y, $\Delta$) configurations. Finally, simulation results for all the cases are reported. [ABSTRACT FROM AUTHOR]

Cooperative adaptive cruise control (CACC), as an extension of adaptive cruise control, connects multiple vehicles in a platoon via wireless communication. In practice, different vehicles may have different dynamic parameters and their exact values are unknown/uncertain to designers. In this brief, we propose a new control structure that uses an estimate of dynamic parameters to transform the heterogeneous CACC problem into the regulation problem of error dynamics for each vehicle in the platoon. An adaptive optimal control is proposed to learn the optimal feedback based on online data. The position transfer function between adjacent vehicles is further analyzed in the frequency domain. By sum of squares programming, the minimum headway values that ensure the vehicle string stability are found. Experiments on numerical and complex systems validate our method. [ABSTRACT FROM AUTHOR]

This paper investigates the problem of designing a robust controller for continuous polynomial fuzzy systems with external disturbances. The input matrix $\mathbf {B}_i(x)$ of the considered system is not equal to one another. To solve this problem, first, we rewrite every column vector of input matrix $\mathbf {B}_i(x)$ using the vectors of the basis matrix $\mathbb {B}(x)$. Second, by use of the column vector of $\mathbb {B}(x)$ , the subsliding mode surface $s_p(t)$ is designed. Based on the rewritten system, a novel sliding mode surface $s(t)$ is devised. The sliding mode surface parameter matrix can be characterized in terms of the solution of the provided sum of squares conditions. Then, a sliding mode controller is proposed to stabilize the considered system. It could make the state of the considered system drive onto $s(t)$ and avoid the state escaping from the surface in the subsequent time. A lemma is provided to obtain the final result. Finally, practical and numerical examples are provided to demonstrate the validity of the proposed approach. [ABSTRACT FROM AUTHOR]

A decentralized verification procedure is proposed to verify stability and performance for systems with multiple controllers designed by noncooperative agents. The key concept is to use Lyapunov functions as measure of the influence of each controller on the system. Sum of squares programming is used to verify Lyapunov derivative conditions, thus providing a sufficient condition for the specification. Dual decomposition is then used to decentralize the algorithm with the guarantee that decentralized verification is equivalent to centralized verification. The verification procedure is extended to decentralized control synthesis. To reduce the conservatism caused by improper choice of Lyapunov candidate, a perturbation algorithm is proposed to modify the Lyapunov candidate such that it better suits the purpose of verification. [ABSTRACT FROM AUTHOR]

In safety verification of hybrid systems, barrier certificates are generated by solving the verification conditions derived from non-negative representations of different types. This paper presents a new computational method, sequential linear programming projection, for directly solving the set of verification conditions represented by the Krivine–Vasilescu–Handelman’s positivstellensatz. The key idea is to decompose it into two successive optimization problems that refine the desired barrier certificate and those undetermined multipliers, respectively, and solve it in an iterative scheme. The most important benefit of the proposed approach lies in that it is much more effective than the LP relaxation method in producing real barrier certificates, and possesses a much lower computational complexity than the popular sum of square relaxation methods, which is demonstrated by the theoretical analysis on complexity and the experiment on a set of examples gathered from the literature. [ABSTRACT FROM AUTHOR]

A homogeneously state-dependent polynomial Lyapunov function for an observed-state feedback polynomial fuzzy control system is proposed. From which an advanced sufficient sum of squares (SOS) condition formulated in terms of state-dependent matrix inequalities to achieve fuzzy stabilization is derived. Three main features, compared with existing nonhomogeneously polynomial methods, are as follows: 1) homogeneous Lyapunov function and its time derivative are nicely linked via the Hessian matrix; 2) removing the nonconvex obstacles on $\dot{P}(x)$ when deriving a nonhomogeneous Lyapunov stabilization condition $\dot{V}(x)$ ; 3) separation principle holds; since common $P$ falls out as a special case, the proposed homogeneous SOS approach is placed ahead of the existing SOS-based methods found in polynomial fuzzy stabilization controls. To verify the problem-solving theories of the homogeneous polynomial method announced, four examples are demonstrated to show the promising features of the approach adduced. Finally, an Appendix illustrating the solving procedure is added for clarification on how the examples are solved via SOS. [ABSTRACT FROM AUTHOR]

