State Variables Research Articles

Fault estimation for a class of nonlinear algebro-differential parameter-varying systems

This paper presents a methodology to simultaneous estimate state variables and actuator fault for descriptor nonlinear parameter-varying systems. This class of systems is composed of an interpolated parameter-varying linear part and Lipschitz nonlinear one. The proposed observer structure allows some robustness and steady state accuracy in face to parametric uncertainties. The conditions of existence and stability are given in terms of LMIs (Linear Matrix Inequalities). The obtained results are illustrated on the heat exchanger system with two countercurrent cells model with actuator fault.

Exact and Approximate Moment Derivation for Probabilistic Loops With Non-Polynomial Assignments

Many stochastic continuous-state dynamical systems can be modeled as probabilistic programs with nonlinear non-polynomial updates in non-nested loops. We present two methods, one approximate and one exact, to automatically compute, without sampling, moment-based invariants for such probabilistic programs as closed-form solutions parameterized by the loop iteration. The exact method applies to probabilistic programs with trigonometric and exponential updates and is embedded in the Polar tool. The approximate method for moment computation applies to any nonlinear random function as it exploits the theory of polynomial chaos expansion to approximate non-polynomial updates as the sum of orthogonal polynomials. This translates the dynamical system to a non-nested loop with polynomial updates, and thus renders it conformable with the Polar tool that computes the moments of any order of the state variables. We evaluate our methods on an extensive number of examples ranging from modeling monetary policy to several physical motion systems in uncertain environments. The experimental results demonstrate the advantages of our approach with respect to the current state-of-the-art.

A thermodynamically consistent machine learning-based finite element solver for phase-field approach

In this article, a thermodynamics-based data-driven approach utilizing machine learning is proposed to accelerate multiscale phase-field simulations. To obtain training data, the interface propagation kinetics, integrated into a physics-based phase-field model, are monolithically solved using a finite element method-based code developed within the Python-based open-source platform FEniCS. The admissible sets of internal state variables (e.g., stress, strain, order parameter, and its gradient) are extracted from the simulations and then utilized to identify the deformation fields of the microstructure at a given state in a thermodynamics-based artificial neural network. Finally, the high performance of the proposed machine learning-enhanced solver is illustrated through detailed comparisons with nanostructural calculations at the nanoscale. Unlike previous methods, the current analysis is not restricted by specific morphologies and boundary conditions, given the length and time scales required to reproduce these results.

Investment Timing and Technological Breakthroughs

We study the optimal investment policy of a firm facing both technological and cash-flow uncertainty. At any point in time, the firm can irreversibly invest in a stand-alone technology or wait for a technological breakthrough. Breakthroughs occur when market conditions become favorable enough, exceeding a threshold value that is ex ante unknown to the firm. The Markov state variables for the optimal investment policy are the current market conditions and their historic maximum, and the firm optimally invests in the stand-alone technology only when market conditions deteriorate enough after reaching a maximum. The path-dependent return required for investing in the stand-alone technology is always higher than if no technological breakthroughs could occur and can take arbitrarily large values following certain histories. Decreases in development costs or increases in the value of the new technology make the firm more prone to bearing downside risk and delaying investment in the stand-alone technology. Funding: This research has benefited from financial support of the ANR [Programmes d’Investissements d’Avenir CHESS ANR-17-EURE-0010 and ANITI ANR-19-PI3A-0004] and the research foundation TSE-Partnership [Chaire Marchés des Risques et Création de Valeur, Fondation du Risque/SCOR].

Takagi-Sugeno fuzzy sampled-data observer design for nonlinear permanent magnet synchronous generator-based wind turbine systems using auxiliary function-based integral inequality technique

This study focuses on designing the fuzzy sampled-data observer (FSDO) scheme for nonlinear permanent magnet synchronous generator (PMSG)-based wind turbine systems (WTS). The primary objective of this problem is to solve an unmeasurable state problem under the mismatched premise variables conditions among system, observer, and controller, respectively. To do this, firstly, the proposed wind turbine model is described in a Takagi-Sugeno fuzzy model due to the complex nonlinearities in PMSG-based WTS. Next, based on the measured output signals and sampled estimated states, the FSDO is designed to understand some unmeasurable state variables of the studied system. Then, a novel auxiliary function-based integral inequality (AFBII) is presented to approximate the integral quadratic terms related to sampling information. Thanks to the proposed AFBII technique and the introduction of slack variables, several new and less conservative stability requirements are derived in the formulations of linear matrix inequalities (LMIs) using the looped Lyapunov function. Finally, the simulation studies for the considered wind turbine model are validated numerically, and then some comparative results are provided to show the superiority and applicability of the theoretical observations.

