Inverse Approach Research Articles

Optimizing PID control for enhanced stability of a 16‐DOF biped robot during ditch crossing

AbstractThe current research article discusses the design of a proportional–integral–derivative (PID) controller to obtain the optimal gait planning algorithm for a 16‐degrees‐of‐freedom biped robot while crossing the ditch. The gait planning algorithm integrates an initial posture, position, and desired trajectories of the robot's wrist, hip, and foot. A cubic polynomial trajectory is assigned for wrist, hip, and foot trajectories to generate the motion. The foot and wrist joint angles of the biped robot along the polynomial trajectory are obtained by using the inverse kinematics approach. Moreover, the dynamic balance margin was estimated by using the concept of the zero‐moment point. To enhance the smooth motion of the gait planner and reduce the error between two consecutive joint angles, the authors designed a PID controller for each joint of the biped robot. To design a PID controller, the dynamics of the biped robot are essential, and it was obtained using the Lagrange–Euler formulation. The gains, that is, KP, KD, and KI of the PID controller are tuned with nontraditional optimization algorithms, such as particle swarm optimization (PSO), differential evolution (DE), and compared with modified chaotic invasive weed optimization (MCIWO) algorithms. The result indicates that the MCIWO‐PID controller generates more dynamically balanced gaits when compared with the DE and PSO‐PID controllers.

Analytical Inverse QCD Coupling Constant Approach and Its Result for αs

We propose a model for the QCD running coupling constant based on the analytical inverse QCD coupling constant concept with an additional regularization in the low momentum region. Analyticity in the q2-complex plane, where q is the four-momentum transfer, is imposed by methods of the Analytic Perturbation Theory. The model incorporates a peculiar low-momentum behavior for αs(q2) as a divergence at q2=0 to retrieve color confinement, without spoiling its correct high-momentum behavior. This was achieved by means of a two-parameter regularization function, for which we considered three possible analytic expressions. In fact, within the framework of the Analytic Perturbation Theory, αs(q2) assumes a finite value for q2=0, at all perturbative orders (infrared stability), hence the infrared divergence cannot be implemented. For this reason, we found it more straightforward to work with its reciprocal, namely, εs(q2)=1/αs(q2), imposing its vanishing at the origin of the q2-complex plane via the multiplication of the aforementioned regularizing functions and the spectral density. Once the two free parameters of the regularization functions were settled by fitting to the experimental values of αs(q2) at the momenta where these data were available and reliable, the model could reproduce the QCD running coupling constant at any other momentum transferred.

Estimation of Surface Temperature and Heat Flux over a Hollow Cylinder and Slab using an Inverse Heat Conduction Approach

A non-iterative approximation of the inverse heat conduction problem has been developed through energy balance between the control volumes. The heat flow domain along the surface normal was divided into three control volumes and studied in three cases, specifically on a heated hollow metallic cylinder cooled in crossflow of air, a heating flat plate in still air, and a heated flat plate when cooled in still air with random air blows. The time derivatives of temperature and heat flux estimates at the surface appearing in derived equations were evaluated by approximate expressions. Both estimates were obtained from the derived equations by simultaneous measurement of temperature-time histories at two locations: one at the inner surface and the other anywhere within the control volume along the surface normal. The deviation was checked by real-time simultaneous measurement of temperature-time history at the outer surface along the normal surface. Comparison between the estimated surface temperature-time history using the derived equations and the real-time measurement showed deviations within 0.5 % for the cylinder, within 0.03 % for the plate in still air and within 0.5 % when air blows were given. Heat fluxes estimated using these time histories were correspondingly arrived at consistent and close approximations for all cases. Estimates from the derived equations were compared with reported equations from the literature, and a wind tunnel experiment for the validation of circumferential distribution of heat transfer was conducted, for which they also showed reasonably good agreements.

Topology Optimization Driven Bone-Remodeling Simulation for Lumbar Interbody Fusion.

This study proposes a numerical approach for simulating bone remodeling in lumbar interbody fusion (LIF). It employs a topology optimization method to drive the remodeling process and uses a pixel function to describe the structural topology and bone density distribution. Unlike traditional approaches based on strain energy density or compliance, this study adopts von Mises stress to guide the remodeling of LIF. A novel pixel interpolation scheme associated with stress criteria is applied to the physical properties of the bone, directly addressing the stress shielding effect caused by the implanted cage, which significantly influences the bone remodeling outcome in LIF. Additionally, a boundary inverse approach is utilized to reconstruct a simplified analysis model. To reduce computational cost while maintaining high structural resolution and accuracy, the Scaled Boundary Finite Element Method (SBFEM) is introduced. The proposed numerical approach successfully generates results that closely resemble human lumbar interbody fusion.

