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In this paper, hybrid dynamical systems theory is applied to the analysis and control of switched converters with Pulse-Width Modulated (PWM) inputs. The system is described by a state-space model with continuous flows and discrete jumps, without averaged equations. The modulation effects are captured in full without using time-dependent signals, by enlarging the state vector to include the PWM waveform generation process. Furthermore, the sample-and-hold mechanism associated with the sampling frequency is also taken into account with this approach. A control law is proposed based on a Lyapunov function candidate. Furthermore, convergence sets and the steady state jitter, inherent to PWM-based controllers, are analyzed estimating limit sets for the augmented state. Consequently, output chattering can be bounded. By using hybrid dynamical system theory, the control designer gains a deeper understanding of the effect of modulation in the closed-loop dynamics, avoiding the problems associated with the use averaged models. Experimental results validate the proposed method. [ABSTRACT FROM AUTHOR]

This paper introduces a new, reference trajectory following, sliding-mode control strategy for disturbed discrete-time systems. The strategy uses an external trajectory generator based on a switching type reaching law. The trajectory following strategy not only ensures all the properties of the quasi-sliding-mode as defined by Gao et al., but with a certain choice of the control parameters it also guarantees a significant reduction of the quasi-sliding-mode band width and the errors of all the state variables. This paper also considers the problem of error calculation in the discrete-time, reaching law based sliding-mode control systems. It is shown that the limitation of the sliding variable in the sliding phase directly results in bounded errors of all state variables. The results are verified with a simulation example. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the proper orthogonal decomposition (POD) method to numerically solve the forward Kolmogorov equation (FKE). Our method aims to explore the low-dimensional structures in the solution space of the FKE and to develop efficient numerical methods. As an important application and our primary motivation to study the POD method to FKE, we solve the nonlinear filtering (NLF) problems with a real-time algorithm proposed by Yau and Yau combined with the POD method. This algorithm is referred as POD algorithm in this paper. Our POD algorithm consists of offline and online stages. In the offline stage, we construct a small number of POD basis functions that capture the dynamics of the system and compute propagation of the POD basis functions under the FKE operator. In the online stage, we synchronize the coming observations in a real-time manner. Its convergence analysis has also been discussed. Some numerical experiments of the NLF problems are performed to illustrate the feasibility of our algorithm and to verify the convergence rate. Our numerical results show that the POD algorithm provides considerable computational savings over existing numerical methods. [ABSTRACT FROM AUTHOR]

This paper presents a COordinate Rotation Digital Computer (CORDIC)-based architecture for the computation of Nth root and proves its feasibility by hardware implementation. The proposed architecture performs the task of Nth root simply by shift-add operations and enables easy tradeoff between the speed (or precision) and the area. Technically, we divide the Nth root computation into three different subtasks, and map them onto three different classes of the CORDIC accordingly. To overcome the drawback of narrow convergence range of the CORDIC algorithm, we adopt several innovative methods to yield a much improved convergence range. Subsequently, in terms of convergence range and precision, a flexible architecture is developed. The architecture is validated using MATLAB with extensive vector matching. Finally, using a pipelined structure with fixed-point input data, we implement the example circuits of the proposed architecture with radicand ranging from zero to one million, and achieve an average mean of approximately 10−7 for the relative error. The design is modeled using Verilog HDL and synthesized under the TSMC 40-nm CMOS technology. The report shows a maximum frequency of 2.083 GHz with $197421.00~{\mu }\text{m}^{2}$ area. The area decreases to $169689.98~{\mu }\text{m}^{2}$ when the frequency lowers to 1.00 GHz. [ABSTRACT FROM AUTHOR]

This paper proposes a novel data-driven control approach to address the problem of adaptive optimal tracking for a class of nonlinear systems taking the strict-feedback form. Adaptive dynamic programming (ADP) and nonlinear output regulation theories are integrated for the first time to compute an adaptive near-optimal tracker without any a priori knowledge of the system dynamics. Fundamentally different from adaptive optimal stabilization problems, the solution to a Hamilton-Jacobi–Bellman (HJB) equation, not necessarily a positive definite function, cannot be approximated through the existing iterative methods. This paper proposes a novel policy iteration technique for solving positive semidefinite HJB equations with rigorous convergence analysis. A two-phase data-driven learning method is developed and implemented online by ADP. The efficacy of the proposed adaptive optimal tracking control methodology is demonstrated via a Van der Pol oscillator with time-varying exogenous signals. [ABSTRACT FROM AUTHOR]

In this paper, we first address the dynamics of the elegant multivalued quaternionic Hopfield neural network (MV-QHNN) proposed by Minemoto et al. Contrary to what was expected, we show that the MV-QHNN, as well as one of its variation, does not always come to rest at an equilibrium state under the usual conditions. In fact, we provide simple examples in which the network yields a periodic sequence of quaternionic state vectors. Afterward, we turn our attention to the continuous-valued quaternionic Hopfield neural network (CV-QHNN), which can be derived from the MV-QHNN by means of a limit process. The CV-QHNN can be implemented more easily than the MV-QHNN model. Furthermore, the asynchronous CV-QHNN always settles down into an equilibrium state under the usual conditions. Theoretical issues are all illustrated by examples in this paper. [ABSTRACT FROM AUTHOR]

