Control Of Dynamic Systems Research Articles

Incremental stability and contraction via impulsive control for continuous-time dynamical systems

This paper investigates the incremental stability and contraction via impulsive control for continuous-time dynamical systems (CDS). By using the methods of Lyapunov-like function and average dwell-time (ADT), criteria are established for incremental stability including incremental global asymptotic stability (δGAS) and incremental global exponential stability (δGES). The notion of rate of control is proposed and the ADT condition is shown to be equivalent to the condition via the inferior limit of rate of control. And it is shown that the δGES via impulsive control is robust with respect to the time-delays and data dropout. The results are then applied to time-varying Lipschitz-type CDS which can achieve δGES via a linear impulsive control. Moreover, the notion of global contracting via impulsive control is proposed for CDS. The global contracting via impulsive control is proved to be equivalent to the δGES via impulsive control. Some less conservative criteria are derived for global contracting/δGES via impulsive control. And the equivalence is used to derive a byproduct of δGES and global contracting for CDS with destabilizing impulses. Finally, three examples with numerical simulations are presented for illustrations.

Fast Online Reinforcement Learning Control Using State-Space Dimensionality Reduction

In this article, we propose a fast reinforcement learning (RL) control algorithm that enables online control of large-scale networked dynamic systems. RL is an effective way of designing model-free linear quadratic regulator (LQR) controllers for linear time-invariant (LTI) networks with unknown state-space models. However, when the network size is large, conventional RL can result in unacceptably long learning times. The proposed approach is to construct a compressed state vector by projecting the measured state through a projective matrix. This matrix is constructed from online measurements of the states in a way that it captures the dominant controllable subspace of the open-loop network model. Next, an RL controller is learned using the reduced-dimensional state instead of the original state such that the resulting cost is close to the optimal LQR cost. Numerical benefits as well as the cyber-physical implementation benefits of the approach are verified using illustrative examples including an example of wide-area control of the IEEE 68-bus benchmark power system.

A Computational Analysis of Decomposition Strategies for Model Predictive Control of Resource-Constrained Dynamic Systems

This paper presents two decomposition approaches, Bilevel Optimization and Benders Decomposition, to a model predictive control of resource-constrained dynamic systems. The proposed methods yield a distributed solution that converges to the same optimum that would be obtained by a centralized controller. In this context, it is shown that the decompositions enable the use of multi-core or distributed architectures. A level regularization method is applied to accelerate the convergence of the Benders decomposition. Computational analyses from experiments with synthetic problems and a problem regarding the charging of vehicle batteries are reported and discussed, which showed that the decomposition approaches are effective at solving the distributed problems, achieving a global optimum.

Flatness based trajectory planning and open-loop control of shallow-water waves in a tube

Open-loop control design for a fluid in a pipe is considered. The position (resp. the velocity) of a piston moving within the tube acts as control input. The system dynamics are described by the so-called Saint-Venant equations with a moving boundary condition. Rest-to-rest transitions are parameterized by means of the so called flatness-based approach to the control of dynamical systems the flat output being the water level at the uncontrolled boundary. The control algorithms are implemented on a test bench and verified in numerical and experimental studies.