Asymptotics for some logistic maps and the renormalization group

Abstract We explain the relation between the r = 1 case of the logistic map x i+1 = r x i (1 − x i ), x i ∈ R , i = 0, 1, 2, …, r > 0 and x 0 ≥ 0, and the renormalization group flow arising in the multiscale analysis of interesting zero fixed point, asymptotic free quantum field theory models such as the ultraviolet (1 + 1)-dimensional Gross-Neveu model and QCD, and the infrared ϕ 4 4 model . We obtain the asymptotics of the mapping, which shows an inverse power decay approach to the fixed point x * = 0, Gaussian fixed point, with additional logarithmic-like corrections. This asymptotic behavior is independent of the initial condition x 0 ∈ (0, 1) (hence, there is no constraint for x 0 to be small, as usual in quantum field models), and only depends on the lowest orders in a polynomial perturbation. In asymptotic free quantum field theory, this amounts to say that knowing the renormalization group β-function expansion in the coupling constant, up to higher orders, does not improve our knowledge of the asymptotics of the coupling flow. A comparison with a similar differential equation with continuous time is made by analyzing stability of this kind of solution and higher order monomial perturbations. We also obtain the detailed asymptotics for 0 < r < 1. As well, our methods can be applied when r ∈ (1, 3]. It is known, but without detailed asymptotics, that all trajectories with initial condition x 0 ∈ ( − 1, 1) converge to the fixed point x * = (r − 1)/r. For r = 2, the super attractive case, we obtain an explicit exact solution which exhibits an exploding, non-constant exponential decay rate approach to the x * = (1/2) fixed point. Our methods include the use of iterations, a discrete version of the Fundamental theorem of Calculus, a discrete version of the integrating factor method for first order linear ODEs and, sometimes, a scaling transformation. To obtain these results, we do not use the traditional Banach contraction mapping theorem, which only provides an upper bound on the asymptotics. We expect that our methods can be employed to determine the asymptotics of the logistic map for a wider range of parameters, where other fixed points are present.

Identification of Groundwater Potential Zone Existence in GAR Housing Using Electrical Resistivity Method

The GAR (Grand Aceh Residence) housing estate is located in Baet Village, Aceh Besar District and was constructed on the land of a pond that has been filled in and is close to the coast. The majority of residents use clean water sources from PDAM because of the difficulty of obtaining clean water. The purpose of the research was to identify potential groundwater zones and determine the conditions. The research method used was electrical resistivity method, SuperSting R8/IP with Wenner-Schlumberger configuration. The research was conducted in 3 lines with 6 m spacing. RES2DINV software based on the least square inversion approach was used for data processing. The results obtained show resistivity values varying from 0.1 - 100 Ohm.m with a depth penetration of up to 28.8m. There are 3 lithological layers obtained, namely clay (0.1 - 1.5 Ohm.m), clayey sand (1.5 - 17.7 Ohm.m), and sand (17.7 - 100 Ohm.m). The groundwater presence zone is assumed to be in the sand layer. There are 2 types of groundwater obtained, which are shallow groundwater (phreatic) located from the center to the north of the lines to a depth of ± 13 m and deep groundwater, located varies in the middle of the lines from a depth of ± 15 m to the end with groundwater conditions may still be brackish due to the influence of seawater intrusion with a resistivity value of 0.1 Ohm.m identified to a depth of ± 25 m

Probabilistic deconvolution of the distribution of relaxation times from multiple electrochemical impedance spectra

Electrochemical impedance spectroscopy (EIS) is widely used to study the properties of electrochemical materials and systems. However, analyzing EIS data remains challenging. Among various analysis methods, the distribution of relaxation times (DRT) has emerged as a novel non-parametric approach capable of providing timescale information. Among the various DRT inversion methods, those based on Gaussian processes (GP) are particularly promising because they provide uncertainty estimates for both EIS and DRT. However, current GP-based DRT implementations can only handle one spectrum at a time. This work extends these models to allow concurrent analysis of multiple impedance spectra as a function of experimental conditions. The new method, called the quasi-Gaussian process distribution of relaxation times, treats the DRT as a GP with respect to the experimental state and as a finite approximation of a positively constrained GP with respect to timescales. This new DRT inversion approach is validated against noise-corrupted artificial EIS data and applied to experimental data, allowing us to expedite EIS data analysis of multiple EIS data from a probabilistic perspective.