In this paper, a novel analysis method based on wave digital (WD) principles is presented. The method is employed for modeling and efficiently simulating large photovoltaic (PV) arrays under partial shading conditions. The WD method allows rapid exploration of the current-voltage curve at the load of the PV array, given: the irradiation pattern, the nonlinear PV unit model (e.g., exponential junction model with bypass diode) and the corresponding parameters. The maximum power point can therefore easily be deduced. The main features of the proposed method are the use of a scattering matrix that is able to incorporate any PV array topology and the adoption of independent 1-D nonlinear solvers to handle the constitutive equations of PV units. It is shown that the WD method can be considered as an iterative relaxation method that always converges to the PV array solution. Rigorous proof of convergence and results about the speed of convergence are provided. Compared with standard spice-like simulators, the WD method results to be 35 times faster for PV arrays made of some thousands elements. This paves the way to possible implementations of the method in specialized hardware/software for the real time control and optimization of complex PV plants. [ABSTRACT FROM AUTHOR]

Multiview assisted learning has gained significant attention in recent years in supervised learning genre. Availability of high-performance computing devices enables learning algorithms to search simultaneously over multiple views or feature spaces to obtain an optimum classification performance. This paper is a pioneering attempt of formulating a mathematical foundation for realizing a multiview aided collaborative boosting architecture for multiclass classification. Most of the present algorithms apply multiview learning heuristically without exploring the fundamental mathematical changes imposed on traditional boosting. Also, most of the algorithms are restricted to two class or view setting. Our proposed mathematical framework enables collaborative boosting across any finite-dimensional view spaces for multiclass learning. The boosting framework is based on a forward stagewise additive model, which minimizes a novel exponential loss function. We show that the exponential loss function essentially captures the difficulty of a training sample space instead of the traditional “1/0” loss. The new algorithm restricts a weak view from overlearning and thereby preventing overfitting. The model is inspired by our earlier attempt on collaborative boosting, which was devoid of mathematical justification. The proposed algorithm is shown to converge much nearer to global minimum in the exponential loss space and thus supersedes our previous algorithm. This paper also presents analytical and numerical analyses of convergence and margin bounds for multiview boosting algorithms and we show that our proposed ensemble learning manifests lower error bound and higher margin compared with our previous model. Also, the proposed model is compared with traditional boosting and recent multiview boosting algorithms. In the majority of instances, the new algorithm manifests a faster rate of convergence on training set error and also simultaneously offers better generalization performance. The kappa-error diagram analysis reveals the robustness of the proposed boosting framework to labeling noise. [ABSTRACT FROM PUBLISHER]

In this paper, we analyse convergence and stability properties for piecewise affine models of gene regulatory networks, by means of piecewise quadratic Lyapunov functions. In the first part, we present the piecewise affine model of a gene regulatory network then, after proving a result on the existence of a minimal, attractive, and positively invariant box, we describe a linear matrix inequalitie framework to construct a Lyapunov function for the system. In the second part of the work, after a characterization of the system solutions when considering also isolated Zeno behavior of the trajectories, a monotonicity property of the so found Lyapunov function is formally proved, together with a result on the convergence of the trajectories, in the sense of measure. Finally, we present two examples, showing the applicability and utility of the main theoretical results previously explained. [ABSTRACT FROM AUTHOR]

Many practical problems can be solved by being formulated as time-varying quadratic programing (TVQP) problems. In this paper, a novel power-type varying-parameter recurrent neural network (VPNN) is proposed and analyzed to effectively solve the resulting TVQP problems, as well as the original practical problems. For a clear understanding, we introduce this model from three aspects: design, analysis, and applications. Specifically, the reason why and the method we use to design this neural network model for solving online TVQP problems subject to time-varying linear equality/inequality are described in detail. The theoretical analysis confirms that when activated by six commonly used activation functions, VPNN achieves a superexponential convergence rate. In contrast to the traditional zeroing neural network with fixed design parameters, the proposed VPNN has better convergence performance. Comparative simulations with state-of-the-art methods confirm the advantages of VPNN. Furthermore, the application of VPNN to a robot motion planning problem verifies the feasibility, applicability, and efficiency of the proposed method. [ABSTRACT FROM AUTHOR]

Due to the lack of enough generalization in the state space, common methods of reinforcement learning suffer from slow learning speed, especially in the early learning trials. This paper introduces a model-based method in discrete state spaces for increasing the learning speed in terms of required experiences (but not required computation time) by exploiting generalization in the experiences of the subspaces. A subspace is formed by choosing a subset of features in the original state representation. Generalization and faster learning in a subspace are due to many-to-one mapping of experiences from the state space to each state in the subspace. Nevertheless, due to inherent perceptual aliasing (PA) in the subspaces, the policy suggested by each subspace does not generally converge to the optimal policy. Our approach, called model-based learning with subspaces (MoBLeSs), calculates the confidence intervals of the estimated $Q$ -values in the state space and in the subspaces. These confidence intervals are used in the decision-making, such that the agent benefits the most from the possible generalization while avoiding from the detriment of the PA in the subspaces. The convergence of MoBLeS to the optimal policy is theoretically investigated. In addition, we show through several experiments that MoBLeS improves the learning speed in the early trials. [ABSTRACT FROM AUTHOR]