This paper proposes a novel approach on controller design for a doubly fed wind generator based on input-to-state stability (ISS) theory. In order to guarantee the stability of the nonlinear system with external disturbances, a systematic methodology for constructing locally ISS stabilizing (LISS) control Lyapunov functions and designing the corresponding robust LISS control law is proposed. This method avoids the Hamilton-Jacobi-Isaacs (HJI) partial differential equation and the limitation of exact linearization. The proposed ISS control law is proved to be inverse optimal and can guarantee the stability of the wind generation system under external disturbances. The simulation studies verify the effectiveness of the proposed ISS controller. Compared with conventional proportional-integral (PI) controllers, and exact linearization-based nonlinear controllers, the proposed ISS controller has the ability to enhance the transient stability of the wind generation system during and after faults, and can significantly improve the dynamic performance of the system. [ABSTRACT FROM PUBLISHER]

This paper presents a systematic approach to deal with the saturated control of a class of distributed parameter systems that can be modeled by the first-order hyperbolic partial differential equations (PDE). The approach extends (also improves over) the existing fuzzy Takagi–Sugeno (TS) state feedback designs for such systems by applying the concepts of the polynomial sum-of-squares (SOS) techniques. First, a fuzzy-polynomial model via Taylor series is used to model the semilinear hyperbolic PDE system. Second, the closed-loop exponential stability of the fuzzy-PDE system is studied through the Lyapunov theory. This allows us to derive a design methodology in which a more complex fuzzy state-feedback control is designed in terms of a set of SOS constraints, able to be numerically computed via semidefinite programming. Finally, the proposed approach is tested in simulation with the standard example of a nonisothermal plug-flow reactor. [ABSTRACT FROM PUBLISHER]

Cardiac magnetic resonance perfusion examinations enable noninvasive quantification of myocardial blood flow. However, motion between frames due to breathing must be corrected for quantitative analysis. Although several methods have been proposed, there is a lack of widely available benchmarks to compare different algorithms. We sought to compare many algorithms from several groups in an open benchmark challenge. Nine clinical studies from two different centers comprising normal and diseased myocardium at both rest and stress were made available for this study. The primary validation measure was regional myocardial blood flow based on the transfer coefficient (K^\rmtrans), which was computed using a compartment model and the myocardial perfusion reserve (MPR) index. The ground truth was calculated using contours drawn manually on all frames by a single observer, and visually inspected by a second observer. Six groups participated and 19 different motion correction algorithms were compared. Each method used one of three different motion models: rigid, global affine, or local deformation. The similarity metric also varied with methods employing either sum-of-squared differences, mutual information, or cross correlation. There were no significant differences in K^\rmtrans or MPR compared across different motion models or similarity metrics. Compared with the ground truth, only K^\rmtrans for the sum-of-squared differences metric, and for local deformation motion models, had significant bias. In conclusion, the open benchmark enabled evaluation of clinical perfusion indices over a wide range of methods. In particular, there was no benefit of nonrigid registration techniques over the other methods evaluated in this study. The benchmark data and results are available from the Cardiac Atlas Project ( www.cardiacatlas.org). [ABSTRACT FROM AUTHOR]

A complementary set of $K$ binary $\pm 1$ codes of length $N$ has the useful property that the sum of the autocorrelation sequences of the codes has only one nonvanishing element, its size-$KN$ peak. The $N\times K$ matrix whose columns are the codes of a binary complementary set, arranged in order, is the code set's complementary code matrix (CCM). One might ask for which $K$ and $N$ such matrices exist. A simple necessary condition for the existence of an $N\times K$ CCM is introduced, involving the sum of the squares of the imbalance values of the codes in the set (the imbalance of a binary $\pm 1$ code being the difference between the number of 1 and number of $-1$s in the code). The one-to-one relationship between binary CCMs and binary complementary code sets allows the necessary condition for the $N\times K$ CCM existence to extend to a necessary condition for sets of $K$ complementary code sets of length $N$. We examine the sum-of-squares condition for the separate cases of $N$ even and $N$ odd. The odd case is especially interesting, since representations in terms of sums of squares of odd integers are equivalent to representations as sums of triangular numbers, a subject of recent research in Number Theory. Furthermore, we exhibit a refinement of the existence condition in terms of the imbalance values of pairs of interlaced subcodes. This refinement is new, to the best of our knowledge. Finally, we investigate whether odd-length complementary code sets exist for $K>2$, unlike the Golay case of $K=2$ where odd-length sets cannot exist. We easily find, by computer search, a four-code set of length 15, suggesting that these are likely not uncommon. [ABSTRACT FROM AUTHOR]