Seismic source analysis and directivity of the November 2021 Fin doublet earthquake in southern Iran: challenges and findings

Studying the source characteristics of doublet or multiple earthquake sequences presents significant challenges in seismology, especially with short time intervals between events. On November 14, 2021, a doublet earthquake (Mw 6.0 and Mw 6.1) occurred near Fin city, southern Iran, within a span of less than two minutes and 10 km apart. We employed the Kinematic Waveform Inversion (KIWI) procedure to determine the point and extended source parameters of these events, using a multistep inversion approach for stable solutions. Our analysis highlighted the directivity of the earthquakes: the first event exhibited bilateral directivity, causing a rupture area that reached the surface, while the second event showed unilateral westward directivity, supported by waveform amplitude differences observed at various stations. This directivity analysis plays an essential role in seismic hazard studies. Our findings regarding the source parameters of these recent doublet earthquakes in the Fin region align well with regional geological trends and fault patterns. However, retrieving the main fault plane for the second earthquake was challenging due to the complexities of the waveform. Moment tensor decomposition revealed significant non-double-couple components for the second event, indicating the complexity inherent in analyzing doublet events. This study underscores the critical role of precise waveform analysis and robust inversion techniques in understanding complex seismic events.

Source analysis of low frequency seismicity at Mt. Vesuvius by a hybrid moment tensor inversion

Seismicity at Mt. Vesuvius has been relatively weak in the last decades. While the occurrence of shallow volcano-tectonic (VT) events at Mt. Vesuvius is well known, the occurrence of deeper low frequency events (LF) was only recently recognized. Previous source studies only targeted VT events, which were found to have quite heterogeneous focal mechanisms. In this paper, we perform for the first time the source inversion of LF seismicity at Mt. Vesuvius, analysing 27 LF events recorded from 2012 to 2021 with the aim to investigate their source processes. Given the challenges of analysing weak LF earthquakes, we implement a specific moment tensor (MT) inversion approach that combines the fit of displacement seismograms in the time domain and amplitude spectra in the frequency domain. The inversion is simultaneously performed for the source depth and moment tensor components in the 2–7 and 2–5 Hz frequency band, assuming either a full or deviatoric MT representation. Source parameter uncertainties are estimated by using a Bayesian bootstrapping scheme. Our results confirm a larger depth of LF events compared to VTs and show a strong heterogeneity of the LF seismic sources, which present various rupture types, different orientations and heterogeneous, whilst poorly resolved, non-double-couple components. The MT variability is qualitatively confirmed by significant differences among the recorded waveforms. The heterogeneity of both VT and LF source processes is attributed to complex source processes in a highly fractured seismogenic volume submitted to a heterogeneous stress field.

A Game-Theoretic Framework for Generic Second-Order Traffic Flow Models Using Mean Field Games and Adversarial Inverse Reinforcement Learning

A traffic system can be interpreted as a multiagent system, wherein vehicles choose the most efficient driving approaches guided by interconnected goals or strategies. This paper aims to develop a family of mean field games (MFG) for generic second-order traffic flow models (GSOM), in which cars control individual velocity to optimize their objective functions. GSOMs do not generally assume that cars optimize self-interested objectives, so such a game-theoretic reinterpretation offers insights into the agents’ underlying behaviors. In general, an MFG allows one to model individuals on a microscopic level as rational utility-optimizing agents while translating rich microscopic behaviors to macroscopic models. Building on the MFG framework, we devise a new class of second-order traffic flow MFGs (i.e., GSOM-MFG), which control cars’ acceleration to ensure smooth velocity change. A fixed-point algorithm with fictitious play technique is developed to solve GSOM-MFG numerically. In numerical examples, different traffic patterns are presented under different cost functions. For real-world validation, we further use an inverse reinforcement learning approach (IRL) to uncover the underlying cost function on the next-generation simulation (NGSIM) data set. We formulate the problem of inferring cost functions as a min-max game and use an apprenticeship learning algorithm to solve for cost function coefficients. The results show that our proposed GSOM-MFG is a generic framework that can accommodate various cost functions. The Aw Rascle and Zhang (ARZ) and Light-Whitham-Richards (LWR) fundamental diagrams in traffic flow models belong to our GSOM-MFG when costs are specified. History: This paper has been accepted for the Transportation Science Special Issue on ISTTT25 Conference. Funding: X. Di is supported by the National Science Foundation [CAREER Award CMMI-1943998]. E. Iacomini is partially supported by the Italian Research Center on High-Performance Computing, Big Data and Quantum Computing (ICSC) funded by MUR Missione 4-Next Generation EU (NGEU) [Spoke 1 “FutureHPC & BigData”]. C. Segala and M. Herty thank the Deutsche Forschungsgemeinschaft (DFG) for financial support [Grants 320021702/GRK2326, 333849990/IRTG-2379, B04, B05, and B06 of 442047500/SFB1481, HE5386/18-1,19-2,22-1,23-1,25-1, ERS SFDdM035; Germany’s Excellence Strategy EXC-2023 Internet of Production 390621612; and Excellence Strategy of the Federal Government and the Länder]. Support through the EU DATAHYKING is also acknowledged. This work was also funded by the DFG [TRR 154, Mathematical Modelling, Simulation and Optimization Using the Example of Gas Networks, Projects C03 and C05, Project No. 239904186]. Moreover, E. Iacomini and C. Segala are members of the Indam GNCS (Italian National Group of Scientific Calculus).

