Control Of Complex Dynamic Systems Research Articles

Stability Analysis of Switched Linear Systems with Neural Lyapunov Functions

Neural-based, data-driven analysis and control of dynamical systems have been recently investigated and have shown great promise, e.g. for safety verification or stability analysis. Indeed, not only do neural networks allow for an entirely model-free, data-driven approach, but also for handling arbitrary complex functions via their power of representation (as opposed to, e.g. algebraic optimization techniques that are restricted to polynomial functions). Whilst classical Lyapunov techniques allow to provide a formal and robust guarantee of stability of a switched dynamical system, very little is yet known about correctness guarantees for Neural Lyapunov functions, nor about their performance (amount of data needed for a certain accuracy). We formally introduce Neural Lyapunov functions for the stability analysis of switched linear systems: we benchmark them on this paradigmatic problem, which is notoriously difficult (and in general Turing-undecidable), but which admits existing recently-developed technologies and theoretical results. Inspired by switched systems theory, we provide theoretical guarantees on the representative power of neural networks, leveraging recent results from the ML community. We additionally experimentally display how Neural Lyapunov functions compete with state-of-the-art results and techniques, while admitting a wide range of improvement, both in theory and in practice. This study intends to improve our understanding of the opportunities and current limitations of neural-based data-driven analysis and control of complex dynamical systems.

Finite-time stochastic control for complex dynamical systems: The estimate for control time and energy consumption

Controlling complex dynamical systems has garnered significant attention within academic circles in recent decades. While most existing works have focused on closed-loop control schemes with infinite-time durations, this paper introduces a novel finite-time, closed-loop stochastic controller that considers control time, energy consumption, and their dependence on system parameters. This stochastic control technique not only enables finite-time control in chaotic dynamical systems but also facilitates finite-time synchronization in unidirectionally coupled systems. Importantly, our proposed scheme offers several advantages over existing deterministic finite-time controllers, particularly in terms of time and energy consumption. Through numerical experiments utilizing random ecosystems, neural networks, and Lorenz systems, we provide evidence of the effectiveness of our analytical results. We anticipate that this stochastic scheme will find wide-ranging applications in the control of complex dynamical systems and in achieving network synchronization.

Physics-informed neural ODE (PINODE): embedding physics into models using collocation points

Building reduced-order models (ROMs) is essential for efficient forecasting and control of complex dynamical systems. Recently, autoencoder-based methods for building such models have gained significant traction, but their demand for data limits their use when the data is scarce and expensive. We propose aiding a model’s training with the knowledge of physics using a collocation-based physics-informed loss term. Our innovation builds on ideas from classical collocation methods of numerical analysis to embed knowledge from a known equation into the latent-space dynamics of a ROM. We show that the addition of our physics-informed loss allows for exceptional data supply strategies that improves the performance of ROMs in data-scarce settings, where training high-quality data-driven models is impossible. Namely, for a problem of modeling a high-dimensional nonlinear PDE, our experiments show times 5 performance gains, measured by prediction error, in a low-data regime, times 10 performance gains in tasks of high-noise learning, times 100 gains in the efficiency of utilizing the latent-space dimension, and times 200 gains in tasks of far-out out-of-distribution forecasting relative to purely data-driven models. These improvements pave the way for broader adoption of network-based physics-informed ROMs in compressive sensing and control applications.

Optimal Control of Dynamical Systems using Calculus of Variations

This paper explores the application of calculus of variations techniques for optimizing the control of complex dynamical systems. Determining control strategies that minimize cost metrics and satisfy constraints is critical across engineering disciplines like robotics, aerospace, and process operations. Classical optimal control methods, such as Pontryagin's Maximum Principle, transform an optimal control problem into a calculus of variations framework amenable to analytical and numerical optimization. We present a unified framework for applying these techniques, enabling dynamical systems defined by ordinary and partial differential equations to be optimized by conversion into a nonlinear programming form. Analytical approaches provide theoretical guarantees on control performance while numerical methods, like direct collocation and transcription, enable large-scale optimal control problems to be efficiently solved. The connections between dynamical systems, calculus of variations, and modern numerical optimization methods establish a holistic methodology for control engineers and applied mathematicians to design optimal controllers for physical systems. Case studies on real-time trajectory optimization, adaptive path planning, and dynamic process operations demonstrate the efficacy of the proposed optimal control framework across robotics, aerospace, power systems, and other applications.

