On the approximate discrete KLT of fractional Brownian motion and applications

This paper establishes connection between discrete cosine transform (DCT) and the discrete-time fractional Brownian motion process (dfBm). It is proved that the eigenvectors of the auto-covariance matrix of a dfBm can be approximated by DCT basis vectors in the asymptotic sense. This shows that DCT basis acts as discrete Karhunen–Loève transform (DKLT) for these processes in the approximate sense. Analytic perturbation theory of linear operators is used to prove this result. This result will be of great practical significance in applications where one is looking for an appropriate basis to work with signals that can perhaps be modeled as belonging to fBm processes. The utility of the proposed work has been illustrated with two real-life data (a) on compressive sampling based reconstruction of financial time-series and (b) in denoising gravitational wave event GW150914 data obtained from a binary black hole merger.     

Orthogonal-polynomials-based integral inequality and its applications to systems with additive time-varying delays

Recently, a polynomials-based integral inequality was proposed by extending the Moon’s inequality into a generic formulation. By imposing certain structures on the slack matrices of this integral inequality, this paper proposes an orthogonal-polynomials-based integral inequality which has lower computational burden than the polynomials-based integral inequality while maintaining the same conservatism. Further, this paper provides notes on relations among recent general integral inequalities constructed with arbitrary degree polynomials. In these notes, it is shown that the proposed integral inequality is superior to the Bessel–Legendre (B–L) inequality and the polynomials-based integral inequality in terms of the conservatism and computational burden, respectively. Moreover, the effectiveness of the proposed method is demonstrated by an illustrative example of stability analysis for systems with additive time-varying delays.     

The obstacle problem of integro-partial differential equations with applications to stochastic optimal control/stopping problem

This paper is devoted to existence and uniqueness of minimal mild super solutions to the obstacle problem governed by integro-partial differential equations. We first study the well-posedness and local Lipschitz regularity of L^p solutions (p?≥?2) to reflected forward-backward stochastic differential equations (FBSDEs) with jump and lower barrier. Then we show that the solutions to reflected FBSDEs provide a probabilistic representation for the mild super solution via a nonlinear Feynman–Kac formula. Finally, we apply the results to study stochastic optimal control/stopping problems.     

Parametric delta operator Riccati equation and applications to semi-global stabilization in the presence of actuator saturation

In this paper, a parametric delta operator Riccati equation is established for low gain feedbacks of linear delta operator systems. Some properties for the parametric delta operator Riccati equation are given based on a parameter-dependent cost function. An explicit solution is also given for the delta operator parametric Riccati equation. Semi-global stabilization is described for a linear delta operator system with actuator saturation via low gain state and output feedback control laws. A numerical example is given to illustrate the effectiveness and potential for the developed techniques.     

Super-twisting observer-based sliding mode control with fuzzy variable gains and its applications to fully-actuated hexarotors

In this paper, we consider the super-twisting observer-based sliding mode control algorithm with fuzzy variable gains (STOSMC) for the fully-actuated hexarotor. Our hexarotor has full actuation due to six titled propellers that allows to control position and orientation (attitude) simultaneously, and resolves the singularity problem of the rotational matrix by using the quaternion modeling framework. We show that the proposed STOSMC for the hexarotor guarantees finite-time convergence of the estimation error and asymptotic stability of the hexarotor. In simulations, we demonstrate the nonsingularity and fully-actuated control performance of the hexarotor by considering extreme position and attitude control scenarios. Moreover, the simulation results show that the hexarotor achieves the fast and precise tracking performance to the desired position and the desired attitude and the chattering phenomenon is reduced compared with the fixed-gains observer-based super-twisting sliding mode control due to the fuzzy mechanism.     

Stabilization of periodic orbits of discrete-time dynamical systems using the Prediction-Based Control: New control law and practical aspects

This paper tackles in the stabilization of periodic orbits of nonlinear discrete-time dynamical systems with chaotic sets. The problem is approximated locally to the stabilization of linear time-periodic systems and the theory of modern control is applied to the Prediction-Based Control, resulting in a new control law. This control law sets all the Floquet multipliers of the stabilized orbit to zero, resulting in fast convergence of trajectories in its vicinity. Another important characteristic of the control law is that no previous knowledge about the periodic orbit is required for stabilization. Using numerical simulations, this control law was analysed and compared to an optimal Delayed Feedback Control evidencing its advantages in theoretical and practical aspects.     

Subset selection for visualization of relevant image fractions for deep learning based semantic image segmentation

Semantic image segmentation is a challenging problem from image processing where deep convolutional neural networks (CNN) have been applied with great success in the recent years. It deals with pixel-wise classification of an input image, dividing it into regions of multiple object classes. However, CNNs are opaque models. Given a trained CNN, it is hard to tell which information encoded in the input image is important for the network to perform segmentation. Such information could be useful to judge whether a trained network learned to segment in a plausible way or how its performance can be improved.For a trained CNN, we formulate an optimization problem to extract relevant image fractions for semantic segmentation. We try to identify a subset of pixels that contain the relevant information for the segmentation of one selected object class. In experiments on the Cityscapes dataset, we show that this is an easy way to gain valuable insight into a CNN trained for semantic segmentation. Looking at the relevant image fractions, we can identify possible limits of a trained network and draw conclusions about possible improvements.     

