Control Of Dynamic Systems Research Articles

Design of Suboptimal Local Piecewise Fuzzy Controller With Multiple Constraints for Quasi-Linear Spatiotemporal Dynamic Systems.

This paper discusses the problem of suboptimal local piecewise H ∞ fuzzy control of quasi-linear spatiotemporal dynamic systems with control magnitude constraints. A Takagi-Sugeno fuzzy partial differential equation (PDE) model with space-varying coefficient matrices is first assumed to be derived for exactly describing nonlinear system dynamics. In the light of the fuzzy model, a local piecewise fuzzy feedback controller is then constructed to guarantee the exponential stability with a prescribed H ∞ disturbance attenuation level for the resulting closed-loop system, while the control constraints are also ensured. A sufficient condition on the existence of such fuzzy controller is developed by the Lyapunov direct method and an integral inequality and presented in terms of space algebraic linear matrix inequalities (LMIs) coupled with LMIs. By virtue of extreme value theorem, a suboptimal-constrained local piecewise H ∞ fuzzy control design in the sense of minimizing the disturbance attenuation level is formulated as a minimization optimization problem with LMI constraints. Finally, the proposed method is applied to solve the feedback control of a quasi-linear FitzHugh-Nagumo equation with space-varying coefficients, and simulation results show its effectiveness and merit.

High-gain fractional disturbance observer control of uncertain dynamical systems

Disturbance observer-based control allows to compensate unknown inputs, however, in most cases, requiring their integer-order differentiability. In this paper, a novel disturbance observer-based state feedback controller is proposed to compensate a more general class of fractional-, but not necessarily integer-order, differentiable unknown inputs. The proposed fractional PI-like structure yields precise conditions for feedback gain tuning. Remarkably, the resulting controller rejects non-differentiable disturbances with a smooth controller, guaranteeing robustness, an outstanding features for tracking tasks, under a prescribed practical stability regimen. A comparison to a fractional sliding mode observer is conducted via simulations to highlight the reliability of the proposed scheme.

Two-Stage Bayesian Optimization for Scalable Inference in State-Space Models.

State-space models (SSMs) are a rich class of dynamical models with a wide range of applications in economics, healthcare, computational biology, robotics, and more. Proper analysis, control, learning, and decision-making in dynamical systems modeled by SSMs depend on the accuracy of the inferred/learned model. Most of the existing inference techniques for SSMs are capable of dealing with very small systems, unable to be applied to most of the large-scale practical problems. Toward this, this article introduces a two-stage Bayesian optimization (BO) framework for scalable and efficient inference in SSMs. The proposed framework maps the original large parameter space to a reduced space, containing a small linear combination of the original space. This reduced space, which captures the most variability in the inference function (e.g., log likelihood or log a posteriori), is obtained by eigenvalue decomposition of the covariance of gradients of the inference function approximated by a particle filtering scheme. Then, an exponential reduction in the search space of parameters during the inference process is achieved through the proposed two-stage BO policy, where the solution of the first-stage BO policy in the reduced space specifies the search space of the second-stage BO in the original space. The proposed framework's accuracy and speed are demonstrated through several experiments, including real metagenomics data from a gut microbial community.

Physical Deep Learning Based on Optimal Control of Dynamical Systems

Deep learning is the backbone of artificial intelligence technologies, and it can be regarded as a kind of multilayer feedforward neural network. An essence of deep learning is information propagation through layers. This suggests that there is a connection between deep neural networks and dynamical systems in the sense that information propagation is explicitly modeled by the time-evolution of dynamical systems. In this study, we perform pattern recognition based on the optimal control of continuous-time dynamical systems, which is suitable for physical hardware implementation. The learning is based on the adjoint method to optimally control dynamical systems, and the deep (virtual) network structures based on the time evolution of the systems are used for processing input information. As a key example, we apply the dynamics-based recognition approach to an optoelectronic delay system and demonstrate that the use of the delay system allows for image recognition and nonlinear classifications using only a few control signals. This is in contrast to conventional multilayer neural networks, which require a large number of weight parameters to be trained. The proposed approach provides insight into the mechanisms of deep network processing in the framework of an optimal control problem and presents a pathway for realizing physical computing hardware.