Inverse design of highly-efficient and broadband polarization beam splitter on SOI platform

Polarization beam splitters (PBSs) are essential components in integrated optics, particularly for applications demanding high polarization purity. However, most existing PBS designs rely on complex forward design methods, often constrained by large size and limited performance. In this study, we introduce an inverse design approach based on shape optimization to develop a high-performance PBS on the silicon-on-insulator (SOI) platform. By optimizing the boundary shape, the proposed PBS exhibits low insertion loss (<1.4 dB) and high extinction ratio (>9.2 dB) across a bandwidth range of 65 nm (1500 nm–1565 nm), as confirmed by experimental results. The footprint of the device measures 1.7 × 16 μm2, and the entire structure can be fabricated through a single lithography step. This work holds great promise for the convenient and efficient design of on-chip PBSs.

Minimum entropy constrained cooperative inversion of electrical resistivity, seismic and magnetic data

Geophysical methods are widely used to gather information about the subsurface as they are non-intrusive and comparably cheap. However, the solution to the geophysical inverse problem is inherently non-unique, which introduces considerable uncertainties. As a partial remedy to this problem, independently acquired geophysical data sets can be jointly inverted to reduce ambiguities in the resulting multi-physical subsurface images. A novel cooperative inversion approach with joint minimum entropy constraints is used to create more consistent multi-physical images with sharper boundaries with respect to the single-method inversions. Here, this approach is implemented in an open-source software and its applicability on electrical resistivity tomography (ERT), seismic refraction tomography (SRT), and magnetic data is investigated. A synthetic 2D ERT and SRT data study is used to demonstrate the approach and to investigate the influence of the governing parameters. The findings showcase the advantage of the joint minimum entropy (JME) stabilizer over separate, conventional smoothness-constrained inversions. The method is then used to analyze field data from Rockeskyller Kopf, Germany. 3D ERT and magnetic data are combined and the results confirm the expected volcanic diatreme structure with improved details. The multi-physical images of both methods are consistent in some regions, as similar boundaries are produced in the resulting models. Because of its sensitivity to hydrologic conditions in the subsurface, observations suggest that the ERT method senses different structures than the magnetic method. These structures in the ERT result do not seem to be enforced on the magnetic susceptibility distribution, showcasing the flexibility of the approach. Both investigations outline the importance of a suitable parameter and reference model selection for the performance of the approach and suggest careful parameter tests prior to the joint inversion. With proper settings, the JME inversion is a promising tool for geophysical imaging, however, this work also identifies some objectives for future studies and additional research to explore and optimize the method.

Extracting Multimodal Surface-Wave Dispersion Curves from Ambient Seismic Noise Using High-Resolution Linear Radon Transform