Compressed sensing for real measurements of quaternion signals

The paper concerns compressed sensing methods in the quaternion algebra. We prove that it is possible to uniquely reconstruct – by ?₁ norm minimization – a sparse quaternion signal from a limited number of its real linear measurements, provided the measurement matrix satisfies so-called restricted isometry property with a sufficiently small constant. We also provide error estimates for the approximated reconstruction of a non-sparse quaternion signal from noisy and noiseless data.     

Coordination of nonholonomic mobile robots for diffusive threat defense

This paper studies coordination of a team of nonholonomic mobile robots with smart actuators for defending against invasive threat to a planar convex area. The threat refers to a kind of harmful substance such as chemical pollutant appearing outside and moving towards the area. The invasion of threat can be modeled by a 2D unsteady reaction-diffusion process. To reflect the adverse effect of threat on the area, a so-called risk intensity field is introduced. The value of risk intensity is equal to the concentration of threat measured by a static mesh sensor network. Based on this risk intensity field, a coordination control scenario using Voronoi tessellation is formulated. In order to minimize the actuator performance loss and reduce the total average risk intensity simultaneously, a generalized centroidal Voronoi tessellation (CVT) algorithm including optimal motion control and risk mitigation control is designed. The proposed algorithm is gradient-based and guides mobile robots to track their optimal trajectories asymptotically. Meanwhile, two conditions of choosing control gains are derived to keep the total average risk intensity below a safety level. Several simulation examples with different cases of threat invasion are provided and the advantage of proposed algorithm over traditional control method is presented.     

Discrete Legendre polynomials-based inequality for stability of time-varying delayed systems

This paper proposes Discrete Legendre Polynomial(DLP)-based inequality by solving the best weighted approximation of a given time series. The proposed inequality could significantly reduce the conservativeness in stability analysis of systems with constant or interval time-varying delays. Also former well-known integral inequities, such as discrete Jensen inequality, discrete Wirtinger-based inequality, are both included in the proposed DLP-based inequality as special cases with lower-order approximation. Stability criterion with less conservatism is then developed for both constant and time-varying delayed systems. Several numerical examples are given to demonstrate the effectiveness and benefit of the proposed method.     

Modification of Mikhailov stability criterion for fractional commensurate order systems

In this paper we present the modification of the Mikhailov stability criterion for linear fractional commensurate order systems. The modification consists in determining the appropriate measure for the total argument change depending on the highest fractional order ${\alpha }_n=n\alpha$ of the system and not only on the integer n as stated in the literature. The validity of the result is illustrated by means of several examples.     

Nonlinear trajectory tracking controller for a class of robotic vehicles

A global state feedback tracking controller for a class of vehicles, namely marine vehicles, hovercrafts and indoor airships is considered in this paper. The control algorithm uses a velocity transformation of the vehicle equations of motion. It is shown that this algorithm is suitable for control of fully actuated systems and leads to fast response. This property arises from the fact that the dynamical couplings in the vehicle are taken into account in the control gain matrix. A Lyapunov-like function is proposed for the stability analysis of the system under the controller. The algorithms robustness issue is considered too. Numerical simulations are given to illustrate effectiveness of the approach.     

New modeling approach of secondary control layer for autonomous single-phase microgrids

In a microgrid (MG) topology, the secondary control is introduced to compensate for the voltage amplitude and frequency deviations, mainly caused by the inherent characteristics of the droop control strategy. This paper proposes an accurate approach to derive small signal models of the frequency and amplitude voltage at the point of common coupling (PCC) of a single-phase MG by analyzing the dynamics of the second-order generalized integrator-based frequency-locked loop (SOGI-FLL). The frequency estimate model is then introduced in the frequency restoration control loop, while the derived model of the amplitude estimate is introduced for the voltage restoration loop. Based on the obtained models, the MG stability analysis and proposed controllers’ parameters tuning are carried out. Also, this study includes the modeling and design of the synchronization control loop that enables a seamless transition from island mode to grid-connected mode operation. Simulation and practical experiments of a hierarchical control scheme, including traditional droop control and the proposed secondary control for two single-phase parallel inverters, are implemented to confirm the effectiveness and the robustness of the proposal under different operating conditions. The obtained results validate the proposed modeling approach to provide the expected transient response and disturbance rejection in the MG.     

Formation control and collision avoidance for a class of multi-agent systems

In this paper, a control scheme is proposed for a group of elliptical agents to achieve a predefined formation. The agents are assumed to have the same dynamics, and communication among the agents are limited. The desired formation is realized based on the reference formation and the mapping decision. In the control design, searching algorithms for both cases of minimum distance and tangents are established for each agent and its neighbors. In order to avoid collision, an optimal path planning algorithm based on collision angles, and a self-center-based rotation algorithm are also proposed. Moreover, randomized method is used to provide the optimal mapping decision for the underlying system. Two examples and analyses are presented to demonstrate the effectiveness and potential of the new control scheme.     

