State and input simultaneous estimation for a class of nonlinear systems

This paper addresses the problem of estimating simultaneously the state and input of a class of nonlinear systems. Here, the systems nonlinear part comprises a Lipschitz nonlinear function with respect to the state and input, and a state-dependent unknown function including additive disturbance as well as uncertain/nonlinear/time-varying terms. Upon satisfying some conditions, the observer design problem can be solved via a Riccati inequality or a LMI-based technique with asymptotic estimation guaranteed. A numerical example is included for illustration.

Can dietary lipid source circadian alternation improve omega-3 deposition in rainbow trout?

With the salmonid industry currently exploiting the vast majority of globally available fish oil, there is the need to optimise fish oil utilisation by increasing its efficiency in terms of transferring the health-promoting long chain omega-3 fatty acids (n−3 LC-PUFA) into farmed fish flesh. The aim of this study was to evaluate if dietary fatty acid deposition is affected by the time of feeding, and hence identify possible innovative feeding strategies towardsmore efficient use of dietary fish oil. Over a period of 12 weeks, three diets with different lipid sources, canola oil (CO), fish oil (FO) or a 50/50 blend of the two oils (Mix), were alternated daily and fed to rainbow trout (Oncorhynchus mykiss). Six treatments were administered to fish, reference treatment (REF, continuously fed FO), control treatment (CT, continuously fed Mix), am canola oil ration (amCOR), pm canola oil ration (pmCOR), am canola oil satiation (amCOS) and pm canola oil satiation (pmCOS). Fish received either the CO diet in the am or pm feeds and received the FO diet at the opposite time. A significant increase in growth and feed consumption was noted in the pmCOS treatment. Fillet fatty acid profile was modified by associated feeding schedules and was generally reflective of dietary fatty acid profile. No significant increases in n−3 LCPUFA deposition were observed. However, both linoleic acid (18:2n−6) and α-linolenic acid (18:3n−3) contents were significantly higher in pmCOR compared to amCOR and CT. The results of the present study suggest the existence of cyclical circadian patterns in fatty acid deposition in rainbow trout.

Observer-based control for time-varying delay neural networks with nonlinear observation

This paper studies the problem of designing observer-based controllers for a class of delayed neural networks with nonlinear observation. The system under consideration is subject to nonlinear observation and an interval time-varying delay. The nonlinear observation output is any nonlinear Lipschitzian function and the time-varying delay is not required to be differentiable nor its lower bound be zero. By constructing a set of appropriate Lyapunov-Krasovskii functionals and utilizing the Newton-Leibniz formula, some delay-dependent stabilizability conditions which are expressed in terms of Linear Matrix Inequalities (LMIs) are derived. The derived conditions allow simultaneous computation of two bounds that characterize the exponential stability rate of the closed-loop system. The unknown observer gain and the state feedback observer-based controller are directly obtained upon the feasibility of the derived LMIs stabilizability conditions. A simulation example is presented to verify the effectiveness of the proposed result.

Nonnegative Matrix Factorization Applied to Nonlinear Speech and Image Cryptosystems

Nonnegative matrix factorization (NMF) is widely used in signal separation and image compression. Motivated by its successful applications, we propose a new cryptosystem based on NMF, where the nonlinear mixing (NLM) model with a strong noise is introduced for encryption and NMF is used for decryption. The security of the cryptosystem relies on following two facts: 1) the constructed multivariable nonlinear function is not invertible; 2) the process of NMF is unilateral, if the inverse matrix of the constructed linear mixing matrix is not nonnegative. Comparing with Lin's method (2006) that is a theoretical scheme using one-time padding in the cryptosystem, our cipher can be used repeatedly for the practical request, i.e., multitme padding is used in our cryptosystem. Also, there is no restriction on statistical characteristics of the ciphers and the plaintexts. Thus, more signals can be processed (successfully encrypted and decrypted), no matter they are correlative, sparse, or Gaussian. Furthermore, instead of the number of zero-crossing-based method that is often unstable in encryption and decryption, an improved method based on the kurtosis of the signals is introduced to solve permutation ambiguities in waveform reconstruction. Simulations are given to illustrate security and availability of our cryptosystem.

