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  1. 9 Journal of Theoretical and Applied Mechanics
  2. 7 Vibrations in Physical Systems
  3. 4 Bulletin of the Polish Academy of Sciences. Technical Sciences
  4. 4 Mechanics and Mechanical Engineering
  5. 3 Archives of Civil and Mechanical Engineering
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  1. 4 Awrejcewicz J.
  2. 4 Dąbrowski A.
  3. 3 Pielorz A.
  4. 3 Starosta R.
  5. 2 Balcerzak M.
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  1. 1 2023
  2. 1 2022
  3. 2 2021
  4. 4 2020
  5. 3 2019
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1
Content available Investigation of the pad stiffness effects on the initiation of brake squeal phenomenon
Yavuz Akif, Sen Osman
Journal of Theoretical and Applied Mechanics
|
2023
|
Vol. 61 nr 2
219--232
EN
The main objective of this study is to investigate pad stiffness effects on the instability of a nonlinear brake squeal model. Hence, a nonlinear mathematical model is developed. The nonlinear model is linearized to check the system stability through complex eigenvalue analysis. The results of linear stability analyses are compared to the numerical solution of the nonlinear model, and it is observed that the dynamic behavior predicted by the linear stability analysis is in accordance with the numerical solutions. Though, a discrepancy may occur at the predicted squeal frequencies with both approaches, especially at high pad stiffness levels.
2
Content available Modeling and energy recovery from a system with two pseudo-levitating magnets
Mitura Andrzej, Kecik Krzysztof
Bulletin of the Polish Academy of Sciences. Technical Sciences
|
2022
|
Vol. 70, nr 4
art. no. e141721
EN
In this paper, a model of an electromagnetic system with two levitating magnets is presented. Modeling was performed using the results of experiments. The data obtained make it possible to fit the magnetic forces between two magnets using a 5th order polynomial. The time series show that dry friction constitutes an important part of damping forces. The differential equations of motion consider strong nonlinearities of magnetic and damping forces. These terms cause the nonlinear hardening effect. The energy recovered by magnetic induction is dissipated in the resistors. Numerical simulations show that resistance has an impact on magnet dynamics and energy recovery. From the resonance characteristics obtained, optimal resistance is determined when energy recovery is the highest.
3
Content available Nonlinear double-beam system dynamics
Koziol Piotr, Pilecki Rafał
Archives of Civil Engineering
|
2021
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Vol. 67, nr 2
337--353
EN
Double-beam model is considered in many investigations both theoretical and typically engineering ones. One can find different studies concerning analysis of such structures behaviour, especially in the cases where the system is subjected to dynamic excitations. This kind of model is successfully considered as a reliable representation of railway track. Inclusion of nonlinear physical and geometrical properties of rail track components has been justified by various computational studies and theoretical analyses. In order to properly describe behaviour of real structures their nonlinear properties cannot be omitted. Therefore a necessity to search appropriate analytical nonlinear models is recognized and highlighted in published literature. This paper presents essential extension of previously carried out double-beam system analysis. Two nonlinear factors are taken into account and parametrical analysis of the semi-analytical solution is undertaken with special emphasis on different range of parameters describing nonlinear stiffness of foundation and layer between beams. This study is extended by preliminary discussion regarding the dynamic effects produced by a series of loads moving along the upper beam. A new solution for the case of several forces acting on the upper beam with different frequencies of their variations in time is presented and briefly discussed.