Heparosan biosynthesis in recombinant Bacillus megaterium: Influence of N-acetylglucosamine supplementation and kinetic modeling.

Heparosan, an unsulfated polysaccharide, plays a pivotal role as a primary precursor in the biosynthesis of heparin-an influential anticoagulant with diverse therapeutic applications. To enhance heparosan production, the utilization of metabolic engineering in nonpathogenic microbial strains is emerging as a secure and promising strategy. In the investigation of heparosan production by recombinant Bacillus megaterium, a kinetic modeling approach was employed to explore the impact of initial substrate concentration and the supplementation of precursor sugars. The adapted logistic model was utilized to thoroughly analyze three vital parameters: the B. megaterium growth dynamics, sucrose utilization, and heparosan formation. It was noted that at an initial sucrose concentration of 30gL-1 (S1), it caused an inhibitory effect on both cell growth and substrate utilization. Intriguingly, the inclusion of N-acetylglucosamine (S2) resulted in a significant 1.6-fold enhancement in heparosan concentration. In addressing the complexities of the dual substrate system involving S1 and S2, a multi-substrate kinetic models, specifically the double Andrew's model was employed. This approach not only delved into the intricacies of dual substrate kinetics but also effectively described the relationships among the primary state variables. Consequently, these models not only provide a nuanced understanding of the system's behavior but also serve as a roadmap for optimizing the design and management of the heparosan production method.

Adaptive fixed-time neural consensus control for a class of uncertain nonlinear multi-agent systems with full state constraints

This paper is concerned with the fixed-time consensus control problem for non-strict feedback multi-agent systems with asymmetric output constraints and full state constraints. Considering the feasibility of controlling execution, a novel practical virtual control signal is developed utilizing both saturation function and hyperbolic tangent function to ensure that this signal can remain within the same restricted range as the corresponding state variable throughout entire operation process. In backstepping steps, the design of ideal virtual control signal also adopts a different form of piecewise function than before, introducing high-order polynomial functions to avoid singularity problems in the derivation process. In addition, function approximation ability of radial basis function neural networks technique is applied to estimate uncertainties derived from the system functions and controller design procedure. Moreover, universal barrier Lyapunov function approach is improved for constructing an adaptive constrained synchronization control scheme. By fixed-time stability theory, it is shown that the tracking errors of the MAS converge to an adjustable region around the origin in a fixed time and the state variables always obey their constraints. And the upper bound of the settling time is merely dependent on design parameters, which is not affected by the initial states of MAS. The effectiveness of the proposed control strategy is shown by a numerical simulation example at last. Two scenarios are provided to demonstrate the advantages of the control protocol proposed in this paper.

Experimental and numerical investigations of cake baking in mold

This article deals with the in-mold cake baking process. The methodology relies on numerical and experimental investigations to validate a multiphysics developed model. This numerical model is next exploited to enhance the comprehension of the physical processes that occur during a typical cake baking phase. Based on the governing equations for heat and mass transport and under few assumptions (deformable porous medium, local thermodynamic equilibrium, ideal gas mixture …), the problem consists in solving a system of five coupled partial derivative equations. Temperature, moisture content, total gas pressure, porosity and displacement are used as state variables in this study. The swelling of the dough caused by the increase in total gas pressure is predicted by a viscoelastic model. This thermo-hydro-mechanical model is implemented in a finite element code. Moreover, an experimental laboratory set-up was developed to continually acquire temperatures, water losses and gas pressure inside the product. The browning kinetic is also studied. Furthermore, the cake deformation is tracked by camera. The numerical model is validated based on the conducted experiments. Different operating conditions are tested to verify the robustness of the model. Finally, a sensitivity analysis is performed to understand the impact of estimated parameters on the outputs of the developed model.