Abstract In the past two decades or so, ambient noise tomography (ANT) has emerged as an established method for imaging subsurface seismic velocity structures. One of the key steps in ANT is to extract surface-wave dispersion curves. The predominant approach for subsurface shear-wave velocity structure inversion involves utilizing fundamental-mode surface waves in ANT. Nevertheless, a notable challenge encountered is the issue of nonuniqueness when employing the dispersion information of fundamental-mode surface waves to invert for shear-wave velocity models. The inclusion of higher-mode dispersion curves in the inversion offers several benefits, including the reduction of nonuniqueness, enhancement of inversion stability, and decreased dependence on the initial model. In this study, we illustrate the applicability of the high-resolution linear radon transform method (HRLRT) for extracting multimodal surface-wave dispersion energy from ambient seismic noise data. We apply HRLRT to both the synthetic noise data and real data recorded by USArray. Our results of applications show that the HRLRT method can extract multimodal surface-wave dispersion information. Compared with established methods such as the frequency–Bessel transform and multicomponent frequency–Bessel transform, the HRLRT exhibits an advantage in suppressing “crossed” artifacts and the second-/third-type artifacts caused by sparse spatial sampling, and the resulting dispersion energy from HRLRT has narrower peaks, meaning high resolution of dispersion curves based on the HRLRT method.

The Effect of Wind Speed and Sea Surface Temperature on Chlorophyll –A Concentration in Sea Water Off the Libyan Coast

The effect of winds and sea surface temperature on the concentration of chlorophyll-a, which is the primary source for phytoplankton to produce carbon through photosynthesis, is one of the climatic changes formed in the atmosphere and oceans that are the focus of current global studies. The study found a strong correlation between the concentration of chlorophyll-a and wind speed. The concentration of chlorophyll-a rises with increasing wind speed and reaches 0.85. Conversely, the relationship between sea surface temperatures and chlorophyll-a concentration is inverse, meaning that the higher the sea surface temperatures, the lower the concentration of chlorophyll-a. The inverse relationship approaches -0.798 in seawater. The intensity of chlorophyll-a concentration at sea and its relationship with wind speed and sea surface temperature explain why the percentage of the effect of variable wind speed and sea surface temperature on the concentration of chlorophyll-a is affected by (73.6%, 63.8%) on the concentration of chlorophyll-a, respectively.

Magnetic surface geometry inversion of Kimberlites in Botswana

AbstractSurface geometry inversion of geophysical data has recently been introduced as an effective approach for generating surface‐based geological models. The models obtained through surface geometry inversion clearly delineate the contacts between distinct rock units, making them easily interpretable by geologists. Surface geometry inversion has shown promising preliminary results in other works, but the practical application of surface geometry inversion on real geophysical data has not been thoroughly investigated. To move towards a better understanding of the practicalities involved, we applied surface geometry inversion to a real magnetic dataset acquired over two kimberlite pipes located in north‐central Botswana. The objective was to assess the effectiveness and limitations of the surface geometry inversion approach in accurately characterizing the subsurface geometry and identifying the boundaries of the kimberlite pipes. We first perform an anomaly separation approach to isolate the magnetic anomalies associated with the kimberlite pipes. A surface geometry inversion algorithm was applied to the original and separated datasets using various initial models and other control parameters. Several tests were performed to investigate the effects that data processing, initial models, and other parameter choices have on the surface geometry inversion results. We successfully recover the geometry, extension and dip of the two kimberlite pipes. We discuss the results of our various tests and provide advice for practitioners interested in applying surface geometry inversion methods to their data. Our work indicates that surface geometry inversion can be used as a complementary approach to voxel inversion, and we propose an iterative surface geometry inversion algorithm as a possible alternative approach to voxel inversion for simple geological scenarios. This work provides valuable insights into the appropriate application of surface geometry inversion on real geophysical datasets.

The impact of homocysteine on patients with diabetic nephropathy: a mendelian randomization study.

Homocysteine (Hcy) has been associated with an increased risk of diabetic nephropathy (DN) in patients, but there is still controversy. This study aims to investigate the causal relationship between plasma Hcy and DN. A Mendelian randomization (MR) study using data from 2 samples was employed to infer causal relationships. The aggregated genetic data associated with Hcy was derived from the largest genome-wide association study (GWAS) to date, involving 44,147 individuals of European ancestry.Data on SNP-diabetic nephropathy, creatinine, and urea nitrogen were obtained from the IEU GWAS database. The analysis method employed a fixed-effect or random-effect inverse variance-weighted approach to estimate effects.Additional analysis methods were used to assess stability and sensitivity. The potential for pleiotropy was evaluated using the MR-Egger intercept test. Using 12 SNPs as instrumental variables, two-sample MR analysis revealed no evidence of a causal relationship between genetically predicted plasma Hcy levels and diabetic nephropathy, as well as creatinine and blood urea nitrogen levels. This finding is consistent with the results obtained from other testing methods. Two-sample Mendelian Randomization analysis found no evidence of a causal relationship between plasma homocysteine levels and diabetic nephropathy, creatinine, or urea.