PL
Model belki podwójnej jest często wykorzystywany w budowie układów wielowarstwowych opisujących zjawiska związane z ruchomymi obciążeniami. Nieliniowe i stochastyczne właściwości tych układów wpływają znacząco na ich dynamiczne zachowania, co zostało potwierdzone zarówno eksperymentalnie, jak i w wyniku badań teoretycznych. Dlatego wskazana jest szczegółowa analiza czułości rozważanych modeli na różne parametry, przed ich zastosowaniem do badania rzeczywistych konstrukcji. W artykule rozważany jest problem odpowiedzi układu belki podwójnej na system sił poruszających się wzdłuż górnej belki ze stałą prędkością i różnymi częstotliwościami, przy założeniu różnych wartości parametrów opisujących nieliniową sztywność dwóch warstw: podłoża i warstwy łączącej belki. Otrzymane semi-analityczne rozwiązanie dla opisanego przypadku jest znaczącym rozszerzeniem poprzednio opublikowanych rezultatów. Założenie dotyczące występowania dwóch nieliniowości prowadzi do konieczności zastosowania szeregu analitycznych aproksymacji, włączając dekompozycję Adomiana i falkową estymację szukanego rozwiązania. Te nakładające się przybliżenia czynią całą procedurę bardziej skomplikowaną i dlatego kontrolowanie zbieżności rozwiązań jest trudniejsze niż w przypadku poprzednio rozważanych uproszczonych modeli. Analiza parametryczna, wykonana dla szerokiego zakresu różnych parametrów, pokazuje, że nieliniowość warstwy pomiędzy belkami wpływa bardziej znacząco na zachowanie układu, w porównaniu do podobnego założenia dotyczącego podłoża. Analiza przedstawiona w artykule może być traktowana jako kolejny etap określenia zakresu stosowalności modelu i zbadania możliwości jego zastosowania w inżynierii kolejowej, w odniesieniu do dwuwarstwowego modelu toru kolejowego, opartego na układzie belki podwójnej, w którym pierwsza warstwa opisuje szyny, a druga modeluje warstwę podkładów. Takie podejście do modelowania drogi szynowej zostało już wcześniej poddane walidacji razem z hybrydową semi-analityczną metodą rozwiązania opartą o aproksymacje wykorzystujące filtry falkowe typu „coiflet”. Rozszerzenie tego modelu o wprowadzenie dodatkowej nieliniowości, stanowi ważny element badań w zakresie analizy dynamiki dróg szynowych.
4
Content available Differentiating fallers from nonfallers using nonlinear variability analyses of data from a low-cost portable footswitch device: a feasibility study
Gonabadi Arash, Antonellis Prokopios, Malcolm Philippe
Acta of Bioengineering and Biomechanics
|
2021
|
Vol. 23, no. 2
139--145
EN
Purpose: Falls are one of the main causes of injuries in older adults. This study evaluated a low-cost footswitch device that was designed to measure gait variability and investigates whether there are any relationships between variability metrics and clinical balance tests for individuals with a history of previous falls. Methods: Sixteen older adults completed a history of falls questionnaire, three functional tests related to fall risk, and walked on a treadmill with the footswitch device. We extracted the stride times from the device and applied two nonlinear variability analyses: coefficient of variation and detrended fluctuation analysis. Results: The temporal variables and variability metrics from the footswitch device correlated with gold-standard measurements based on ground reaction force data. One variability metric (detrended fluctuation analysis) showed a significant relationship with the presence of past falls with a sensitivity of 43%. Conclusion: This feasibility study demonstrates the basis for using low-cost footswitch devices to predict fall risk.
5
Content available Ciągły nieliniowy układ belki podwójnej jako wiarygodny model dynamiki drogi kolejowej
Kozioł Piotr, Pilecki Rafał
Zeszyty Naukowo-Techniczne Stowarzyszenia Inżynierów i Techników Komunikacji w Krakowie. Seria: Materiały Konferencyjne
|
2020
|
Nr 2 (121)
67--74
PL
Współczesny transport kolejowy napotyka na nowe wyzwania związane z rosnącymi wymogami bezpieczeństwa. Te stają się konieczne z powodu spodziewanego rozwoju skutkującego wysokimi prędkościami pociągów i częstotliwością połączeń, razem z trudnościami w planowaniu nowych linii umiejscowionych w rejonach o warunkach geotechnicznie wymagających. Utrzymanie istniejących trakcji staje się równie ważne ponieważ ich intensywne użytkowanie prowadzi do szybszej degradacji i zmniejszonej efektywności. Rozważając stan infrastruktury będącej w użyciu jeszcze kilka lat temu, można zauważyć, że poszukiwanie nowych metod analizy tworzonych układów jest obecnie nawet bardziej istotne. Poza problemami związanymi z wytrzymałością i zużyciem, należy zwracać uwagę na dynamiczne właściwości konstrukcji, głównie ze względu na ich rosnące znaczenie w odniesieniu do wpływu nieliniowych i stochastycznych charakterystyk. Nowe materiały używane w konstrukcjach drogi kolejowej mają bardzo często nieliniowe właściwości fizyczne, w sposób oczywisty potwierdzone i zbadane laboratoryjnie. Jednak ich wpływ na odpowiedź dynamiczną układów transportowych pozostaje dotychczas niewystarczająco zbadany. Obecny artykuł opisuje podejście do analitycznego modelowania dynamiki drogi kolejowej oparte na układach „wielobelkowych” posiadających nieliniowe właściwości. Wstępne wyniki obliczeniowe pokazujące dynamikę układu powiązaną z ruchomym obciążeniem złożonym z sił zmieniających się z różnymi częstotliwościami mogą być uważane za oryginalny wkład prezentowały w artykule.