Adaptive Finite-Time Prescribed Performance Control of Nonlinear Power Systems with Symmetry Full-State Constraints

Power system control is commonly based on linear controllers, where linear controllers are designed using a linearized model of the system at a specific operating point. However, when the system’s operating point is changed, the dynamic characteristics of the system shift significantly. At this point, linear controllers often fail to meet system stability requirements. Furthermore, the range of state variables in the power system is limited by the objective conditions. In addition, the power system has high-precision constraints on the deviation of the load frequency and so on. Therefore, it is worth designing a finite-time controller that satisfies the prescribed performance and full-state constraints based on the nonlinear model of the power systems. Firstly, the prescribed performance is incorporated into the barrier Lyapunov function to ensure that the tracking error is within the desired accuracy. Then, the tracking strategy is designed based on backstepping and incorporating a first-order filter to ensure that the controlled system’s signals and tracking errors remain bounded in finite time. Finally, two simulations are given to illustrate the effectiveness of the proposed control scheme, confirming that all states keep within the predefined range.

Special Methods Controllability and Observability in Optimal Control Systems

This article explores a specific case study that examines controllability and observability in general and in specific so that it is easy for the reader to understand these two concepts, which are fundamental in optimal control theory. Algorithms have been written to determine the controllability and observability of optimal control systems using the MATLAB programming language, and new techniques have been developed to deal with them. In addition, a critical test was created in which the state variables of the system or, more precisely, their corresponding states were split together, illustrating this with more than one example. Divided into four groups in a linear manner, as the article explains. To understand the controllability and observability of some more complex systems, this article is a starting point for the future expansion of these two concepts through the development of new algorithms or other applied solution methods or the creation of new algorithms.

Investigation of a high-performance control algorithm for a unified chaotic system synchronization control based on parameter adaptive method

With the rapid development of computer technology, parameter adaptive control methods are becoming more and more widely used in nonlinear systems. However, there are still many problems with synchronous controllers with multiple inputs and a single output, uncertainty, and dynamic characteristics. This paper analyzed a synchronization control strategy of uncoupled nonlinear systems based on parameter dynamic factors to adjust the performance of the synchronization controller, and briefly introduced the manifestations of chaotic motion. The characteristics and differences of continuous feedback control methods and transmission and transfer control methods were pointed out. Simple, effective, stable, and feasible synchronous control was analyzed using parameter-adaptive control theory. By analyzing the non-linear relationships between various models at different orders, the fuzzy distribution of the second-order mean and their independent and uncorrelated matrices were obtained, and their corresponding law formulas were established to solve the functional expression between the corresponding state variables and the dynamic characteristics of the system. The error risk test, computational complexity test, synchronization performance score test, and chaos system control effect score test were carried out on the control algorithms of traditional chaos system synchronization methods and chaos system synchronization methods based on parameter adaptive methods. Parameter adaptive methods were found to effectively reduce the error risk of high-performance control algorithms for synchronization of the unified chaos system. The complexity of the calculation process was simplified and the complexity score of the calculation process was reduced by 0.6. The application of parameter adaptive methods could effectively improve the synchronization performance of control algorithms, and the control effectiveness rating of control algorithms was improved. The experimental test results proved the effectiveness of control algorithms, which greatly enriched the field of modern control applications and also drove the vigorous development of nonlinear dynamics research, thus making significant progress in chaos application research.

CGNSDE: Conditional Gaussian neural stochastic differential equation for modeling complex systems and data assimilation

A new knowledge-based and machine learning hybrid modeling approach, called conditional Gaussian neural stochastic differential equation (CGNSDE), is developed to facilitate modeling complex dynamical systems and implementing analytic formulae of the associated data assimilation (DA). In contrast to the standard neural network predictive models, the CGNSDE is designed to effectively tackle both forward prediction tasks and inverse state estimation problems. The CGNSDE starts by exploiting a systematic causal inference via information theory to build a simple knowledge-based nonlinear model that nevertheless captures as much explainable physics as possible. Then, neural networks are supplemented to the knowledge-based model in a specific way, which not only characterizes the remaining features that are challenging to model with simple forms but also advances the use of analytic formulae to efficiently compute the nonlinear DA solution. These analytic formulae are used as an additional computationally affordable loss to train the neural networks that directly improve the DA accuracy. This DA loss function promotes the CGNSDE to capture the interactions between state variables and thus advances its modeling skills. With the DA loss, the CGNSDE is more capable of estimating extreme events and quantifying the associated uncertainty. Furthermore, crucial physical properties in many complex systems, such as the translate-invariant local dependence of state variables, can significantly simplify the neural network structures and facilitate the CGNSDE to be applied to high-dimensional systems. Numerical experiments based on chaotic systems with intermittency and strong non-Gaussian features indicate that the CGNSDE outperforms knowledge-based regression models, and the DA loss further enhances the modeling skills of the CGNSDE.