Full-order observer design for nonlinear complex large-scale systems with unknown time-varying delayed interactions

This article is concerned with the problem of state observer for complex large-scale systems with unknown time-varying delayed interactions. The class of large-scale interconnected systems under consideration is subjected to interval time-varying delays and nonlinear perturbations. By introducing a set of argumented Lyapunov–Krasovskii functionals and using a new bounding estimation technique, novel delay-dependent conditions for existence of state observers with guaranteed exponential stability are derived in terms of linear matrix inequalities (LMIs). In our design approach, the set of full-order Luenberger-type state observers are systematically derived via the use of an efficient LMI-based algorithm. Numerical examples are given to illustrate the effectiveness of the result

Mixing vector construction for single channel semi-blind source separation using empirical mode decomposition

The Empirical Mode Decomposition (EMD) method is a commonly used method for solving the problem of single channel blind source separation (SCBSS) in signal processing. However, the mixing vector of SCBSS, which is the base of the EMD method, has not yet been effectively constructed. The mixing vector reflects the weights of original signal sources that form the single channel blind signal source. In this paper, we propose a novel method to construct a mixing vector for a single channel blind signal source to approximate the actual mixing vector in terms of keeping the same ratios between signal weights. The constructed mixing vector can be used to improve signal separations. Our method incorporates the adaptive filter, least square method, EMD method and signal source samples to construct the mixing vector. Experimental tests using audio signal evaluations were conducted and the results indicated that our method can improve the similar values of sources energy ratio from 0.2644 to 0.8366. This kind of recognition is very important in weak signal detection.

Global finite-time stabilisation for a class of stochastic nonlinear systems by output feedback

In this paper, the problem of global finite-time stabilisation by output feedback is considered for a class of stochastic nonlinear systems. First, based on homogeneous systems theory and the adding a power integrator technique, a homogeneous reduced order observer and control law are constructed in a recursive manner for the nominal system. Then, the homogeneous domination approach is used to deal with the nonlinearities in drift and diffusion terms; it is shown that the proposed output-feedback control law can guarantee that the closed-loop system is global finite-time stable in probability. Finally, simulation examples are carried out to demonstrate the effectiveness of the proposed control scheme.

Robust non-fragile control for offshore steel jacket platform with nonlinear perturbations

This study is concerned with the design of a non-fragile controller for an offshore steel jacket platform with nonlinear perturbations. The delay-dependent sufficient conditions are derived in terms of linear matrix inequalities based on suitable Lyapunov–Krasovskii functional, the second-order reciprocally convex approach and the lower bound lemma. The results indicate asymptotic stability of the offshore steel jacket platform utilizing the proposed non-fragile controller. Besides that, robust stability conditions are derived for an uncertain offshore platform subject to the non-fragile controller. A numerical example is given to illustrate the effectiveness of the proposed theoretical results.

Optimisation of nonlinear motion cueing algorithm based on genetic algorithm

Motion cueing algorithms (MCAs) are playing a significant role in driving simulators, aiming to deliver the most accurate human sensation to the simulator drivers compared with a real vehicle driver, without exceeding the physical limitations of the simulator. This paper provides the optimisation design of an MCA for a vehicle simulator, in order to find the most suitable washout algorithm parameters, while respecting all motion platform physical limitations, and minimising human perception error between real and simulator driver. One of the main limitations of the classical washout filters is that it is attuned by the worst-case scenario tuning method. This is based on trial and error, and is effected by driving and programmers experience, making this the most significant obstacle to full motion platform utilisation. This leads to inflexibility of the structure, production of false cues and makes the resulting simulator fail to suit all circumstances. In addition, the classical method does not take minimisation of human perception error and physical constraints into account. Production of motion cues and the impact of different parameters of classical washout filters on motion cues remain inaccessible for designers for this reason. The aim of this paper is to provide an optimisation method for tuning the MCA parameters, based on nonlinear filtering and genetic algorithms. This is done by taking vestibular sensation error into account between real and simulated cases, as well as main dynamic limitations, tilt coordination and correlation coefficient. Three additional compensatory linear blocks are integrated into the MCA, to be tuned in order to modify the performance of the filters successfully. The proposed optimised MCA is implemented in MATLAB/Simulink software packages. The results generated using the proposed method show increased performance in terms of human sensation, reference shape tracking and exploiting the platform more efficiently without reaching the motion limitations.