EN
Recent rail transportation meets new challenges associated with increasing safety requirements. These become a strong necessity due to expected development resulting in high speeds of trains and frequency of connections, along with difficulties in planning and construction of new lines placed in demanding geotechnical conditions. Maintenance of existing tracks becomes equally important as their more intensive use leads to faster degradation and decreased efficiency. Seeking new methods of analysis for newly developed systems is even more important compared to study the infrastructure being operational yet a few years ago. Besides the issues of strength and wear, one should pay attention to the dynamic properties of structures, mainly due to their increasing importance in terms of stochastic and nonlinear features influence. New materials used in rail track structures have very often nonlinear physical characteristics which are obviously confirmed and determined in laboratory conditions. However their effects on the dynamic response of transportation systems remain insufficiently unexplored so far. This paper describes an idea of rail track dynamics analytical modelling based on multibeam systems possessing nonlinear stiffness. Preliminary computational examples of the system dynamics arising from a load consisting of forces with varying frequencies can be recognized as a novelty of presented study.
6
Content available Control of complex dynamic nonlinear loading process for electromagnetic mill
Ogonowski Szymon, Bismor Dariusz, Ogonowski Zbigniew
Archives of Control Sciences
|
2020
|
Vol. 30, No. 3
471--500
EN
Electromagnetic mill installation for dry grinding represents a complex dynamical system that requires specially designed control system. The paper presents model-based predictive control which locates closed loop poles in arbitrary places. The controller performs as gains cheduling prototype where nonlinear model – artificial recurrent neural network, is parameterized with additional measurements and serves as a basis for local linear approximation. Application of such a concept to control electromagnetic mill load allows for stable performance of the installation and assures fulfilment of the product quality as well as the optimization of the energy consumption.
7
Content available remote On size-dependent large-amplitude free oscillations of FGPM nanoshells incorporating vibrational mode interactions
Yi Hongwei, Sahmani Saeid, Safaei Babak
Archives of Civil and Mechanical Engineering
|
2020
|
Vol. 20, no. 2
257--279
EN
At nanoscale, surface free energies of the atoms located on the free surfaces of structures significantly affect their mechanical characteristics. In this study, nonlinear large-amplitude free vibration response of nanoshells prepared from functionally graded porous materials (FGPM) is investigated by taking into account surface stress size effects and vibrational mode interactions. Non-classical shell model is constructed on the basis of the Gurtin–Murdoch type of the surface theory of elasticity having the capability of capturing surface stress size dependency. The accuracy of nonlinear vibration analysis is improved by incorporating the interaction of the main vibration mode and the first, third and fifth symmetric oscillation modes. Moreover, the closed-cell Gaussian-Random field scheme is put to use to extract the mechanical characteristics of FGPM nanoshell. Multiple timescales technique is then applied to achieve surface stress elastic-based nonlinear frequency of FGPM nanoshell analytically for different interactions between vibrational modes. It is revealed that by incorporating the interactions of the main vibration mode and higher symmetric oscillation modes, the behavior of the backbone curves belongs to the nonlinear free oscillation response of FGPM nanoshells changes from hardening to softening schema. It is found that when only the main vibration mode is taken into account, surface elasticity effects makes an enhancement in the significance of the hardening schema. However, by considering the interactions of higher symmetric oscillation modes, surface elasticity effects makes a reduction in the significance of the softening schema.
8
Content available remote Nonlinear coupled moving-load excited dynamics of beam-mass structures
Ghayesh M. H., Farokhi H., Zhang Y., Gholipour A.