This paper is concerned with the stability analysis of positive polynomial-fuzzy-model-based control systems with time delay. Each of the polynomial fuzzy model and the polynomial fuzzy controller is allowed to have its own set of premise membership functions, which can improve the design and realization flexibility. Conditions showing the positivity of the system are first obtained. Then, to deal with the difficulty resulting from the mismatched premise membership functions to the stability/stabilization analysis, approximated membership functions representing the original ones are constructed, and the information of membership functions is brought into the stability conditions. This way, the stability conditions can be relaxed, since the extra knowledge on the system is considered. Stability conditions are obtained by using the sum-of squares approach based on the Lyapunov stability theory. A simulation example is provided to verify the effectiveness of this method. [ABSTRACT FROM PUBLISHER]

This paper deals with a sum-of-squares (SOS)-based control Lyapunov function (CLF) design for polynomial fuzzy control of nonlinear systems. The design starts with exactly replacing (smooth) nonlinear systems dynamics with polynomial fuzzy models, which are known as universal approximators. Next, global stabilization conditions represented in terms of SOS are provided in the framework of the CLF design, i.e., a stabilizing controller with nonparallel distributed compensation form is explicitly designed by applying Sontag's control law, once a CLF for a given nonlinear system is constructed. Furthermore, semiglobal stabilization conditions on operation domains are derived in the same fashion as in the global stabilization conditions. Both global and semiglobal stabilization problems are formulated as SOS optimization problems, which reduce to numerical feasibility problems. Five design examples are given to show the effectiveness of our proposed approach over the existing linear matrix inequality and SOS approaches. [ABSTRACT FROM PUBLISHER]

This paper analyses the sum-of-squares (SoS) detector that is designed to reveal the presence of a spoofing attack. The SoS decision statistic is computed using carrier phase measurements from two spatially separated Global Navigation Satellite System receivers and assumes a simple form that makes it suitable for real-time applications. The detector is theoretically characterized, and its effectiveness is shown using simulations and experiments involving real Global Positioning System data. [ABSTRACT FROM PUBLISHER]

This paper presents a new sum-of-squares (SOS, for brevity) design framework for robust control of polynomial fuzzy systems with uncertainties. Two kinds of robust stabilization conditions are derived in terms of SOS. One is global SOS robust stabilization conditions that guarantee the global and asymptotical stability of polynomial fuzzy control systems. The other is semiglobal SOS robust stabilization conditions. The latter is available for very complicated systems that are difficult to guarantee the global and asymptotical stability of polynomial fuzzy control systems. The main feature of all the SOS robust stabilization conditions derived in this paper are to be expressed as nonconvex formulations with respect to polynomial Lyapunov function parameters and polynomial feedback gains. Since a typical transformation from nonconvex SOS design conditions to convex SOS design conditions often results in some conservative issues, the new design framework presented in this paper gives key ideas to avoid the conservative issues. The first key idea is that we directly solve nonconvex SOS design conditions without applying the typical transformation. The second key idea is that we bring a so-called copositivity concept. These ideas provide some advantages in addition to relaxations. To solve our SOS robust stabilization conditions efficiently, we introduce a gradient algorithm formulated as a minimizing optimization problem of the upper bound of the time derivative of an SOS polynomial that can be regarded as a candidate of polynomial Lyapunov functions. Three design examples are provided to illustrate the validity and applicability of the proposed design framework. The examples demonstrate advantages of our new SOS design framework for the existing linear matrix inequality approaches and the existing convex SOS approach. [ABSTRACT FROM PUBLISHER]

This paper presents the stability analysis of polynomial fuzzy-model-based (PFMB) control systems, in which both the polynomial fuzzy model and the polynomial fuzzy controller are allowed to have their own set of premise membership functions. In order to address the input nonlinearity, the control signal is considered to be bounded by a sector with nonlinear bounds. These nonlinear lower and upper bounds of the sector are constructed by combining local bounds using fuzzy blending such that local information of input nonlinearity can be taken into account. With the consideration of imperfectly matched membership functions and input nonlinearity, the applicability of the PFMB control scheme can be further enhanced. To facilitate the stability analysis, a general form of approximated membership functions representing the original ones is introduced. As a result, approximated membership functions can be brought into the stability analysis leading to relaxed stability conditions. The sum-of-squares approach is employed to obtain the stability conditions based on Lyapunov stability theory. Simulation examples are presented to demonstrate the feasibility of the proposed method. [ABSTRACT FROM AUTHOR]