Robust Trajectory Planning of Gliding-Guided Projectiles with Weak Maneuverability

Due to constraints in launch platforms and cost, the maneuverability of gliding-guided projectiles is limited, necessitating a rational design of their trajectory schemes. To reduce the sensitivity of trajectory schemes to uncertainties while ensuring compatibility between flight schemes and guidance control systems and fully exploiting the control capability of the projectile, a closed-loop robust trajectory planning method is proposed. Models of major uncertain factors and state deviation at the control start point are established. Based on the NIPCE method, the stochastic dynamic model is transformed into a high-dimensional deterministic model with PCE coefficients as state variables, and the uncertainty propagation law is obtained. A PID algorithm is employed to design a tracking guidance law based on position error feedback, and open-loop and closed-loop robust trajectory planning models are established accordingly. The optimal control problem is solved by transforming it into a nonlinear programming problem using the direct shooting method. Our simulation results indicate that the NIPCE method can significantly improve the computational efficiency of uncertainty propagation while ensuring accuracy; compared with parallel MCS, the computation time is reduced by 96.8%. Open-loop robust planning can effectively mitigate the sensitivity of gliding trajectories to uncertainties (the standard deviations of terminal altitude and lateral deviations are reduced by 23.6% and 35.3%, respectively, compared to deterministic planning) but cannot completely eliminate terminal dispersion. Closed-loop robust planning effectively improves control effort consumption on the basis of open-loop planning.

Deep learning model predictive control of a high-density polyethylene reactor with a physics-guided sequence-to-sequence model with memory

In chemical process industry, the input-output data of processes display complex nonlinear dynamics and strong influences of unobserved hidden states. Their behavior must be modeled using nonlinear time series with an observer-predictor structure. To address this, a sequence-to-sequence model with a memory layer was proposed for a high-density polyethylene slurry reactor. The memory layer retains the chronological contribution of the observer and predictor and effectively captures the lengthy time response. A physics-guided approach was adopted to ensure the directional consistency between input and output variables in key control loops. In this way, a deep learning model can be obtained with historical data and there is no need for plant tests. The resulting model can be used in a nonlinear model predictive control system that not only quickly navigates different grade transitions but also provides steady-state control even though key internal state variables such as catalyst activity change.

Research on a Path Tracking Control Strategy for Autonomous Vehicles Based on State Parameter Identification

With the rapid development of autonomous driving technology, estimating and controlling key vehicle state parameters under complex road conditions have become critical challenges. This study combines Unscented Kalman Filtering (UKF) and Sliding Mode Control (SMC) methods to propose an integrated control model for achieving more efficient control. First, a three-degrees-of-freedom vehicle dynamics model based on the Dugoff tire model is constructed to accurately estimate key vehicle state parameters. Next, UKF is used to estimate road friction coefficients and key vehicle state parameters, and its performance is compared with Extended Kalman Filtering (EKF) under various conditions. The results show the superiority of UKF in identifying road friction coefficients. Based on SMC theory, a sliding surface is designed, and the functional relationship between state variables and control variables is derived to establish the corresponding control model. Joint simulations using Carsim and Simulink under different conditions validate the real-time performance and effectiveness of the designed UKF-SMC integrated control strategy in the presence of external disturbances and system uncertainties. Simulation results indicate that this strategy effectively enhances the overall performance and safety of autonomous vehicles, providing an accurate real-time solution capable of handling complex and variable road conditions. The proposed UKF-SMC integrated control strategy not only proves its theoretical superiority but also demonstrates promising practical applications in simulation experiments. This study provides reliable technical support for the development of autonomous driving technology under complex road conditions.