MODELING OF INTELLECTUAL CONTROL SYSTEMS WITH APPLICATION OF MODIFIED FUZZY COLORED PETRI NETS

A modification of the Petri nets is proposed  a Fuzzy Colored Petri Net (FCPN), leading to the integration of Fuzzy Petri Nets (FPN) and Colored Petri Nets (CPN). Separately, the shortcomings of FPN and CPN and the advantages the developed FCPN for modeling intelligent control systems are identified and justified. In the developed modified FCPN the membership functions of the terms of a linguistic variable are applied to markers of the CPN as color and fuzzy existence conditions are assigned to arcs depending on the values of the linguistic variable. As a result, FCPN with enhanced capabilities was obtained, which eliminates the shortcomings of CPN and FPN. The FCPN and a simulation approach are defined, which includes a reasoning algorithm, as well as a detailed procedure for modeling and analysis of nonlinear discrete objects. The structure is organized in the CPN Tools system with the synchronization of the CPN ML (Markup Language) language with the MatLab package. The choice of membership function and fuzzification of term values is performed in the Fuzzy Toolbox application of the MatLab system. The proposed approach is illustrated by simple example, including the control of water pumps, to maintain the required water level in the pumping well. A model is developed for the automation of adaptive fuzzy control of water pumps based on modified FCPN. Based on the criteria for the operation of water pumps according to the water levels in the pumping well, many positions and transitions of the FCPN are formed. Describing the necessary behavior of the system by the relations between the positions and transitions of the FCPN using the logic “If ... Then ...” an adaptation algorithm is developed. Based on the algorithm, the matrices of input and output incidents are determined. The graph model of the FCPN is developed. Visualization of the model is implemented in the CPN Tools system. The computer simulations and net analysis experiments demonstrate the convenience of the developed approach when modeling the intelligent control of dynamic systems.

Optimally designed Lyapunov–Krasovskii terminal costs for robust stable–feasible model predictive control of uncertain time-delay nonlinear dynamical systems

This article details a new Model Predictive Control algorithm ensuring robust stability and control feasibility for uncertain nonlinear multi-input multi-output dynamical systems considering uncertain time-delay effects. The proposed control algorithm is based on construction of a Lyapunov–Krasovskii functional as terminal cost. Incorporation of this terminal cost into the Model Predictive Control optimization problem and calculation of the associated admissible set result in robust feasibility and robust stability of closed-loop system in presence of uncertain time-delay effects and bounded disturbance signals. The Lyapunov–Krasovskii functional term is constructed with respect to predicted sliding functions over the prediction horizon and considers the effects of dynamical variations over the prediction horizon in generation of control inputs. As dynamical variations are investigated in a sample-to-sample basis, feasible sliding regions are updated at each sample as well. Finally, based on expression of sliding functions as a combination of dynamical variations and input-based terms, required control inputs are calculated in the admissible bound by the optimization algorithm. Construction of control scheme on this basis permits straightforward calculation of robust stability and feasibility conditions for a general class of uncertain nonlinear system in finite prediction horizon whereas in the previous works, often-restrictive conditions were considered for the investigated dynamical systems. Numerical illustrations indicate precision and efficiency of control algorithm and improved stability and convergence rate for multivariable nonlinear dynamical systems considering uncertain time-delay effects. Finally, hardware-in-the-loop implementation indicates applicability of the proposed scheme in real-time control applications particularly in case appropriate compromises between optimality and calculation speed are considered.

POTÊNCIA GERADA EM UM SISTEMA DINÂMICO DECAPTAÇÃO DE ENERGIA CONTROLADO VIA MÉTODO LQR: COMPARAÇÃO ENTRE EXCITAÇÃO PERIÓDICA E NÃO-IDEAL

Most of active control in vibrational dynamic systems is used to reduce vibrations. However,the aim of this research is specifically the use of vibrations to generate electrical energy, in such a way that the vibration becomes a desired phenomenon. In this way, the intention is to use the Optimal Control via Linear Quadratic Regulator (LQR), resulting in greater transduction of vibrational energy to electric power, varying the excitation type and performing an analysis of the stabilityand the effects of control to the dynamic system.The analyzed system is a bimodal mass-spring-damper with piezoelectric coupling-mechanic who suffers excitations periodic and non-ideal. This work intends to determine which system generates more electric power.