Robust observer design by sign-stability for the monitoring of population systems

Monitoring problem in population ecology can be formalized as observer design for the population system in question: Supposing that we observe only certain species considered indicators, we want to recover or estimate the whole state process of the population system, where the state vector is usually composed from the biomasses of the single populations. In the present paper, for stably coexisting population systems, a new approach to the design of the corresponding observer system is proposed which, from the knowledge of the observed indicator(s), estimates the state process with exponential convergence. In the usual observer design, an auxiliary matrix, the so-called gain matrix must be found that guarantees the mentioned exponential convergence. The novelty is in that due to the required sign-stability (or qualitative stability) of the interaction pattern, the designed observer system (i.e. the gain matrix) is robust against quantitative changes in the inter- and intra-specific interactions. (Here the interaction pattern is described by a matrix having the signs as entries, indicating the quality of the interactions within and between the considered species.) In other words, under sign-stability conditions, in the observer design the same gain matrix can be used even if, due to environmental changes, the intensities of certain interactions suffer a quantitative change in the meanwhile. The requirement of sign-stability of the interaction pattern can be considered rather natural, since in a stably coexisting population system, it means for example that a predator–prey relation does not change into a prey–predator interaction, and interactions neither appear nor disappear within the system. Our approach to robust observer design is illustrated on model population systems, such as trophic chains of type resource-producer-primary consumer-secondary consumer and Lotka–Volterra system with vertical structure. For the latter system a Lyapunov function is also constructed that guarantees the global asymptotic stability of the positive equilibrium of the considered model.     

Dissipative observers for discrete-time nonlinear systems

This paper addresses the problem of designing a state observer for a class of nonlinear discrete-time systems using the dissipativity theory. We show that the dissipative observation methodology, originally proposed by one of the authors for continuous-time nonlinear systems, can be extended to the discrete-time case. For constructing a convergent observer, the methodology is applied to the nonlinear estimation error dynamics, which is decomposed into a discrete-time Linear Time-Invariant (LTI) subsystem in the forward loop, connected to a time-varying static nonlinearity in the feedback loop. In order to assure asymptotic stability of the closed-loop, complementary dissipativity conditions are imposed on each of the subsystems: (i) the static nonlinearity is required to be dissipative with respect to a quadratic supply rate, and (ii) the observer gains are designed such that the LTI system is dissipative with respect to a complementary supply rate. As in the continuous time framework, the proposed method includes as special cases, unifies and generalizes some observer design methods proposed previously in the literature. A great advantage of the Dissipative Observer Design Method proposed here is that it leads to Matrix Inequalities for the design of the observer gains, and these can be usually converted into Linear Matrix Inequalities (LMI’s). The results are illustrated using Chua’s Chaotic system.     

Self-triggered MPC for trajectory tracking of unicycle-type robots with external disturbance

In this paper, a self-triggered model predictive controller (MPC) strategy for nonholonomic vehicle with coupled input constraint and bounded disturbances is presented. First, a self-triggered mechanism is designed to reduce the computation load of MPC based on a Lyapunov function. Second, by designing a robust terminal region and proper parameters, recursive feasibility of the optimization problem is guaranteed and stability of the the closed-loop system is ensured. Simulation results show the effectiveness of proposed algorithm.     

State feedback design for set stabilization of probabilistic Boolean control networks

Set stabilization of probabilistic Boolean control networks (PBCNs) is investigated in this paper and some interesting results are derived. The main results consist of three parts. (1) A definition of set stabilizability with probability one by closed-loop control is proposed for PBCNs, which is not a natural extension from deterministic Boolean control networks to PBCNs due to the random feature of PBCNs. (2) A necessary and sufficient set stabilizability condition is provided for PBCNs. (3) An algorithm for designing a state feedback controller is developed. It is guaranteed that all designed controllers can stabilize a PBCN to a given subset with probability one. The design method is constructive, so it is convenient to use this method in practical application. The results derived above are fundamental and important, since based on them many problems about PBCNs can be solved, for example partial stabilization, synchronization, and so on. Finally, a practical example is employed to show the effectiveness of our results.     

Integrated guidance and control strategy for homing of unmanned underwater vehicles

This paper presents a novel integrated guidance and control strategy for homing of unmanned underwater vehicles (UUVs) in 5-degree-of-freedom (DOF), where the vehicles are assumed to be underactuated at high speed and required to move towards the final docking path. During the initial homing stage, the guidance system is first designed by geometrical analysis method to generate a feasible reference trajectory. Then, in the backstepping framework, the proposed trajectory tracking controller can achieve all the tracking errors in the closed-loop system convergence to a small neighbourhood of zero. It means that the vehicle's dynamics are consistent with the reference trajectory derived in the previous step. To demonstrate the effectiveness of the proposed guidance and control strategy, the complete stability analysis used Lyapunov's method is given in the paper, and simulation results of all initial conditions are presented and discussed.