Data-driven probabilistic definition of the low energy conformational states of protein residues.

Protein dynamics and related conformational changes are essential for their function but difficult to characterise and interpret. Amino acids in a protein behave according to their local energy landscape, which is determined by their local structural context and environmental conditions. The lowest energy state for a given residue can correspond to sharply defined conformations, e.g.in a stable helix, or can cover a wide range of conformations, e.g.in intrinsically disordered regions. A good definition of such low energy states is therefore important to describe the behaviour of a residue and how it changes with its environment. We propose a data-driven probabilistic definition of six low energy conformational states typically accessible for amino acid residues in proteins. This definition is based on solution NMR information of 1322 proteins through a combined analysis of structure ensembles with interpreted chemical shifts. We further introduce a conformational state variability parameter that captures, based on an ensemble of protein structures from molecular dynamics or other methods, how often a residue moves between these conformational states. The approach enables a different perspective on the local conformational behaviour of proteins that is complementary to their static interpretation from single structure models.

Preferences reveal dissociable encoding across prefrontal-limbic circuits.

Individual preferences for the flavor of different foods and fluids exert a strong influence on behavior. Most current theories posit that preferences are integrated with other state variables in the orbitofrontal cortex (OFC), which is thought to derive the relative subjective value of available options to guide choice behavior. Here, we report that instead of a single integrated valuation system in the OFC, another complementary one is centered in the ventrolateral prefrontal cortex (vlPFC) in macaques. Specifically, we found that the OFC and vlPFC preferentially represent outcome flavor and outcome probability, respectively, and that preferences are separately integrated into value representations in these areas. In addition, the vlPFC, but not the OFC, represented the probability of receiving the available outcome flavors separately, with the difference between these representations reflecting the degree of preference for each flavor. Thus, both the vlPFC and OFC exhibit dissociable but complementary representations of subjective value, both of which are necessary for decision-making.

Dynamics of synchronous Boolean networks with non-binary states.

In this paper, we study the dynamics of synchronous Boolean networks and extend previously obtained results for binary Boolean networks to networks with state variables in a general Boolean algebra of 2p elements, with p>1. The method to do this is based on the Stone representation theorem and the relation of such systems on general Boolean algebras with those with binary-state values. Specifically, we deal with the main periodic orbit problems and predecessor problems (existence, coexistence, uniqueness, and number of them), which allows us to determine the periodic structure and the attractor cycles of the system. These results open opportunities to explore novel applications by means of such general systems.

Characterizing Climatic Socio‐Environmental Tipping Points in Coastal Communities: A Conceptual Framework for Research and Practice

AbstractThe concept of climate tipping points in socio‐environmental systems is increasingly being used to describe nonlinear climate change impacts and encourage social transformations in response to climate change. However, the processes that lead to these tipping points and their impacts are highly complex and deeply uncertain. This is due to numerous interacting environmental and societal system components, constant system evolution, and uncertainty in the relationships between events and their consequences. In the face of this complexity and uncertainty, this research presents a conceptual framework that describes systemic processes that could lead to tipping points socio‐environmental systems, with a focus on coastal communities facing sea level rise. Within this context, we propose an organizational framework for system description that consists of elements, state variables, links, internal processes, and exogenous influences. This framework is then used to describe three mechanisms by which socio‐environmental tipping could occur: feedback processes, cascading linkages, and nonlinear relationships. We presented this conceptual framework to an expert panel of coastal practitioners and found that it has potential to characterize the effects of secondary climatic impacts that are rarely the focus of coastal risk analyses. Finally, we identify salient areas for further research that can build upon the proposed conceptual framework to inform practical efforts that support climate adaptation and resilience.

New Equilibria and Dynamic Structures Under Continuous Optimal Feedback Control

In this paper, the new equilibria realized by continuous optimal control inputs and the dynamic structure around them are studied. Using the Euler–Lagrange equation, which is a necessary condition for optimal control problems, the equations of motion of a dynamic system with optimal control inputs that minimize the quadratic cost function are described in terms of state and adjoint variables. Based on the equations of motion, equilibrium conditions are derived, and the properties of equilibria are analyzed for the two-body and Hill three-body problems. The stability and dynamic structure around unstable equilibria are also characterized to get insights into the properties of optimal trajectories.