Optimal Control of Dynamical Systems using Calculus of Variations

This paper explores the application of calculus of variations techniques for optimizing the control of complex dynamical systems. Determining control strategies that minimize cost metrics and satisfy constraints is critical across engineering disciplines like robotics, aerospace, and process operations. Classical optimal control methods, such as Pontryagin's Maximum Principle, transform an optimal control problem into a calculus of variations framework amenable to analytical and numerical optimization. We present a unified framework for applying these techniques, enabling dynamical systems defined by ordinary and partial differential equations to be optimized by conversion into a nonlinear programming form. Analytical approaches provide theoretical guarantees on control performance while numerical methods, like direct collocation and transcription, enable large-scale optimal control problems to be efficiently solved. The connections between dynamical systems, calculus of variations, and modern numerical optimization methods establish a holistic methodology for control engineers and applied mathematicians to design optimal controllers for physical systems. Case studies on real-time trajectory optimization, adaptive path planning, and dynamic process operations demonstrate the efficacy of the proposed optimal control framework across robotics, aerospace, power systems, and other applications.

DC BOOST CONVERTER USING A FUZZY CONTROL SYSTEM, SIMULATED IN SIMULINK

Decisive for the operation of voltage, current and power converters is the choice of control method. Control of complex dynamic systems in conditions of insufficient or fuzzy information requires the involvement of non-standard approaches during the construction of the control system. There are two possible ways out of the traditional framework of linear control. The first, is to develop more accurate nonlinear models on which high-performance controller design can be based. However, when choosing this way, one has to develop very complex control algorithms, and, consequently, the controller will perform complex mathematical calculations, which can have a negative impact on the control speed and response. Another way is to use a neural network controller based on fuzzy logic. Fuzzy logic is a generalization of mathematical logic and set theory, which is a function of the object belonging to a set and can take any value in the range [0; 1], not only 0 or 1. In the case of fuzzy logic we don't need simulation, because the whole work on designing of the controller is reduced to the transformation of the rules included in the fuzzy logic into the algorithm of automatic control.

A low-cost pole-placement MPC algorithm for controlling complex dynamic systems

Due to the ability to handle constraints systematically and predict system evolution with models, model predictive control (MPC) methods have been widely studied and implemented in many industries. At the same time, low-cost MPC has received widespread attention due to its simple principle and easy implementation. This paper proposes a new low-cost MPC method and uses this method to put forward new insights on the performance improvement of complex dynamic system control. Firstly, using the concept of preprocessing, a novel MPC prediction structure is proposed under the independent model mode. Then through rigorous proofs, the properties of the proposed MPC algorithm are analyzed. Finally, through the study of three industrial cases, the proposal’s deployment procedure and efficacy are illustrated in detail. Compared with other low-cost predictive control algorithms, the effectiveness of the method has been presented.

Outracing champion Gran Turismo drivers with deep reinforcement learning.

Many potential applications of artificial intelligence involve making real-time decisions in physical systems while interacting with humans. Automobile racing represents an extreme example of these conditions; drivers must execute complex tactical manoeuvres to pass or block opponents while operating their vehicles at their traction limits1. Racing simulations, such as the PlayStation game Gran Turismo, faithfully reproduce the non-linear control challenges of real race cars while also encapsulating the complex multi-agent interactions. Here we describe how we trained agents for Gran Turismo that can compete with the world's best e-sports drivers. We combine state-of-the-art, model-free, deep reinforcement learning algorithms with mixed-scenario training to learn an integrated control policy that combines exceptional speed with impressive tactics. In addition, we construct a reward function that enables the agent to be competitive while adhering to racing's important, but under-specified, sportsmanship rules. We demonstrate the capabilities of our agent, Gran Turismo Sophy, by winning a head-to-head competition against four of the world's best Gran Turismo drivers. By describing how we trained championship-level racers, we demonstrate the possibilities and challenges of using these techniques to control complex dynamical systems in domains where agents must respect imprecisely defined human norms.

AI Pontryagin or how artificial neural networks learn to control dynamical systems

The efficient control of complex dynamical systems has many applications in the natural and applied sciences. In most real-world control problems, both control energy and cost constraints play a significant role. Although such optimal control problems can be formulated within the framework of variational calculus, their solution for complex systems is often analytically and computationally intractable. To overcome this outstanding challenge, we present AI Pontryagin, a versatile control framework based on neural ordinary differential equations that automatically learns control signals that steer high-dimensional dynamical systems towards a desired target state within a specified time interval. We demonstrate the ability of AI Pontryagin to learn control signals that closely resemble those found by corresponding optimal control frameworks in terms of control energy and deviation from the desired target state. Our results suggest that AI Pontryagin is capable of solving a wide range of control and optimization problems, including those that are analytically intractable.