An Online Energy-Saving Driving Strategy for Metro Train Operation Based on the Model Predictive Control of Switched-Mode Dynamical Systems

With the rapid development of urban rail transit systems and the consequent sharp increase of energy consumption, the energy-saving train operation problem has been attracting much attention. Extensive studies have been devoted to optimal control of a single metro train in an inter-station run to minimize the energy consumption. However, most of the existing work focuses on offline optimization of the energy-saving driving strategy, which still needs to be tracked in real train operation. In order to attain better performance in the presence of disturbances, this paper studies the online optimization problem of the energy-saving driving strategy for a single metro train, by employing the model predictive control (MPC) approach. Firstly, a switched-mode dynamical system model is introduced to describe the dynamics of a metro train. Based on this model, an MPC-based online optimization problem is formulated for obtaining the optimal mode switching times with minimal energy consumption for a single train in an inter-station run. Then we propose an algorithm to solve the constrained optimization problem at each time step by utilizing the exterior point penalty function method. The proposed online optimal train control algorithm which determines the mode switching times can not only improve the computational efficiency but also enhances the robustness to disturbances in real scenarios. Finally, the effectiveness and advantages of this online optimal train control algorithm are illustrated through case studies of a single train in an inter-station run.

Estimation, control, and games of dynamical systems with uncertainty

The rapid development and widespread applications of information technology have provided unprecedented tools for the investigation and regulation of various types of complex systems, and have yielded new opportunities for the development of systems and control sciences. The future development of information science cannot be achieved without the existing basic researches and insights. After a brief review of the development of control theory, this paper focuses on some basic scientific problems concerning the estimation, control, and games of dynamical systems with uncertainty. We review some related theoretical progress achieved by the authors research group, share some research experiences, and provide new insights and perspectives. We mainly consider the theoretical foundation of the following topics: proportional-integral-derivative (PID) control, adaptive estimation, adaptive filtering, adaptive control, the maximum capability of feedback, adaptive games, collective behaviors, and game-based control systems. Because there are various feedback loops in dynamical systems, the properties of the systems observed data are usually determined using complex nonlinear dynamical equations; therefore, classical statistical assumptions such as independency and stationarity are far from being satisfied, which is a prominent feature of the theoretical investigation in this field.

Benchmark analysis of novel multi-agent optimization algorithm using linear regulators for agents motion control

The aim of this paper is to develop algorithm and software for a novel multi-agent constrained global optimization method. In multi-agent algorithms, the solution search area is populated with agents. Some transformations occur over them, which lead to a global extremum. It was proposed to take as a basis the use of linear regulators to control the movement of agents group. At each stage of the algorithm, a search is made by closed loop agents control with various types of criteria. Using criteria of various types, a more detailed study of the solution search area and finding a global extremum is provided. This is the main feature and novelty of the algorithm under consideration. The method efficiency is studied on a standard set of test functions of two variables with a complex structure of level lines using the software developed. Efficiency analysis is carried out for Schweffel function and multifunction from the benchmark set. During the study, statistical characteristics were calculated, according to which the most suitable parameters were selected. The results obtained indicate that the algorithm successfully copes with such problems and can be used, for example, for problems in the theory of optimal control of dynamic systems.

Simultaneous path-following and vibration control for uncertain nonlinear flexible mechanical systems without dependency on oscillatory mathematical model

In this paper, a novel multiobjective algorithm for simultaneous path-following control (PFC) of multivariable flexible dynamical systems and maintaining boundedness of transverse vibrational effects is proposed. This method is specifically designed for control of complicated dynamical systems where obtaining precise mathematical models describing vibrational and translational dynamics is difficult or unattainable. To facilitate the control task, the proposed scheme is constructed such that it would be capable of stabilizing the closed-loop system solely using a rigid approximation of system dynamics while considering vibrational effects as unstructured uncertainties. This permits the designer to forgo the troublesome task of precisely modeling and numerically analyzing the flexible vibrational system, prioritizing important path-following and closed-loop stability characteristics. The proposed control algorithm incorporates a discrete sliding mode control (DSMC) scheme constructed on the basis of calculation of input bounds. This method does not introduce additional chattering effects as generation of control inputs is not directly dependent on switching functions. Unstructured uncertainties are estimated using one-step approximation technique which removes the need for employing difficult techniques used in the existing literature. The control algorithm is constructed in two distinct modes, the first of which considers appropriate path following as its objective. The second control mode halts the tracking task unless an assigned cost function resides in an acceptable interval, resulting in gradual reduction of intensity of vibrational effects. The control algorithm is numerically simulated in ANSYS® Mechanical APDL environment. The obtained results express the accuracy and efficiency of the control algorithm despite the use of considerably simpler procedure in comparison with existing works.