This paper is concerned with variational optimal control constructions whose solution yields a sampling algorithm. The particular form of the sampling algorithm considered here is a particle filter, designed to numerically approximate the solution to the global optimization problem. The theoretical significance of this study comes from its variational aspects. Specifically, the control input represents the solution of a mean-field-type optimal control problem. Its parametric counterpart, obtained when a parametric form of density is known a priori, is shown to be equivalent to the natural gradient algorithm. Explicit formulae for the filter are derived when the objective function is quadratic and the density is Gaussian. The optimal control construction of the particle filter is a significant departure from the classical importance sampling–resampling-based approaches. [ABSTRACT FROM AUTHOR]

The recently proposed DeGroot–Friedkin model describes the dynamical evolution of individual social power in a social network that holds opinion discussions on a sequence of different issues. This paper revisits that model, and uses nonlinear contraction analysis, among other tools, to establish several novel results. First, we show that for a social network with constant topology, each individual's social power converges to its equilibrium value exponentially fast, whereas previous results only concluded asymptotic convergence. Second, when the network topology is dynamic (i.e., the relative interaction matrix may change between any two successive issues), we show that the initial (perceived) social power of each individual is exponentially forgotten. Specifically, individual social power is dependent only on the dynamic network topology, and initial social power is forgotten as a result of sequential opinion discussion. Finally, we provide an explicit upper bound on an individual's social power as the number of issues discussed tends to infinity; this bound depends only on the network topology. Simulations are provided to illustrate our results. [ABSTRACT FROM AUTHOR]

It is well known that for a linear time-invariant plant whose transfer function has relative degree $n^*$ and stable zeros, a model reference adaptive control (MRAC) system ensures that the plant output $y(t)$ asymptotically tracks the output $y_m(t)$ of a stable reference model system of the same relative degree $n^*$ : $\lim _{t \rightarrow \infty } (y(t) - y_m(t)) = 0$. In this note, it is shown that under the same MRAC design conditions without the knowledge of the plant parameters, an MRAC system ensures that the tracking error $e(t)= y(t) - y_m(t)$ has the stronger higher order convergence property: $\lim _{t\rightarrow \infty } \frac{d^i e(t)}{d t^i} = 0$ , for $i=0,1,\ldots, n^*\text{$-$}1$. Such a new MRAC system property leads to several new results of adaptive stabilization and tracking control using either state feedback or output feedback, as clarified in this paper. [ABSTRACT FROM AUTHOR]

In this paper, we consider a delay differential inclusion $\dot{x}(t)\in F(t,x_t)$ , where $x_t$ denotes the history function of $x(\cdot)$ along an interval of time. We extend the celebrated Filippov's theorem to this case. Then, we further generalize this theorem to the case when the state variable $x$ is constrained to the closure of an open subset $K\subset \mathbb {R}^n$. Under a new “inward pointing condition,” we give a relaxation result stating that the set of trajectories lying in the interior of the state constraint is dense in the set of constrained trajectories of the convexified inclusion ${\dot{x}(t)\in \mbox{co}\,F(t,x_t)}$. [ABSTRACT FROM AUTHOR]

We detail in this paper the importance of a change of strategy for the delay robust control of systems composed of two linear first-order hyperbolic equations. One must go back to the classical tradeoff between convergence rate and delay robustness. More precisely, we prove that, for systems with strong reflections, canceling the reflection at the actuated boundary will yield zero delay robustness. Indeed, for such systems, using a backstepping controller, the corresponding target system should preserve a small amount of this reflection to ensure robustness to a small delay in the loop. This implies, in some cases, giving up finite time convergence. [ABSTRACT FROM AUTHOR]

Periodic optimal control problems (POCPs) based on dynamic models holding invariants are often problematic to treat using standard numerical methods. The difficulty stems from a failure of standard constraint qualifications and typically hinders the convergence of the numerical solver, or even defeats it. Optimization problems having weak constraint qualifications can be treated using dedicated solvers, at the price of a more involved algorithmic. In this paper, we analyze the constraint qualification of POCPs holding invariants, and propose three simple and computationally inexpensive modifications of the formulation that allow for a recovery of linear independence constraint qualification, while not affecting the second-order sufficient conditions for optimality. Hence, the resulting POCP can be tackled via standard solvers, without special treatment. The application of these approaches is detailed for the case of POCPs holding index-reduced differential-algebraic equations and representations of the $\mathrm{SO}\left(3\right)$ Lie group. [ABSTRACT FROM AUTHOR]

In this paper, we consider nonlinear stochastic systems and intersect ideas from nonlinear control theory and numerical analysis. In particular, we use the idea of relative degree. This concept guarantees smoothness properties of the output and this, in turn, allows one to establish properties that are unique to the control-theoretic perspective. The contributions of the current paper are threefold. Firstly, we define different error measures that extend the ideas of local and global approximation errors for nonlinear stochastic systems. Secondly, we demonstrate that the concept of relative degree plays a key role in obtaining higher order of accuracy for integration procedures compared to Euler-Maruyama integration. We show that a particular state-space model, named STTS model, has an improved order of accuracy when compared to an Euler-Maruyama approximation, at no significant extra computational cost. Thirdly, we show that a further approximation to the STTS model, named MSTTS model, while retaining the order of local errors, has explicit sampling zero dynamics, associated with the noise processes, that have no continuous-time counterpart. The extra zero dynamics are shown to be a function of the Euler-Frobenius polynomials. To the best of the authors' knowledge, this is the first reference to sampling zero dynamics for stochastic nonlinear systems. [ABSTRACT FROM AUTHOR]