Parametric and Non-parametric Mathematical Modelling Techniques: A Practical Approach of an Electrical Machine Identification

Mathematical modeling is an important feature concerning the analysis and control of dynamic systems. Also, system identification is an approach for building mathematical expressions from experimental data taken from processes performance. In this context, the contemporaneous state of the art describes several modelling and identification techniques which are excellent alternatives to determine systems behavior through time. This paper presents a comprehensive review of the main techniques for modeling and identification from a parametric and no parametric perspective. Experimental data are taken from an electrical machine that is a DC motor from a didactic platform. The paper concludes with the analysis of results taken from different identification procedures.

The effective graph reveals redundancy, canalization, and control pathways in biochemical regulation and signaling

The ability to map causal interactions underlying genetic control and cellular signaling has led to increasingly accurate models of the complex biochemical networks that regulate cellular function. These network models provide deep insights into the organization, dynamics, and function of biochemical systems: for example, by revealing genetic control pathways involved in disease. However, the traditional representation of biochemical networks as binary interaction graphs fails to accurately represent an important dynamical feature of these multivariate systems: some pathways propagate control signals much more effectively than do others. Such heterogeneity of interactions reflects canalization-the system is robust to dynamical interventions in redundant pathways but responsive to interventions in effective pathways. Here, we introduce the effective graph, a weighted graph that captures the nonlinear logical redundancy present in biochemical network regulation, signaling, and control. Using 78 experimentally validated models derived from systems biology, we demonstrate that 1) redundant pathways are prevalent in biological models of biochemical regulation, 2) the effective graph provides a probabilistic but precise characterization of multivariate dynamics in a causal graph form, and 3) the effective graph provides an accurate explanation of how dynamical perturbation and control signals, such as those induced by cancer drug therapies, propagate in biochemical pathways. Overall, our results indicate that the effective graph provides an enriched description of the structure and dynamics of networked multivariate causal interactions. We demonstrate that it improves explainability, prediction, and control of complex dynamical systems in general and biochemical regulation in particular.

Special Functions-Based Fixed-Time Estimation and Stabilization for Dynamic Systems

Fixed-time stability (FXTS) and fixed-time control (FXTC) of dynamic systems are reconsidered in this article based on special functions from the view of improving the estimate accuracy of settling time (ST) and reducing the chattering caused by the sign function. First, by means of the idea of contradiction and variable transformations, some generic FXTS criteria are established and some upper bounds of ST are directly calculated and expressed by several special functions. It is further proved that these estimates are the most accurate compared with the existing results. Besides, to suppress the chattering caused by the sign function, some saturation functions are constructed to replace the sign function and the FXTS of the new system obtained by replacing is ensured by rigorous theoretical analysis. As applications, the problem of stabilization for chaotic systems in fixed or preassigned time is explored. Especially, an innovative saturation controller is developed to realize preassigned-time stabilization, where the convergence time is prescribed in advance according to actual requirement and the control gains are finite, the existing control methods with time-varying infinite gains are essentially improved. Lastly, three numerical examples are provided to verify the improved estimates of ST and the chattering reduction.

Static gain estimation for nonlinear dynamic systems from steady-state values hidden in historical data

Static gains are often required for control, diagnosis and optimization of nonlinear dynamic systems. This paper proposes a new approach to estimate static gains for nonlinear dynamic systems from steady-state values hidden in historical data. First, steady-state values of system inputs and outputs are extracted by automatically finding data segments in steady-state conditions. Second, static gains of nonlinear dynamic systems in different operating conditions are estimated via linear regression from these steady-state values. The proposed approach has two practical features: (i) estimated static gains can be verified in a convincing way, because the validness of extracted steady-state values is confirmed by visualizing data segments in steady-state conditions, and the accuracy of estimated static gains is verified by comparing the extracted steady-state values and their estimates; (ii) the proposed approach is simple to understand and implement in practice, since it only involves a linear equation between steady-state values and static gains, as well as a basic technique of linear regression. Numerical simulation and industrial application demonstrate the effectiveness of the proposed approach.