Archives of Civil and Mechanical Engineering
|
2020
|
Vol. 20, no. 2
207--217
EN
Investigated in this paper is the first on the moving-load-caused nonlinear coupled dynamics of beam-mass systems. A constant value load excites the beam-mass system where its position on the beam-mass system changes periodically. The energy contribution of the moving load is included via a virtual work formulation. The kinetic energy of the mass together with the beam as well as energy stored in the beam after deflection is formulated. Hamilton’s principle gives nonlinear equations of the beam-mass system under a moving load in a coupled transverse/longitudinal form. A weighted-residual-based discretisation gives a 20 degree of freedom which is numerically integrated via continuation/time integration along with Floquet theory techniques. The resonance dynamics in time, frequency, and spatial domains is investigated. As we shall see, torus bifurcations are present for some beam-mass structure parameters as well as travelling waves. A finite element analysis is performed for a simpler linear version of the problem for to-some-extend verifications.
9
Content available remote The Nosé-Hoover, Dettmann, and Hoover-Holian Oscillators
Hoover W. G., Sprott J. C., Hoover C. G.
Computational Methods in Science and Technology
|
2019
|
Vol. 25, No. 3
121--124
EN
To follow up recent work of Xiao-Song Yang [1] on the Nosé-Hoover oscillator [2–5] we consider Dettmann’s harmonic oscillator [6, 7], which relates Yang’s ideas directly to Hamiltonian mechanics. We also use the Hoover-Holian oscillator [8] to relate our mechanical studies to Gibbs’ statistical mechanics. All three oscillators are described by a coordinate q and a momentum p. Additional control variables (ζ, ξ) vary the energy. Dettmann’s description includes a time-scaling variable s, as does Nosé’s original work [2, 3]. Time scaling controls the rates at which the (q, p, ζ) variables change. The ergodic Hoover-Holian oscillator provides the stationary Gibbsian probability density for the time-scaling variable s. Yang considered qualitative features of Nosé-Hoover dynamics. He showed that longtime Nosé-Hoover trajectories change energy, repeatedly crossing the ζ = 0 plane. We use moments of the motion equations to give two new, different, and brief proofs of Yang’s long-time limiting result.
10
Content available remote Aspects of Dynamical Simulations, Emphasizing Nosé and Nosé-Hoover Dynamics and the Compressible Baker Map
Hoover W. G., Hoover C. G.
Computational Methods in Science and Technology
|
2019
|
Vol. 25, No. 3
125--141
EN
Aspects of the Nosé and Nosé-Hoover dynamics developed in 1983–1984 along with Dettmann’s closely related dynamics of 1996, are considered. We emphasize paradoxes associated with Liouville’s Theorem. Our account is pedagogical, focused on the harmonic oscillator for simplicity, though exactly the same ideas can be, and have been, applied to manybody systems. Nosé, Nosé-Hoover, and Dettmann flows were all developed in order to access Gibbs’ canonical ensemble directly from molecular dynamics. Unlike Monte Carlo algorithms dynamical flow models are often not ergodic and so can fail to reproduce Gibbs’ ensembles. Accordingly we include a discussion of ergodicity, the visiting of all relevant microstates corresponding to the desired ensemble. We consider Lyapunov instability too, the usual mechanism for phasespace mixing. We show that thermostated harmonic oscillator dynamics can be simultaneously expanding, incompressible, or contracting, depending upon the chosen “phase space”. The fractal nature of nonequilibrium flows is also illustrated for two simple two-dimensional models, the hard-disk-based Galton Board and the time-reversible Baker Map. The simultaneous treatment of flows as one-dimensional and many-dimensional suggests some interesting topological problems for future investigations.
11
Content available Chaos synchronization of uncertain coronary artery systems through sliding mode
Qian D. W., Xi Y. F., Tong S. W.
Bulletin of the Polish Academy of Sciences. Technical Sciences
|
2019
|
Vol. 67, nr 3
455--462
EN
The chaotic phenomena of coronary artery systems are hazardous to health and may induce illness development. From the perspective of engineering, the potential harm can be eliminated by synchronizing chaotic coronary artery systems with a normal one. This paper investigates the chaos synchronization problem in light of the methodology of sliding mode control (SMC). Firstly, the nonlinear dynamics of coronary artery systems are presented. Since the coronary artery systems suffer from uncertainties, the technique of derivative-integral terminal SMC is employed to achieve the chaos synchronization task. The stability of such a control system is proven in the sense of Lyapunov. To verify the feasibility and effectiveness of the proposed method, some simulation results are illustrated in comparison with a benchmark.