This paper presents a projection neural network described by a dynamic system for solving constrained quadratic minimax programming problems. Sufficient conditions based on a linear matrix inequality are provided for global convergence of the proposed neural network. Compared with some of the existing neural networks for quadratic minimax optimization, the proposed neural network in this paper is capable of solving more general constrained quadratic minimax optimization problems, and the designed neural network does not include any parameter. Moreover, the neural network has lower model complexities, the number of state variables of which is equal to that of the dimension of the optimization problems. The simulation results on numerical examples are discussed to demonstrate the effectiveness and characteristics of the proposed neural network. [ABSTRACT FROM PUBLISHER]

This paper develops and validates a comprehensive and universally applicable computational concept for solving nonlinear differential equations (NDEs) through a neurocomputing concept based on cellular neural networks (CNNs). High-precision, stability, convergence, and lowest-possible memory requirements are ensured by the CNN processor architecture. A significant challenge solved in this paper is that all these cited computing features are ensured in all system-states (regular or chaotic ones) and in all bifurcation conditions that may be experienced by NDEs.One particular quintessence of this paper is to develop and demonstrate a solver concept that shows and ensures that CNN processors (realized either in hardware or in software) are universal solvers of NDE models. The solving logic or algorithm of given NDEs (possible examples are: Duffing, Mathieu, Van der Pol, Jerk, Chua, Rössler, Lorenz, Burgers, and the transport equations) through a CNN processor system is provided by a set of templates that are computed by our comprehensive templates calculation technique that we call nonlinear adaptive optimization. This paper is therefore a significant contribution and represents a cutting-edge real-time computational engineering approach, especially while considering the various scientific and engineering applications of this ultrafast, energy-and-memory-efficient, and high-precise NDE solver concept. For illustration purposes, three NDE models are demonstratively solved, and related CNN templates are derived and used: the periodically excited Duffing equation, the Mathieu equation, and the transport equation. [ABSTRACT FROM PUBLISHER]

This paper studies the effects of uniform input noise and Gaussian input noise on the dual neural network-based $k$ WTA (DNN- $k$ WTA) model. We show that the state of the network (under either uniform input noise or Gaussian input noise) converges to one of the equilibrium points. We then derive a formula to check if the network produce correct outputs or not. Furthermore, for the uniformly distributed inputs, two lower bounds (one for each type of input noise) on the probability that the network produces the correct outputs are presented. Besides, when the minimum separation amongst inputs is given, we derive the condition for the network producing the correct outputs. Finally, experimental results are presented to verify our theoretical results. Since random drift in the comparators can be considered as input noise, our results can be applied to the random drift situation. [ABSTRACT FROM AUTHOR]

In this paper, source localization by a network of primitive binary sensors under various imperfections are studied. Detailed analysis and mathematical modeling of imperfect binary sensors are presented. Imperfections include sensor failures of two types, drifting, uncertainty, and heterogeneity in binary sensor trigger thresholds, presence of noise, and nonradial symmetry of sensing ranges. Theoretical results, including asymptotical convergence, are established, in particular in the presence of substantial outliers due to sensor failure and large noise. Efficient numerical algorithms are proposed and simulated supporting the theoretical analysis. [ABSTRACT FROM PUBLISHER]

For decades, scientists have studied opinion formation in social networks, where information travels via word of mouth. The particularly interesting case is when polar opinions—Democrats versus Republicans or iOS versus Android—compete in the network. The central problem is to design and analyze a model that captures how polar opinions evolve in the real world. In this paper, we propose a general nonlinear model of polar opinion dynamics, rooted in several theories of sociology and social psychology. The model's key distinguishing trait is that unlike in the existing linear models, such as DeGroot and Friedkin–Johnsen models, an individual's susceptibility to persuasion is a function of his or her current opinion. For example, a person holding a neutral opinion may be rather malleable, while “extremists” may be strongly committed to their current beliefs. We also study three specializations of our general model, whose susceptibility functions correspond to different sociopsychological theories. We provide a comprehensive theoretical analysis of our nonlinear models’ behavior using several tools from nonsmooth analysis of dynamical systems. To study convergence, we use nonsmooth max–min Lyapunov functions together with the generalized Invariance Principle. For our general model, we derive a general sufficient condition for the convergence to consensus. For the specialized models, we provide a full theoretical analysis of their convergence—whether to consensus or disagreement. Our results are rather general and easily apply to the analysis of other nonlinear models defined over directed networks, with Lyapunov functions constructed out of convex components. [ABSTRACT FROM PUBLISHER]

This paper presents a novel neural network for solving generally constrained variational inequality problems by constructing a system of double projection equations. By defining proper convex energy functions, the proposed neural network is proved to be stable in the sense of Lyapunov and converges to an exact solution of the original problem for any starting point under the weaker cocoercivity condition or the monotonicity condition of the gradient mapping on the linear equation set. Furthermore, two sufficient conditions are provided to ensure the stability of the proposed neural network for a special case. The proposed model overcomes some shortcomings of existing continuous-time neural networks for constrained variational inequality, and its stability only requires some monotonicity conditions of the underlying mapping and the concavity of nonlinear inequality constraints on the equation set. The validity and transient behavior of the proposed neural network are demonstrated by some simulation results. [ABSTRACT FROM PUBLISHER]