Nonlinear backstepping controller design for sharing active and reactive power in three-phase grid-connected photovoltaic systems

In this paper, a nonlinear backstepping controller is designed for three-phase grid-connected solar photovoltaic (PV) systems to share active and reactive power. A cascaded control structure is considered for the purpose of sharing appropriate amount of power. In this cascaded control structure, the dc-link voltage controller is designed for balancing the power flow within the system and the current controller is designed to shape the grid current into a pure sinusoidal waveform. In order to balance the power flow, it is always essential to maintain a constant voltage across the dc-link capacitor for which an incremental conductance (IC) method is used in this paper. This approach also ensures the operation of solar PV arrays at the maximum power point (MPP) under rapidly changing atmospheric conditions. The proposed current controller is designed to guarantee the current injection into the grid in such a way that the system operates at a power factor other than unity which is essential for sharing active and reactive power. The performance of the proposed backstepping approach is verified on a three-phase grid-connected PV system under different atmospheric conditions. Simulation results show the effectiveness of the proposed control scheme in terms of achieving desired control objectives.

Explicit invariant solutions associated with nonlinear atmospheric flows in a thin rotating spherical shell with and without west-to-east jets perturbations

A class of non-stationary exact solutions of two-dimensional nonlinear Navier–Stokes (NS) equations within a thin rotating spherical shell were found as invariant and approximately invariant solutions. The model is used to describe a simple zonally averaged atmospheric circulation caused by the difference in temperature between the equator and the poles. Coriolis effects are generated by pseudoforces, which support the stable west-to-east flows providing the achievable meteorological flows. The model is superimposed by a stationary latitude dependent flow. Under the assumption of no friction, the perturbed model describes zonal west-to-east flows in the upper atmosphere between the Ferrel and Polar cells. In terms of nonlinear modeling for the NS equations, two small parameters are chosen for the viscosity and the rate of the earth’s rotation and exact solutions in terms of elementary functions are found using approximate symmetry analysis. It is shown that approximately invariant solutions are also valid in the absence of the flow perturbation to a zonally averaged mean flow.

New results on H∞ filtering for nonlinear large-scale systems with interconnected time-varying delays

This paper proposes a new design method of H∞ filtering for nonlinear large-scale systems with interconnected time-varying delays. The interaction terms with interval time-varying delays are bounded by nonlinear bounding functions including all states of the subsystems. A stable linear filter is designed to ensure that the filtering error system is exponentially stable with a prescribed convergence rate. By constructing a set of improved Lyapunov functions and using generalized Jensen inequality, new delay-dependent conditions for designing H∞ filter are obtained in terms of linear matrix inequalities. Finally, an example is provided to illustrate the effectiveness of the proposed result.

Stochastic stability of nonlinear discrete-time Markovian jump systems with time-varying delay and partially unknown transition rates

This paper is concerned with stochastic stability of a class of nonlinear discrete-time Markovian jump systems with interval time-varying delay and partially unknown transition probabilities. A new weighted summation inequality is first derived. We then employ the newly derived inequality to establish delay-dependent conditions which guarantee the stochastic stability of the system. These conditions are derived in terms of tractable matrix inequalities which can be computationally solved by various convex optimized algorithms. Numerical examples are provided to illustrate the effectiveness of the obtained results.

Robust nonlinear adaptive backstepping excitation controller design for rejecting external disturbances in multimachine power systems

This paper proposes a new approach to design a robust adaptive backstepping excitation controller for multimachine power systems in order to reject external disturbances. The parameters which significantly affect the stability of power systems (also called stability sensitive parameters) are considered as unknown and the external disturbances are incorporated into the power system model. The proposed excitation controller is designed in such a way that it is adaptive to the unknown parameters and robust to external disturbances. The stability sensitive parameters are estimated through the adaptation laws and the convergences of these adaptation laws are obtained through the negative semi-definiteness of control Lyapunov functions (CLFs). The proposed controller not only provides robustness property against external disturbances but also overcomes the over-parameterization problem of stability sensitive parameters which usually appears in some conventional adaptive methods. Finally, the performance of the proposed controller is tested on a two-area four machine 11-bus power system by considering external disturbances under different scenarios and is compared to that of an existing nonlinear adaptive backstepping controller. Simulation results illustrate the robustness of the proposed controller over an existing one in terms of rejecting external disturbances.