Functional observability and target state estimation in large-scale networks

The quantitative understanding and precise control of complex dynamical systems can only be achieved by observing their internal states via measurement and/or estimation. In large-scale dynamical networks, it is often difficult or physically impossible to have enough sensor nodes to make the system fully observable. Even if the system is in principle observable, high dimensionality poses fundamental limits on the computational tractability and performance of a full-state observer. To overcome the curse of dimensionality, we instead require the system to be functionally observable, meaning that a targeted subset of state variables can be reconstructed from the available measurements. Here, we develop a graph-based theory of functional observability, which leads to highly scalable algorithms to 1) determine the minimal set of required sensors and 2) design the corresponding state observer of minimum order. Compared with the full-state observer, the proposed functional observer achieves the same estimation quality with substantially less sensing and fewer computational resources, making it suitable for large-scale networks. We apply the proposed methods to the detection of cyberattacks in power grids from limited phase measurement data and the inference of the prevalence rate of infection during an epidemic under limited testing conditions. The applications demonstrate that the functional observer can significantly scale up our ability to explore otherwise inaccessible dynamical processes on complex networks.

Controlling chaos in two coupled lasers via optoelectronic delayed time cross-feedback

This paper presents an optoelectronic delayed time cross-feedback method to control chaos in two coupled lasers. The technical solution of chaos-control of two lasers is designed out to convert light from one laser into a photocurrent by a photoelectric converter, and then the delayed time photocurrent is cross added on another laser to suppress chaos or guide other dynamics behaviours. We adjust feedback levels or delayed time to realize chaos-control, and which can lead to show all kinds of dynamics states. We find that chaos of two lasers is suppressed into different cycle-one states while the cycle-one controlled region is found. We analyse also the laser’s damping oscillation process for chaos-control of two lasers from chaos becoming of a cycle-one state when feedback levels shift. We find that chaos in the two lasers can be controlled in different quasi-periodic states, such as a cycle-one, cycle-2, a cycle-3, a cycle-5, and other quasi-cycle states while we find some quasi-cycle controlled distribution regions. The listed results imply that chaos-control of two coupled lasers can be effectively realized via the optoelectronic delayed time cross-feedback method. Our Result is very helpful for our studies of controlling complex dynamic systems, chaos, and laser technology.

A test of synergy in dynamic system control tasks.

Individual performance in controlling complex dynamic systems such as managing production in a company or keeping ecosystems in balance is often suboptimal. In this article, we provide the first unequivocal test of whether groups are superior to individuals when controlling dynamic systems. In addition, we test to what extent performance advantages of groups are simply the result of statistically aggregating a larger number of individual opinions and to what extent they represent true synergy attributable to within-group interaction. In 3 experiments, we compared the system control performance of interacting real groups with that of equally sized nominal groups and with individuals. We provide evidence that groups indeed perform better than individuals in dynamic system control tasks. Furthermore, in comparing real groups with nominal groups, we show that, although the majority of real groups' performance advantage stems from statistical aggregation, there is also evidence of true synergy. Finally, we identify the mechanism by which groups achieve synergy, namely group-to-individual transfer. Discussion allows group members to exchange critical information about the system, leading to an improved individual capability to control the system, which, in turn, improves group performance. (PsycInfo Database Record (c) 2021 APA, all rights reserved).

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.

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.

Learning Optimal Controllers for Linear Systems With Multiplicative Noise via Policy Gradient

The linear quadratic regulator (LQR) problem has reemerged as an important theoretical benchmark for reinforcement learning-based control of complex dynamical systems with continuous state and action spaces. In contrast with nearly all recent work in this area, we consider multiplicative noise models, which are increasingly relevant because they explicitly incorporate inherent uncertainty and variation in the system dynamics and thereby improve robustness properties of the controller. Robustness is a critical and poorly understood issue in reinforcement learning; existing methods which do not account for uncertainty can converge to fragile policies or fail to converge at all. Additionally, intentional injection of multiplicative noise into learning algorithms can enhance robustness of policies, as observed in <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ad hoc</i> work on domain randomization. Although policy gradient algorithms require optimization of a nonconvex cost function, we show that the multiplicative noise LQR cost has a special property called <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">gradient domination</i> , which is exploited to prove global convergence of policy gradient algorithms to the globally optimum control policy with polynomial dependence on problem parameters. Results are provided both in the model-known and model-unknown settings where samples of system trajectories are used to estimate policy gradients

Adaptive-learning model predictive control for complex physiological systems: Automated insulin delivery in diabetes

An adaptive-learning model predictive control (AL-MPC) framework is proposed for incorporating disturbance prediction, model uncertainty quantification, pattern learning, and recursive subspace identification for use in controlling complex dynamic systems with periodically recurring large random disturbances. The AL-MPC integrates online learning from historical data to predict the future evolution of the model output over a specified horizon and proactively mitigate significant disturbances. This goal is accomplished using dynamic regularized latent variable regression (DrLVR) approach to quantify disturbances from the past data and forecast their future progression time series. An enveloped path for the future behavior of the model output is extracted to further enhance the robustness of the closed-loop system. The controller set-point, penalty weights of the objective function, and constraints criteria can be modified in advance for the expected periods of the disturbance effects. The proposed AL-MPC is used to regulate glucose concentration in people with Type 1 diabetes by an automated insulin delivery system. Simulation results demonstrate the effectiveness of the proposed technique by improving the performance indices of the closed-loop system. The MPC algorithm integrated with DrLVR disturbance predictor has compared to MPC reinforced with dynamic principal component analysis linked with K-nearest neighbors and hyper-spherical clustering (k-means) technique. The simulation results illustrate that the AL-MPC can regulate the glucose concentrations of people with Type 1 diabetes to stay in the desired range (70–180) mg/dL 84.4% of the time without causing any hypoglycemia and hyperglycemia events.