Use of a gradient descent control law has been a popular method to effectively stabilize undirected rigid formations, by assuming that interagent distances between a certain set of neighboring agent pairs can be accurately specified and measured. This paper examines the collective motion behavior for an infinitesimally rigid formation in a three-dimensional ambient space, in the case that neighboring agent pairs have slightly differing views or measurements of the desired interagent distances they are tasked to maintain. It is shown that the formation shape will converge exponentially fast to a rigid one, while additional rigid helical motions of the final formation will occur. We further discuss the convergence to the equilibrium motions, and derive certain motion parameter formulas to describe the rigid formation movements by employing the angular momentum concept from classical mechanics. Finally, we explain how the idea can be used for steering a rigid formation to move as a rigid body. [ABSTRACT FROM AUTHOR]

The main objective of this paper is to revisit one of the key steps of immersion and invariance stabilizing controller design. Namely, the one that ensures attractivity of the manifold whose internal dynamics contains a copy of the desired system behavior. Towards this end we invoke contraction theory principles and propose two alternative procedures to carry out this step: (i) to replace attractivity of the manifold by virtual contraction of the off-the-manifold coordinate and (ii) to ensure the attractivity of the manifold rendering it horizontally contractive. This makes more systematic the design with more explicit degrees of freedom to accomplish the task. Several examples, including the classical case of systems in feedback form, are used to illustrate the proposed design. [ABSTRACT FROM AUTHOR]

In this paper, we propose a neural network modeled by a differential inclusion to solve a class of nonsmooth convex optimization problems, where the constraints are defined by a class of nonsmooth convex inequality constraints and a class of affine equality constraints. For any initial point, the solution of the proposed network is global existent, unique and uniformly bounded, which is just the “slow solution” of network. By the regularization item, without any estimation on the exact penalty parameters, the solution of proposed network is convergent to the optimal solution set of optimization problem. Moreover, when the feasible region satisfies another condition, the solution of proposed network converges to the feasible region in finite time and to the particular element in the optimal solution set with the smallest norm, which indicates that our proposed neural network is globally attractive. Some numerical examples are presented to illustrate the effectiveness of the proposed neural network for solving nonsmooth convex optimization problems. [ABSTRACT FROM AUTHOR]

Unlike many complex networks studied in the literature, social networks rarely exhibit unanimous behavior, or consensus. This requires a development of mathematical models that are sufficiently simple to be examined and capture, at the same time, the complex behavior of real social groups, where opinions and actions related to them may form clusters of different size. One such model, proposed by Friedkin and Johnsen, extends the idea of conventional consensus algorithm (also referred to as the iterative opinion pooling) to take into account the actors’ prejudices, caused by some exogenous factors and leading to disagreement in the final opinions. In this paper, we offer a novel multidimensional extension, describing the evolution of the agents’ opinions on several topics. Unlike the existing models, these topics are interdependent, and hence the opinions being formed on these topics are also mutually dependent. We rigorously examine stability properties of the proposed model, in particular, convergence of the agents’ opinions. Although our model assumes synchronous communication among the agents, we show that the same final opinions may be reached “on average” via asynchronous gossip-based protocols. [ABSTRACT FROM PUBLISHER]

We analyze the convergence aspects of the invariant extended Kalman filter (IEKF), when the latter is used as a deterministic nonlinear observer on Lie groups, for continuous-time systems with discrete observations. One of the main features of invariant observers for left-invariant systems on Lie groups is that the estimation error is autonomous. In this paper we first generalize this result by characterizing the (much broader) class of systems for which this property holds. For those systems, the Lie logarithm of the error turns out to obey a linear differential equation. Then, we leverage this “log-linear” property of the error evolution, to prove for those systems the local stability of the IEKF around any trajectory, under the standard conditions of the linear case. One mobile robotics example and one inertial navigation example illustrate the interest of the approach. Simulations evidence the fact that the EKF is capable of diverging in some challenging situations, where the IEKF with identical tuning keeps converging. [ABSTRACT FROM AUTHOR]

This paper establishes an off-policy integral reinforcement learning (IRL) method to solve nonlinear continuous-time (CT) nonzero-sum (NZS) games with unknown system dynamics. The IRL algorithm is presented to obtain the iterative control and off-policy learning is used to allow the dynamics to be completely unknown. Off-policy IRL is designed to do policy evaluation and policy improvement in the policy iteration algorithm. Critic and action networks are used to obtain the performance index and control for each player. The gradient descent algorithm makes the update of critic and action weights simultaneously. The convergence analysis of the weights is given. The asymptotic stability of the closed-loop system and the existence of Nash equilibrium are proved. The simulation study demonstrates the effectiveness of the developed method for nonlinear CT NZS games with unknown system dynamics. [ABSTRACT FROM PUBLISHER]

This paper proposes a new iterative solution method for nonlinear stochastic optimal control problems based on path integral analysis. First, we provide an iteration law for solving a stochastic Hamilton-Jacobi-Bellman (SHJB) equation associated to this problem, which is a nonlinear partial differential equation (PDE) of second order. Each iteration procedure of the proposed method is represented by a Cauchy problem for a linear parabolic PDE, and its explicit solution is given by the Feynman-Kac formula. Second, we derive a suboptimal feedback controller at each iteration by using the path integral analysis. Third, the convergence property of the proposed method is investigated. Here, some conditions are provided so that the sequence of solutions for the proposed iteration converges, and the SHJB equation is satisfied. Finally, numerical simulations demonstrate the effectiveness of the proposed method. [ABSTRACT FROM PUBLISHER]