Robust and resilient stabilization and tracking control for chaotic dynamical systems with uncertainties

In this article, a robust resilient design methodology for stabilization and tracking control for a class of chaotic dynamical systems is proposed. In particular, a resilient quasi-sliding mode control law is formulated to suppress the chaotic behaviour of these dynamical systems, while considering uncertainties in control input. By using Lyapunov stability theory, sufficient conditions are derived in terms of Linear Matrix Inequalities (LMIs) for a more general class of chaotic nonlinear dynamical systems satisfying the Lipschitz continuity condition. The control gains are obtained via LMI technique in the presence of bounded additive uncertainties in control input. Numerical simulations are provided for Chua’s circuit, Lorenz system, and 4D Lu hyper-chaotic system to show the supremacy and effectiveness of the proposed design methodologies.

Efficient computation of 1D and 2D nonlinear Viscous Burgers’ equation

Model order reduction (MOR) has emerged as a de-facto solution for simulation, control, and optimization of large-scale and complex dynamical systems from the past decades. This paper demonstrates two comprehensive MOR approaches to overcome the overall computational cost required to simulate the nonlinear, viscous Burger’s equation. The former scheme is the approximate proper orthogonal decomposition (APOD), which involves capturing the approximate snapshot ensemble of the states by performing multiple linearizations along the state-trajectory. The latter technique is based on the notion of nonlinear moment matching (NLMM), in which the reduced projection basis is generated by numerically solving the simplified, nonlinear, Sylvester equation. Both the reduction schemes are tested on the high-fidelity finite difference (FD) formulation of 1D and the 2D Burgers’ equation. The results show substantial computational savings in extracting the orthonormal projection basis required to generate the reduced manifold. Furthermore, a comparative study of both methods is presented with proper orthogonal decomposition (POD) for various test signals.

Event-Triggered Sliding-Mode Control of Networked Fuzzy Systems With Strict Dissipativity

In this article, the problem of observer-based sliding-mode control for dynamic fuzzy systems with bounded external disturbances is investigated. First, the sufficient conditions for codesign of an observer and a sliding-mode control law are presented, such that the closed-loop system is asymptotically stable and affords satisfactory dissipative performance. The event-triggering mechanisms are also applied in the observer-based controller design. Then, an integral sliding-mode surface and an observer-based sliding-mode controller are designed such that the system trajectories are steadily maintained on the sliding surfaces. Finally, a numerical example is given to demonstrate the effectiveness of the developed new design method.

Fast just-in-time-learning recursive multi-output LSSVR for quality prediction and control of multivariable dynamic systems

Aiming at quality prediction and control of blast furnace (BF) ironmaking process characterized by complicated nonlinear time-varying dynamics, this paper proposes a just-in-time-learning (JITL) recursive multi-output least squares support vector regression (JITL-R-M-LSSVR) algorithm with fast nonlinear local learning capability for multivariable dynamic systems. The proposed fast JITL-R-M-LSSVR effectively combines the online local learning of JITL with the multi-output LSSVR (M-LSSVR) based on multi-task transfer learning, and focuses on how to ensure the rapid verification of the local model during online learning of M-LSSVR, and how to perform model pruning while recursively updating the model parameters to improve the calculation efficiency. To this end, the proposed algorithm uses a derived multi-output incremental learning algorithm to recursively update model parameters online in a gentle way, which has better modeling stability and smoothness than the traditional way that discards old models. At the same time, when the model is pruned, a novel multi-output reverse decremental learning algorithm is proposed to adaptively delete the modeling data, so as to effectively control the sample size and reduces the calculation cost. In particular, the model verification of the proposed algorithm only needs to construct the M-LSSVR modeling matrix and the matrix inverse operation once, and the matrix after deleting each modeling sample can be easily obtained by reverse decremental learning of the original modeling matrix, which can achieve fast and efficient model verification. Finally, the effectiveness and practicability of the proposed method are verified by applying it to prediction modeling and predictive control of the molten iron quality in BF ironmaking process.