12
Content available Two approaches in the analytical investigation of the spring pendulum
Sypniewska-Kamińska G., Starosta R., Awrejcewicz J.
Vibrations in Physical Systems
|
2018
|
Vol. 29
art. no. 2018005
EN
Dynamics of the nonlinear spring pendulum is analysed using two asymptotic approaches. The multiple scale method is commonly applied with using two time scales. The purpose of the research is to justify the introduction of an additional third scale. Results of the analysis clearly show that introducing the third scale improve correctness of the approximate analytical solution. The obtained results allow for qualitative and quantitative analysis of the behavior of the studied system with a high accuracy. Calculations are made both in the neighbourhood of the resonance and also far from it.
13
Content available Model and dynamical analysis of a tattooing device
Sarbinowski F., Starosta R.
Vibrations in Physical Systems
|
2018
|
Vol. 29
art. no. 2018004
EN
The paper presents the physical model of the tattooing device. The model is described by three degrees of freedom and a series of linear and nonlinear dynamic parameters and excitation, whose values are determined – depending on the available data and resources – by analytical, numerical and experimental methods. There are also presented a solution of motion equations and the assessment of the impact of individual parameters on the nature of solutions, and moreover, it is indicated a modification of the structure, the use of which results in decrease the amplitudes of the body structure vibrations.
14
Description of a composite material deformation by the degenerated model consisting of nonlinear elastic element
Jamroziak K.
Modelowanie Inżynierskie
|
2018
|
T. 38, nr 69
29--36
EN
This paper presents the specific model of the process of piercing the ballistic shields made from fibre material based on aramid fabric. The model of the form of a nonlinear elastic element, in parallel configuration with a Maxwell element, was subjected to an experimental identification in quasi-statistical sample of piercing it at different speeds. The results for impermanent and permanent deformation are presented. Permanent deformation was analyzed using damping and dry friction.
PL
W artykule przedstawiono specyficzny model procesu przebijania osłon balistycznych wykonanych z materiału włóknistego na bazie tkaniny aramidowej. Model postaci nieliniowego elementu sprężystego, w konfiguracji równoległej z elementem Maxwella, poddano eksperymentalnej identyfikacji w quasi-statystycznej próbce przebijania przy różnych prędkościach. Zaprezentowano wyniki dla deformacji nietrwałej jak i trwałej. Deformację trwałą analizowano z wykorzystaniem tłumienia i tarci suchego.
15
Content available Rocking of freestanding objects: theoretical and experimental comparisons
Gesualdo A., Iannuzzo A., Minutolo V., Monaco M.
Journal of Theoretical and Applied Mechanics
|
2018
|
Vol. 56 nr 4
977--991
EN
The methodical study of safeguard of artistic heritage and other devices subjected to earthquake and, in general, to time-dependent forces has considerably spreaded in the last years, thus increasing researchers’ interest in problems concerning motions of rigid objects simply supported on a base plane. The behaviour of piece of equipments, statues, storage tanks, or even tall buildings has been in fact studied as that of rigid bodies with relation to different base excitations. In some cases, the possibility of influencing the quality of motion can be a strong tool to reduce vulnerability, like in the cases in which rocking motion is to be avoided and sliding motion is welcome. This paper focuses the attention on this last problem. This is the same large class of both non-structural and structural elements that can lose their functionality because of earthquake motions. The results of numerical modelling of sliding and rocking motion in presence of both different excitations and mechanical parameters are presented and compared with experimental data performed by the authors. The results developed are in good agreement with the laboratory tests, and this assures the reliability of both the analytical procedure and the determination of the parameters involved.
16
Content available Extension of the Hamiltonian approach with general initial conditions
Navarro H. A., Cveticanin L.
Journal of Theoretical and Applied Mechanics
|
2018
|
Vol. 56 nr 1
255--267
EN
In this paper, the Hamiltonian approach is extended for solving vibrations of nonlinear conservative oscillators with general initial conditions. Based on the assumption that the derivative of Hamiltonian is zero, the frequency as a function of the amplitude of vibration and initial velocity is determined. A method for error estimation is developed and the accuracy of the approximate solution is treated. The procedure is based on the ratio between the average residual function and the total energy of the system. Two computational algorithms are described for determining the frequency and the average relative error. The extended Hamiltonian approach presented in this paper is applied for two types of examples: Duffing equation and a pure nonlinear conservative oscillator.