Distributed averaging (also known as average consensus) is an algorithm that builds on neighbor to neighbor interactions with the ultimate goal of convergence to the average of all initial node values or to some value close to that average. We analyze in this paper the performance of distributed averaging algorithms where the information exchanged between neighboring agents is subject to deterministic uniform quantization (i.e., real values sent by nodes to their neighbors are truncated). With such quantization, convergence to the precise average cannot be achieved in general, but the convergence would be to some value close to it, called quantized consensus. Using Lyapunov stability analysis, we characterize the convergence properties of the resulting nonlinear quantized system. We show that in finite time and depending on initial conditions, the algorithm on any static and connected graph will either cause all agents to reach a quantized consensus where the consensus value is the largest quantized value not greater than the average of their initial values, or will lead all variables to oscillate in a small neighborhood around the average. In the latter case, we identify tight bounds for the size of the neighborhood and we further show that the error can be made arbitrarily small by adjusting the algorithm's parameters in a distributed manner. [ABSTRACT FROM AUTHOR]

Regarding two-player zero-sum games of continuous-time nonlinear systems with completely unknown dynamics, this paper presents an online adaptive algorithm for learning the Nash equilibrium solution, i.e., the optimal policy pair. First, for known systems, the simultaneous policy updating algorithm (SPUA) is reviewed. A new analytical method to prove the convergence is presented. Then, based on the SPUA, without using a priori knowledge of any system dynamics, an online algorithm is proposed to simultaneously learn in real time either the minimal nonnegative solution of the Hamilton–Jacobi–Isaacs (HJI) equation or the generalized algebraic Riccati equation for linear systems as a special case, along with the optimal policy pair. The approximate solution to the HJI equation and the admissible policy pair is reexpressed by the approximation theorem. The unknown constants or weights of each are identified simultaneously by resorting to the recursive least square method. The convergence of the online algorithm to the optimal solutions is provided. A practical online algorithm is also developed. Simulation results illustrate the effectiveness of the proposed method. [ABSTRACT FROM PUBLISHER]

Goal representation heuristic dynamic programming (GrHDP) control design has been developed in recent years. The control performance of this design has been demonstrated in several case studies, and also showed applicable to industrial-scale complex control problems. In this paper, we develop the theoretical analysis for the GrHDP design under certain conditions. It has been shown that the internal reinforcement signal is a bounded signal and the performance index can converge to its optimal value monotonically. The existence of the admissible control is also proved. Although the GrHDP control method has been investigated in many areas before, to the best of our knowledge, this is the first study of presenting the theoretical foundation of the internal reinforcement signal and how such an internal reinforcement signal can provide effective information to improve the control performance. Numerous simulation studies are used to validate the theoretical analysis and also demonstrate the effectiveness of the GrHDP design. [ABSTRACT FROM PUBLISHER]

This paper presents a new method for parametric model order reduction based on balanced truncation. Parametric model order reduction seeks to generate low-order models from larger models without losing the dependence on a parameter. Using a Taylor expansion of the original system, a Taylor expansion of the balanced system can be obtained. In contrast to interpolation-based approaches for the solution of the parametric model order reduction problem, the proposed approach permits calculation of the reduced system as well as the corresponding projection matrix for different parameter values with reduced computation power. This bypasses the problem of incompatible subspaces from different snapshot points potentially occurring in interpolation based approaches that can lead to unexpected behavior up to instability. The presented method can handle multidimensional parameter spaces. Sufficient conditions for the convergence of the Taylor series of the balanced system based on holomorphic functions are derived. The truncation step as well as error bounds are discussed. A Bernoulli beam model is used as an example to demonstrate the performance of the technique. [ABSTRACT FROM PUBLISHER]

This paper considers decentralized control and optimization methodologies for large populations of systems, consisting of several agents with different individual behaviors, constraints and interests, and influenced by the aggregate behavior of the overall population. For such large-scale systems, the theory of aggregative and mean field games has been established and successfully applied in various scientific disciplines. While the existing literature addresses the case of unconstrained agents, we formulate deterministic mean field control problems in the presence of heterogeneous convex constraints for the individual agents, for instance arising from agents with linear dynamics subject to convex state and control constraints. We propose several model-free feedback iterations to compute in a decentralized fashion a mean field Nash equilibrium in the limit of infinite population size. We apply our methods to the constrained linear quadratic deterministic mean field control problem. [ABSTRACT FROM PUBLISHER]

The paper proposes a technique to estimate the angular velocity of a rigid body from single vector measurements. Compared to the approaches presented in the literature, it does not use attitude information nor rate gyros as inputs. Instead, vector measurements are directly filtered through a nonlinear observer estimating the angular velocity. Convergence is established using a detailed analysis of a linear-time varying dynamics appearing in the estimation error equation. This equation stems from the classic Euler equations and measurement equations. As is proven, the case of free-rotation allows one to relax the persistence of excitation assumption. Simulation results are provided to illustrate the method. [ABSTRACT FROM PUBLISHER]