Adaptive versus Conventional Positive Position Feedback Controller to Suppress a Nonlinear System Vibrations

The nonlinear vibration control of a nonlinear dynamical system modeled as the well-known Duffing oscillators is investigated within this article. The conventional Positive Position Feedback (PPF) controller is proposed to mitigate the considered system nonlinear vibrations. The whole system mathematical model is analyzed by applying the multiple time scales perturbation method. The slow-flow modulation equations that govern the oscillation amplitudes of both the main system and controller are derived. The stability analysis is investigated based on Lyapunov’s first method. The effects of the different control parameters on both the main system and controller are explored. The obtained analytical and numerical results illustrated that the PPF controller can eliminate the main system nonlinear vibrations once the controller natural frequency is tuned to be the same value as the external excitation frequency, otherwise, the controller adds excessive vibrational energy to the main system rather than suppressing it. In addition, the PPF controller can destabilize the main system motion when excited by strong excitation force. Therefore, a modified version of the PPF controller named the Adaptive Positive Position Feedback (APPF) controller is proposed to overcome the main drawbacks of the conventional PPF controller. The idea is to track the external excitation frequency using an adaptive frequency measurement technique to update continuously the PPF controller natural frequency to become the same value of the excitation frequency. Based on this strategy, the system mathematical model is analyzed again by making the controller’s natural frequency equal to the external excitation frequency. The obtained analytical and numerical simulations showed that the adaptive positive position feedback controller can suppress the main system nonlinear vibration close to zero regardless of the excitation force amplitude and excitation frequency.

Quadratic Constrained Periodic Optimization for Bandlimited Linear Systems Via the Fourier-Based Method

AbstractMotivated by engineering applications, we address bounded steady-state optimal control of linear dynamical systems undergoing steady-state bandlimited periodic oscillations. The optimization can be cast as a minimization problem by expressing the state and the input as finite Fourier series expansions, and using the expansions coefficients as parameters to be optimized. With this parametrization, we address linear quadratic problems involving periodic bandlimited dynamics by using quadratic minimization with parametric time-dependent constraints. We hence investigate the implications of a discretization of linear continuous time constraints and propose an algorithm that provides a feasible suboptimal solution whose cost is arbitrarily close to the optimal cost for the original constrained steady-state problem. Finally, we discuss practical case studies that can be effectively tackled with the proposed framework, including optimal control of DC/AC power converters, and optimal energy harvesting from pulsating mechanical energy sources.

Implicit Regularization and Momentum Algorithms in Nonlinearly Parameterized Adaptive Control and Prediction.

Stable concurrent learning and control of dynamical systems is the subject of adaptive control. Despite being an established field with many practical applications and a rich theory, much of the development in adaptive control for nonlinear systems revolves around a few key algorithms. By exploiting strong connections between classical adaptive nonlinear control techniques and recent progress in optimization and machine learning, we show that there exists considerable untapped potential in algorithm development for both adaptive nonlinear control and adaptive dynamics prediction. We begin by introducing first-order adaptation laws inspired by natural gradient descent and mirror descent. We prove that when there are multiple dynamics consistent with the data, these non-Euclidean adaptation laws implicitly regularize the learned model. Local geometry imposed during learning thus may be used to select parameter vectors-out of the many that will achieve perfect tracking or prediction-for desired properties such as sparsity. We apply this result to regularized dynamics predictor and observer design, and as concrete examples, we consider Hamiltonian systems, Lagrangian systems, and recurrent neural networks. We subsequently develop a variational formalism based on the Bregman Lagrangian. We show that its Euler Lagrange equations lead to natural gradient and mirror descent-like adaptation laws with momentum, and we recover their first-order analogues in the infinite friction limit. We illustrate our analyses with simulations demonstrating our theoretical results.