Extremum seeking control of nonlinear dynamic systems using Lie bracket approximations

SummaryIn this article, we consider extremum seeking problems for a general class of nonlinear dynamic control systems. The main result of the article is a broad family of control laws which optimize the steady‐state performance of the system. We prove practical asymptotic stability of the optimal steady‐state and, moreover, propose sufficient conditions for the asymptotic stability in the sense of Lyapunov. The results generalize and extend existing results which are based on Lie bracket approximations. In particular, our approach does not rely on singular perturbation theory, as commonly used in extremum seeking of nonlinear dynamic systems.

Online Discovery and Classification of Operational Regimes From an Ensemble of Time Series Data

Abstract One of the pertinent problems in decision and control of dynamical systems is to identify the current operational regime of the physical process under consideration. To this end, there has been an upsurge in (data-driven) machine learning methods, such as symbolic time series analysis, hidden Markov modeling, and artificial neural networks, which often rely on some form of supervised learning based on preclassified data to construct the classifier. However, this approach may not be adequate for dynamical systems with a variety of operational regimes and possible anomalous/failure conditions. To address this issue, the technical brief proposes a methodology, built upon the concept of symbolic time series analysis, wherein the classifier learns to discover the patterns so that the algorithms can train themselves online while simultaneously functioning as a classifier. The efficacy of the methodology is demonstrated on time series of: (i) synthetic data from an unforced Van der Pol equation and (ii) pressure oscillation data from an experimental Rijke tube apparatus that emulates the thermoacoustics in real-life combustors where the process dynamics undergoes changes from the stable regime to an unstable regime and vice versa via transition to transient regimes. The underlying algorithms are capable of accurately learning and capturing the various regimes online in a (primarily) unsupervised manner.

Optimal Control of Stochastic Dynamic Systems of a Random Structure with Poisson Switches and Markov Switching

The problem of synthesis of the optimal control for a stochastic dynamic system of a random structure with Poisson perturbations and Markov switching is solved. To determine the corresponding functions for Bellman functional and optimal control the system of ordinary differential equation is investigated.

Study of the thermo-magneto-hydrodynamic flow of micropolar-nanofluid in square enclosure using dynamic mode decomposition and proper orthogonal decomposition

In the present contribution, we analyze the non-stationary, incompressible, laminar, natural convection flow in a rectangular enclosure filled with a micropolar-nanofluid (Al2O3/water) in the presence of a magnetic field, using Dynamic Mode Decomposition (DMD) and Proper Orthogonal Decomposition (POD) method. DMD method utilizes numerically or experimentally obtained data (often generated by nonlinear dynamics) to compute the eigenvalues and the eigenmodes of an approximated linear model, and the growth/decay (damp) rates, frequencies and spatial structures for each mode. POD provides the energy content measure for different modes. DMD and POD method have been applied in the study, optimization and control of large-scale dynamical systems. They can be used supplementary to each other or separately for cross comparison. We propose an efficient way to (i) snapshots sampling (ii) select the optimal number for analysis and (iii) define the grid resolution (grid density) for obtaining a grid independent solution for the DMD analysis. We numerically solve the flow equations using a meshless point collocation method (MPCM), using the Moving Least Square (MLS) method to approximate the unknown field functions and their spatial derivatives. We demonstrate stability of the system using the Ritz and dynamic spectrum along with the phase portrait of time coefficients of the most dominant DMD modes. We estimate the energy contents of the captured modes for various Hartman (Ha) and Rayleigh (Ra) numbers, nanoparticles volume fractions (φ), magnetic field (ξ) and square enclosure angles (γ). The energy content of each mode for Al2O3/water nanofluid is associated with the corresponding eigenvalue and discloses its contribution to the total energy. The results show that the above mentioned parameters significantly affect the energy contents of the captured modes.