In this paper, a new VLSI implementable Hopf oscillator with dynamic plasticity is proposed for next-generation portable signal processing application. A circuit-realizable piece-wise linear function has been used to govern the frequency adaptation characteristic of the proposed oscillator. Furthermore, a straightforward method is suggested to extract the frequency component of the input signal. Mathematical model of the oscillator is derived and it is shown, using VHDL-AMS model, that despite using a new nonlinear function, the oscillator exhibits the same characteristics and learning behavior as the original one with improved learning time. Subsequently, an equivalent circuit model and transistor level implementation for the oscillator is suggested and the mathematical model is confirmed with system and circuit level simulations. Capability of such oscillator to extract frequency futures without doing explicit signal processing is shown with examples of both synthetic and real-life EMG signals. [ABSTRACT FROM PUBLISHER]

In this paper, we propose and study a master-equation based approach to drive a quantum network with n qubits to a consensus (symmetric) state introduced by Mazzarella et al. The state evolution of the quantum network is described by a Lindblad master equation with the Lindblad terms generated by continuous-time swapping operators, which also introduce an underlying interaction graph. We establish a graphical method that bridges the proposed quantum consensus scheme and classical consensus dynamics by studying an induced graph (with 2^{2n} nodes) of the quantum interaction graph (with n$ qubits). A fundamental connection is then shown that quantum consensus over the quantum graph is equivalent to componentwise classical consensus over the induced graph, which allows various existing works on classical consensus to be applicable to the quantum setting. Some basic scaling and structural properties of the quantum induced graph are established via combinatorial analysis. Necessary and sufficient conditions for exponential and asymptotic quantum consensus are obtained, respectively, for switching quantum interaction graphs. As a quantum analogue of classical synchronization of coupled oscillators, quantum synchronization conditions are also presented, in which the reduced states of all qubits tend to a common trajectory. [ABSTRACT FROM PUBLISHER]

In this paper, a bi-projection neural network for solving a class of constrained quadratic optimization problems is proposed. It is proved that the proposed neural network is globally stable in the sense of Lyapunov, and the output trajectory of the proposed neural network will converge globally to an optimal solution. Compared with existing projection neural networks (PNNs), the proposed neural network has a very small model size owing to its bi-projection structure. Furthermore, an application to data fusion shows that the proposed neural network is very effective. Numerical results demonstrate that the proposed neural network is much faster than the existing PNNs. [ABSTRACT FROM AUTHOR]

In this paper, we explore a variety of new multistability scenarios in the general delayed neural network system. Geometric structure embedded in equations is exploited and incorporated into the analysis to elucidate the underlying dynamics. Criteria derived from different geometric configurations lead to disparate numbers of equilibria. A new approach named sequential contracting is applied to conclude the global convergence to multiple equilibrium points of the system. The formulation accommodates both smooth sigmoidal and piecewise-linear activation functions. Several numerical examples illustrate the present analytic theory. [ABSTRACT FROM PUBLISHER]

How to propagate the label information from labeled examples to unlabeled examples is a critical problem for graph-based semisupervised learning. Many label propagation algorithms have been developed in recent years and have obtained promising performance on various applications. However, the eigenvalues of iteration matrices in these algorithms are usually distributed irregularly, which slow down the convergence rate and impair the learning performance. This paper proposes a novel label propagation method called Fick’s law assisted propagation (FLAP). Unlike the existing algorithms that are directly derived from statistical learning, FLAP is deduced on the basis of the theory of Fick’s First Law of Diffusion, which is widely known as the fundamental theory in fluid-spreading. We prove that FLAP will converge with linear rate and show that FLAP makes eigenvalues of the iteration matrix distributed regularly. Comprehensive experimental evaluations on synthetic and practical datasets reveal that FLAP obtains encouraging results in terms of both accuracy and efficiency. [ABSTRACT FROM AUTHOR]

Stochastic Trust-Region Response-Surface method (STRONG) is a new response-surface-based framework for simulation optimization. The appeal of STRONG lies in that it preserves the advantages, yet eliminates the disadvantages, of traditional response surface methodology (RSM) that has been used for more than 50 years. Specifically, STRONG does not require human involvement in the search process and can guarantee to converge to the true optimum with probability one (w.p.1). In this paper, we propose an improved framework, called STRONG-X, that enhances the efficiency and efficacy of STRONG to widen its applicability to more practical problems. For efficiency improvement, STRONG-X includes a newly-developed experimental scheme that consists of construction of optimal simulation designs and an assignment strategy for random number streams to obtain computational gains. For efficacy improvement, a new variant, called STRONG-XG, is developed to achieve convergence under generally-distributed responses, as opposed to STRONG and STRONG-X where convergence is guaranteed only when the response is normal. An extensive numerical study is conducted to evaluate the efficiency and efficacy of STRONG-X and STRONG-XG. Moreover, two illustrative examples are provided to show the viability of STRONG-X and STRONG-XG in practical settings. [ABSTRACT FROM AUTHOR]

Subspace clustering is the task of identifying clusters in subspaces of the input dimensions of a given dataset. Noisy data in certain attributes cause difficulties for traditional clustering algorithms, because the high discrepancies within them can make objects appear too different to be grouped in the same cluster. This requires methods specially designed for subspace clustering. This paper presents our second approach to subspace and projected clustering based on self-organizing maps (SOMs), which is a local adaptive receptive field dimension selective SOM. By introducing a time-variant topology, our method is an improvement in terms of clustering quality, computational cost, and parameterization. This enables the method to identify the correct number of clusters and their respective relevant dimensions, and thus it presents nearly perfect results in synthetic datasets and surpasses our previous method in most of the real-world datasets considered. [ABSTRACT FROM AUTHOR]