Data-Driven Method for Response Control of Nonlinear Random Dynamical Systems

AbstractThe response control of nonlinear random dynamical systems is an important but also difficult subject in scientific and industrial fields. This work merges the decomposition technique of feedback control and the data-driven identification method of stationary response probability density, converts the constrained functional extreme value problem associated with optimal control to an unconstrained optimization problem of multivariable function, and determines the optimal coefficients of preselected control terms by an optimization algorithm. This data-driven method avoids the difficulty of solving the stochastic dynamic programming equation or forward–backward stochastic differential equations encountered in classical control theories, the miss of the conservative mechanism in the nonlinear stochastic optimal control strategy, and the difficulty of judging the integrability and resonance of the controlled Hamiltonian systems encountered in the direct-control method. The application and efficacy of the data-driven method are illustrated by the random response control problems of the Duffing oscillator, van der Pol system, and a two degrees-of-freedom nonlinear system.

Simulation Relations for Abstraction-based Robust Control of Hybrid Dynamical Systems

The paper addresses the problem of robust control of hybrid dynamical systems with respect to linear-time properties. First, three notions of robust controllers are formulated, that capture imperfect measurements, actuation errors and delays, and uncertain dynamics, respectively. Under mild assumptions of uniform continuity on the transition relation, robust controller synthesis problem with respect to uncertain dynamics is shown to be more general than those with respect to measurement errors, actuation errors and delays. Hence, the paper focuses on the latter notion of robust controllers. Next, foundations for abstraction-based robust controller synthesis are explored, and uniformly continuous alternating simulation relations are shown to preserve the existence of robust controllers with respect to uncertain dynamics.

Синтез H-inf регуляторов на конечном промежутке времени

The article considers a problem of stabilization of an aircraft, which can be solved by finding output control. Sufficient conditions for H-inf- output control for linear dynamic systems are obtained. Two approximate methods of closed-loop systems synthesis are proposed. The first one is based on finding a pseudo-inverse matrix of the linear measuring system model. The second one based on synthesizing an asymptotic observer, which allows to formulate an estimate of a state vector, giving a possibility of further use of the obtained estimate in the control law. The paper contains a step-by-step algorithm of finding an H-inf -control of a closed-loop system.

Grounds for Searching the Best Solution for Controlling the Pressurized Water Reactor in Dynamic Modes when Changing the Controlled Parameters

The article focused on the development of information technology for the optimization of control over complex dynamic systems at the stage of their design that should realize possibilities of modeling of linear and nonlinear dynamic systems, the analysis and synthesis of such systems, their optimization on various quality criteria. The purpose of this article is to develop the structure and elements of information technology to optimize the control of complex dynamic systems, including automated control systems. The general structure and functional model of information technology of the analysis and synthesis of control systems includes modeling of dynamic systems in the form of systems of differential equations and transfer functions, integration of systems of differential equations, calculation of system quality criteria, methods for solving various optimization tasks on solutions of optimization problems of dynamic systems is offered.

Pre-stabilised Predictive Functional Control for Open-loop Unstable Dynamic Systems

Abstract Predictive functional control (PFC) is the simplest model-based algorithm, equipped with the attributes of a fully fledged predictive controller but at the cost and complexity threshold of a standard PID regulator. It has proven benefits in controlling stable SISO dynamic systems, but similarly to its competitor PID, it loses efficacy when a challenging application is introduced. In this paper, we present a modified PFC approach, especially tailored for open-loop unstable processes, using pre-stabilisation to efficiently control the undesirable dynamics at hand. This is essentially a two-stage design scheme with implications for PFC tuning and constraint handling. The proposal, nevertheless, is straightforward and intuitive, and provides improved closed-loop control in the presence of external perturbations against the standard PFC, and significantly better performance overall compared to the common PID algorithm, as demonstrated in a numerical case-study.