17
Content available Iterative methods for efficient sampling-based optimal motion planning of nonlinear systems
Ha J. S., Choi H. L., Jeon J. H.
International Journal of Applied Mathematics and Computer Science
|
2018
|
Vol. 28, no. 1
155--168
EN
This paper extends the RRT* algorithm, a recently developed but widely used sampling based optimal motion planner, in order to effectively handle nonlinear kinodynamic constraints. Nonlinearity in kinodynamic differential constraints often leads to difficulties in choosing an appropriate distance metric and in computing optimized trajectory segments in tree construction. To tackle these two difficulties, this work adopts the affine quadratic regulator-based pseudo-metric as the distance measure and utilizes iterative two-point boundary value problem solvers to compute the optimized segments. The proposed extension then preserves the inherent asymptotic optimality of the RRT* framework, while efficiently handling a variety of kinodynamic constraints. Three numerical case studies validate the applicability of the proposed method.
18
Content available Mathematical modeling of traveling autosolitons in fractional-order activator-inhibitor systems
Datsko B., Gafiychuk V.
Bulletin of the Polish Academy of Sciences. Technical Sciences
|
2018
|
Vol. 66, nr 4
411--418
EN
In the article, basic properties of traveling spatially nonhomogeneous auto-wave solutions in nonlinear fractional-order reactiondiffusion systems are investigated. Such solutions, called autosolitons, arise in a stability region of the system and can coexist with the spatially homogeneous states. By a linear stability analysis and computer simulation, it is shown that the order of the fractional derivative can substantially change the properties of such auto-wave solutions and significantly enrich nonlinear system dynamics. The results of the linear stability analysis are confirmed by computer simulations of the generalized fractional van der Pol-FitzHugh-Nagumo model. A common picture of traveling auto-waves including series in time-fractional two-component activator-inhibitor systems is presented. The results obtained in the article for the distributed system have also been of interest for nonlinear dynamical systems described by fractional ordinary differential equations.
19
Content available Applying a fractional coil model for power system ferroresonance analysis
Majka Ł.
Bulletin of the Polish Academy of Sciences. Technical Sciences
|
2018
|
Vol. 66, nr 4
467--474
EN
This paper addresses the problem of modeling the nonlinear coil used for ferroresonant circuit analysis. The effect of ferroresonance is described and a general modeling approach is presented. The hysteresis modeling problem is also shortly discussed, on the example of a ferromagnetic coil. A brief overview of available literature and contributors to this area are provided. A series RLC circuit supplied from an AC source is discussed. The application of the fractional derivative in the modeling of an iron core coil is presented and suggestions of model implementations are given. The computations performed are illustrated by means of waveform data obtained from computer simulations and compared with those obtained from measurements performed in a specially prepared laboratory setup.
20
Content available remote Linear genetic programming control for strongly nonlinear dynamics with frequency crosstalk
Li R., Noack B., Cordier L., Borée J., Kaiser E., Harambat F.
Archives of Mechanics
|
2018
|
Vol. 70, nr 6
505--534
EN
We advance Genetic Programming Control (GPC) for turbulence flow control application building on the pioneering work of [1]. GPC is a recently proposed model-free control framework which explores and exploits strongly nonlinear dynamics in an unsupervised manner. The assumed plant has multiple actuators and sensors and its performance is measured by a cost function. The control problem is to find a control logic which optimizes the given cost function. The corresponding regression problem for the control law is solved by employing linear genetic programming as an easy and simple regression solver in a high-dimensional control search space. This search space comprises open-loop actuation, sensor-based feedback and combinations thereof — thus generalizing former GPC studies [2, 3]. This new methodology is denoted as linear genetic programming control (LGPC). The focus of this study is the frequency crosstalk between unforced, unstable oscillation and the actuation at different frequencies. LGPC is first applied to the stabilization of a forced nonlinearly coupled three-oscillator model comprising open- and closed-loop frequency crosstalk mechanisms. LGPC performance is then demonstrated in a turbulence control experiment, achieving 22% drag reduction for a simplified car model. In both cases, LGPC identifies the best nonlinear control achieving the optimal performance by exploiting frequency crosstalk. Our control strategy is suited to complex control problems with multiple actuators and sensors featuring nonlinear actuation dynamics. Significant further performance enhancement is envisioned in the more general field of machine learning control [4].
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