The problem of stabilization of nonlinear systems, which depend nonlinearly on fast time-varying parameters, is considered in the technical note. It is assumed that, if the plant parameters were known, a static state-feedback controller that achieves the stabilization objective with a Lyapunov-like function that is independent of the parameters is known. A constructive procedure to update the unknown parameters of the controller, based on the immersion and invariance approach, is proposed. The main contribution of the paper is to show that the proposed controller guarantees global convergence to zero of the systems state for arbitrary time variations of the plant parameters provided the controller parameters are bounded. To ensure the latter condition, an assumption, that in the single parameter case is strictly weaker than the monotonicity condition invoked in previous studies, is imposed. Stabilization is achieved via a, rather unique, combination of gradient-like parameter estimation and the construction of a monotonic signal that counters the deleterious effect of the parameter variations. Several simulation examples illustrate the applicability of the suggested method. [ABSTRACT FROM AUTHOR]

This paper is concerned with the use of \BBH2-control performance metrics in finding optimal actuator locations for a class of infinite-dimensional systems. Conditions that guarantee convergence of the optimal actuator location for the finite-dimensional representation of the infinite-dimensional system to the optimal actuator location of the original infinite-dimensional system are provided. Minimizing an \BBH2-performance index, parameterized by the possible actuator locations and disturbance functions, leads to optimal locations that in addition to enhanced performance, also provide robustness with respect to the spatial distribution of disturbances. Numerical studies for a cantilever beam and a diffusion problem are used to demonstrate the effects of the spatial distribution of disturbances on the optimal actuator location. The effect of the diffusivity parameter on the best actuator locations is also considered. [ABSTRACT FROM AUTHOR]

As a special class of recurrent neural network, Zhang neural network (ZNN) has been recently proposed since 2001 for solving various time-varying problems, and has shown high efficiency and excellent performance for solving the problems in the real domain. In this paper, to solve online the time-varying complex generalized inverse (in most cases, the pseudoinverse) problem in the complex domain, a new type of complex-valued ZNN is further proposed and investigated. The design of such a complex ZNN is based on a complex Zhang function (ZF) which is indefinite and quite different from the usual error function (specially, the scalar-valued energy function) in the studies of conventional algorithms. By introducing five different complex ZFs, five different complex ZNN models (termed complex ZNN-I, ZNN-II, ZNN-III, ZNN-IV, and ZNN-V models) are proposed, developed, and investigated for the online solution of the time-varying complex generalized inverse matrices. Theoretical results of convergence analysis are presented to show the desirable properties of complex ZNN models. In addition, we discover the link between the proposed complex ZNN models and the Getz–Marsden dynamic system in the complex domain. Computer-simulation results further demonstrate the effectiveness of complex ZNN models based on different complex ZFs for the time-varying complex generalized inverse matrices. [ABSTRACT FROM AUTHOR]

This paper presents one-layer projection neural networks based on projection operators for solving constrained variational inequalities and related optimization problems. Sufficient conditions for global convergence of the proposed neural networks are provided based on Lyapunov stability. Compared with the existing neural networks for variational inequalities and optimization, the proposed neural networks have lower model complexities. In addition, some improved criteria for global convergence are given. Compared with our previous work, a design parameter has been added in the projection neural network models, and it results in some improved performance. The simulation results on numerical examples are discussed to demonstrate the effectiveness and characteristics of the proposed neural networks. [ABSTRACT FROM AUTHOR]

Goal representation heuristic dynamic programming (GrHDP) is proposed in this paper to demonstrate online learning in the Markov decision process. In addition to the (external) reinforcement signal in literature, we develop an adaptively internal goal/reward representation for the agent with the proposed goal network. Specifically, we keep the actor-critic design in heuristic dynamic programming (HDP) and include a goal network to represent the internal goal signal, to further help the value function approximation. We evaluate our proposed GrHDP algorithm on two 2-D maze navigation problems, and later on one 3-D maze navigation problem. Compared to the traditional HDP approach, the learning performance of the agent is improved with our proposed GrHDP approach. In addition, we also include the learning performance with two other reinforcement learning algorithms, namely Sarsa(\lambda) and Q-learning, on the same benchmarks for comparison. Furthermore, in order to demonstrate the theoretical guarantee of our proposed method, we provide the characteristics analysis toward the convergence of weights in neural networks in our GrHDP approach. [ABSTRACT FROM PUBLISHER]

Traditionally, the design of extremum seeking algorithm treats the system as essentially a black-box, which for many applications means disregarding known information about the model structure. In contrast to this approach, there have been recent examples where a known plant structure with uncertain parameters has been used in the online optimization of plant operation. However, the results for these approaches have been restricted to specific classes of plants and optimization algorithms. This paper seeks to provide general results and a framework for the design of extremum seekers applied to systems with parameter uncertainties. General conditions for an optimization method and a parameter estimator are presented so that their combination guarantees convergence of the extremum seeker for both static and dynamic plants. Tuning guidelines for the closed loop scheme are also presented. The generality and flexibility of the proposed framework is demonstrated through a number of parameter estimators and optimization algorithms that can be combined to obtain extremum seeking. Examples of anti-lock braking and model reference adaptive control are used to illustrate the effectiveness of the proposed framework. [ABSTRACT FROM AUTHOR]