On the multi‐parameters identification of concrete dams: A novel stochastic inverse approach

AbstractThis paper introduces a novel stochastic inverse method that utilizes perturbation theory and advanced intelligence techniques to solve the multi‐parameter identification problem of concrete dams using displacement field monitoring data. The proposed method considers the uncertainties associated with the dam displacement monitoring data, which are comprised of two distinct sources: the first is related to stochastic mechanical properties of the dam, and the second is due to observation errors. The displacements at different measuring points generated by dam mechanical properties exhibit spatial correlation, while the observation errors at different points can be considered statistically random. In this context, the inversion formulas are derived for unknown stochastic parameters of the dam by combining perturbation equations and Taylor expansion methods. An improved meta‐heuristic optimization method is employed to identify the mean of stochastic parameters, while mathematical and statistical methods are used to determine the variance of stochastic parameters. The feasibility of the proposed method is verified through numerical examples of a typical dam section under different conditions. Additionally, the paper discusses and demonstrates the applicability of this method in a practical dam project. Results indicate that this method can effectively capture the uncertainty of dam's mechanical properties and separates them from observation errors.

Modelling approach integrating climate projections for coastal groundwater management

Climate change and excessive groundwater extraction are major contributors to rising groundwater salinization due to seawater intrusion in coastal aquifers. This study aims to define a wide-applicable approach in which hydrological balance, boundary conditions, and irrigation water demand, defined over time considering climate change predictions, can integrated into a numerical model of the groundwater system. The approach was tested in a selected coastal aquifer. The approach spans from the past, used to define steady or almost natural conditions for calibration purposes (1950–2000 in the test), to the future (2100), divided in decade steps. The water balance analysis is based on an inverse hydrogeological water balance approach. The future climate change predictions are used to assess variations in boundary conditions of the groundwater model concerning salinity and sea level, recharge, and inflow from upstream aquifers. The approach considers changes in agricultural activities, groundwater demand, and river stage. The regional model is generated using the MODFLOW code for the groundwater flow model and the SEAWAT code for the salt transport model. The test concerns the Metaponto coastal plain, in which a porous aquifer is at salinization risk due to seawater intrusion. In this way, different influences of climate change and human activities are combined to define a 3d view of groundwater depletion and salinization effects. Quantifying these potential effects or risks, adaptation scenarios with numerical assessments are outlined in this study.

An Enhanced Reptile Search Algorithm for Inverse Modeling of Unsaturated Seepage Parameters in Clay Core Rockfill Dam Using Monitoring Data during Operation

The seepage characteristics of clay core walls are crucial for the seepage safety of core rockfill dams, with the permeability coefficient in the unsaturated zone being nonlinear. To accurately determine the unsaturated seepage parameters in clay core rockfill dams, this paper first proposes an enhanced reptile search algorithm (ERSA) by applying three improvement strategies: Arnold’s cat chaotic map, nonlinear evolutionary factor, and adaptive Cauchy–Gaussian mutation with variable weight. Then, by integrating the ERSA with the unsaturated seepage finite element method, an inverse modeling approach is developed. This approach is applied to an actual rockfill dam with operational monitoring data to determine the unsaturated seepage parameters of the clay core. Results indicate that the ERSA outperforms the original RSA in test functions, and the calculation results of the seepage parameters determined through inversion are consistent with the monitoring data, showing an overall mean absolute error of 1.086 m. The inverse modeling approach provides a valuable reference for determining unsaturated seepage parameters in similar clay core rockfill dams.

Inverse Optimal Adaptive Neural Control for State-Constrained Nonlinear Systems.

Optimizing a performance objective during control operation while also ensuring constraint satisfactions at all times is important in practical applications. Existing works on solving this problem usually require a complicated and time-consuming learning procedure by employing neural networks, and the results are only applicable for simple or time-invariant constraints. In this work, these restrictions are removed by a newly proposed adaptive neural inverse approach. In our approach, a new universal barrier function, which is able to handle various dynamic constraints in a unified manner, is proposed to transform the constrained system into an equivalent one with no constraint. Based on this transformation, a switched-type auxiliary controller and a modified criterion for inverse optimal stabilization are proposed to design an adaptive neural inverse optimal controller. It is proven that optimal performance is achieved with a computationally attractive learning mechanism, and all the constraints are never violated. Besides, improved transient performance is obtained in the sense that the bound of the tracking error could be explicitly designed by users. An illustrative example verifies the proposed methods.