Supervised learning algorithms for controlling underactuated dynamical systems

Control of underactuated dynamical systems has been studied for decades in robotics, and is now emerging in other fields such as neuroscience. Most of the advances have been in model based control theory, which has limitations when the system under study is very complex and it is not possible to construct a model. This calls for data driven control methods like machine learning, which has spread to many fields in the recent years including control theory. However, the success of such algorithms has been dependent on availability of large datasets. Moreover, due to their black box nature, it is challenging to analyze how such algorithms work, which may be crucial in applications where failure is very costly. In this paper, we develop two related novel supervised learning algorithms. The algorithms are powerful enough to control a wide variety of complex underactuated dynamical systems, and yet have a simple and intelligent structure that allows them to work with a sparse data set even in the presence of noise. Our algorithms output a bang-bang (binary) control input by taking in feedback of the state of the dynamical system. The algorithms learn this control input by maximizing a reward function in both short and long time horizons. We demonstrate the versatility of our algorithms by applying them to a diverse range of applications including: switching between bistable states, changing the phase of an oscillator, desynchronizing a population of synchronized coupled oscillators, and stabilizing an unstable fixed point. For most of these applications we are able to reason why our algorithms work by using traditional dynamical systems and control theory. We also compare our learning algorithms with some traditional control algorithms, and reason why our algorithms work better.

Event trigger-based adaptive sliding mode fault-tolerant control for dynamic systems

Event trigger-based adaptive sliding mode fault-tolerant control for dynamic systems

Analytical periodic motions in a discontinuous system with a switching hyperbola

In this paper, studied are periodic motions in a discontinuous system with three vector fields switching through two branches of a hyperbola. The switchability conditions of flows at the discontinuous boundaries are presented through G-functions. Such conditions are presented for passable motions and grazing motions at the boundary with sliding motions on the boundary. With such analytical conditions, periodic motions with specific mapping structures are analytically predicted, and the corresponding stability and bifurcations are presented through eigenvalue analysis. Numerical illustrations of periodic motions are carried out, and the corresponding G-functions are presented for illustration of motion switchability at the hyperbolic boundaries. The discontinuity of periodic motions is shown in phase trajectories. This study tells the complex motions can be obtained through a few individual systems with arbitrary switching boundaries, and the corresponding discontinuous dynamics can be discussed for dynamical system design and control.

Direct Adaptive Controllers for a Multi Input Multi Output Process

Control of nonlinear dynamic systems is of great practical importance, since virtually all real world systems belong to this class. The prevalent approach is to use a model of the process linearized about the steady state operating point to design linear controllers. The Multi Input Multi Output (MIMO) process considered in this paper has varying system dynamics. This paper focuses on the performance evaluation of multi-loop Adaptive MIT(AMIT) controller and Adaptive PI(API) controller with vanishing adaptation technique for a laboratory interacting coupled tank MIMO process.

Constrained attractor selection using deep reinforcement learning

This study describes an approach for attractor selection (or multistability control) in nonlinear dynamical systems with constrained actuation. Attractor selection is obtained using two different deep reinforcement learning methods: (1) the cross-entropy method and (2) the deep deterministic policy gradient method. The framework and algorithms for applying these control methods are presented. Experiments were performed on a Duffing oscillator, as it is a classic nonlinear dynamical system with multiple attractors. Both methods achieve attractor selection under various control constraints. Although these methods have nearly identical success rates, the deep deterministic policy gradient method has the advantages of a high learning rate, low performance variance, and a smooth control approach. This study demonstrates the ability of two reinforcement learning approaches to achieve constrained attractor selection.