Machine learning dynamical phase transitions in complex networks.

Recent years have witnessed a growing interest in using machine learning to predict and identify critical dynamical phase transitions in physical systems (e.g., many-body quantum systems). The underlying lattice structures in these applications are generally regular. While machine learning has been adopted to complex networks, most existing works concern about the structural properties. To use machine learning to detect phase transitions and accurately identify the critical transition points associated with dynamical processes on complex networks thus stands out as an open and significant problem. Here we develop a framework combining supervised and unsupervised learning, incorporating proper sampling of training data set. In particular, using epidemic spreading dynamics on complex networks as a paradigmatic setting, we start from supervised learning alone and identify situations that degrade the performance. To overcome the difficulties leads to the idea of exploiting confusion scheme, effectively a combination of supervised and unsupervised learning. We demonstrate that the scheme performs well for identifying phase transitions associated with spreading dynamics on homogeneous networks, but the performance deteriorates for heterogeneous networks. To strive to meet this challenge leads to the realization that sampling the training data set is necessary for heterogeneous networks, and we test two sampling methods: one based on the hub nodes together with their neighbors and another based on k-core of the network. The end result is a general comprehensive machine learning framework for detecting phase transition and accurately identifying the critical transition point, which is robust, computationally efficient, and universally applicable to complex networks of arbitrary size and topology. Extensive tests using synthetic and empirical networks verify the virtues of the articulated framework, opening the door to exploiting machine learning for understanding, detection, prediction, and control of complex dynamical systems in general.

Variational Approach for Learning Markov Processes from Time Series Data

Inference, prediction and control of complex dynamical systems from time series is important in many areas, including financial markets, power grid management, climate and weather modeling, or molecular dynamics. The analysis of such highly nonlinear dynamical systems is facilitated by the fact that we can often find a (generally nonlinear) transformation of the system coordinates to features in which the dynamics can be excellently approximated by a linear Markovian model. Moreover, the large number of system variables often change collectively on large time- and length-scales, facilitating a low-dimensional analysis in feature space. In this paper, we introduce a variational approach for Markov processes (VAMP) that allows us to find optimal feature mappings and optimal Markovian models of the dynamics from given time series data. The key insight is that the best linear model can be obtained from the top singular components of the Koopman operator. This leads to the definition of a family of score functions called VAMP-r which can be calculated from data, and can be employed to optimize a Markovian model. In addition, based on the relationship between the variational scores and approximation errors of Koopman operators, we propose a new VAMP-E score, which can be applied to cross-validation for hyper-parameter optimization and model selection in VAMP. VAMP is valid for both reversible and nonreversible processes and for stationary and non-stationary processes or realizations.

농업용 군집드론 시스템을 제어하기 위한 관리제어기 설계 : 예비결과

A discrete event systems (DES) based approach is an efficient method to control complex dynamic systems. This paper describes a DES which uses supervisory control theory to control multiple. Agricultural unmanned aerial vehicles (UAVs). Finite state automata (FSA) are used as a modeling tool to design a supervisor to coordinate the behavior of multiple UAVs. In this paper, DES models for obstacle avoidance, path following, formation control, and task control are modeled by the FSA and controlled by the supervisor. The proposed supervisors are implemented. Their controllability, nonblocking, and non-conflicting behaviors are verified through simulation. The use of the DES formalism reflects a modular controllable system with the potential for reusability and scalability.

Multiple Neural Control Strategies Using a Neuro-Fuzzy Classifier

The paper deals with the control of complex dynamic systems. The main objective is to partition the whole operational system domain in local regions using an incremental neuro-fuzzy classifier in order to achieve multiple neural control strategies for the considered system. In our case, this approach is applied to a greenhouse operating during one day. Therefore, banks of neural controllers and direct neural local models are made from different partitioned greenhouse behaviors and two multiple neural control strategies are proposed to control the greenhouse. The selection of the suitable controller is accomplished by computing the minimal output error between desired and direct neural local models outputs in the case of the first control strategy and from a supervisor block containing the considered neuro-fuzzy classifier in the case of the second control strategy. Simulation results are then carried out to show the efficiency of the two control strategies.