Discrete-time Feedback Research Articles

Nonlinear Model Predictive Control with Evolutionary Data-Driven Prediction Model and Particle Swarm Optimization Optimizer for an Overhead Crane

This paper presents a new approach to the nonlinear model predictive control (NMPC) of an underactuated overhead crane system developed using a data-driven prediction model obtained utilizing the regularized genetic programming-based symbolic regression method. Grammar-guided genetic programming combined with regularized least squares was applied to identify a nonlinear autoregressive model with an exogenous input (NARX) prediction model of the crane dynamics from input–output data. The resulting prediction model was implemented in the NMPC scheme, using a particle swarm optimization (PSO) algorithm as a solver to find an optimal sequence of the control actions satisfying multi-objective performance requirements and input constraints. The feasibility and performance of the controller were experimentally verified using a laboratory crane actuated by AC motors and compared with a discrete-time feedback controller developed using the pole placement technique. A series of experiments proved the effectiveness of the controller in terms of robustness against operating condition variation and external disturbances.

Stabilization of impulsive hybrid stochastic differential equations with Lévy noise by feedback control based on discrete-time state observations

In this paper, we investigate the problem of the mean-square exponential stabilization for a class of unstable impulsive hybrid stochastic differential equations with Lévy noise (IHSDEs-LN) via feedback control based on discrete-time state observations. Our results show that if feedback control of continuous-time observations can stabilize the controlled system in the sense of mean-square exponential stability, then feedback control of discrete-time state observations can also stabilize the controlled system. And there exists an upper bound on the interval between adjacent observation moments that can be accurately computed. Based on this new theory, we first design continuous-time feedback control for unstable IHSDEs-LN to achieve the stabilization problem, and then improve the continuous-time feedback control to discrete-time state observations feedback control.

The Zero-Sum Discrete-Time Feedback Linear Quadratic Dynamic Game: From Two-Player Case to Multi-Player Case

The Zero-Sum Discrete-Time Feedback Linear Quadratic Dynamic Game: From Two-Player Case to Multi-Player Case

Review of DC Motor Modeling and Linear Control: Theory with Laboratory Tests

This review paper introduces the modeling, measurement, identification and control of direct current motors based on the state space modeling and the transfer function representation. These models are identified by real laboratory measurements, and the simulated results are compared with the measurements. Continuous-time and discrete-time PID (Proportional-Integral-Derivative) controllers, discrete-time state feedback and linear quadratic controllers are designed mathematically. The designed controllers are realized by the microcontroller Arduino UNO, and the behavior of the controllers is compared and analyzed. The noisy current signal has been measured by a discrete-time observer, steady-state Kalman filtering is also studied. The practical results of the implemented controllers support the theoretical results very well.

Discrete-Time Adaptive Control for Three-Phase PWM Rectifier.

This paper proposes a dual-loop discrete-time adaptive control (DDAC) method for three-phase PWM rectifiers, which considers inductance-parameter-mismatched and DC load disturbances. A discrete-time model of the three-phase PWM rectifier is established using the forward Euler discretization method, and a dual-loop discrete-time feedback linearization control (DDFLC) is given. Based on the DDFLC, the DDAC is designed. Firstly, an adaptive inductance disturbance observer (AIDO) based on the gradient descent method is proposed in the current control loop. The AIDO is used to estimate lump disturbances caused by mismatched inductance parameters and then compensate for these disturbances in the current controller, ensuring its strong robustness to inductance parameters. Secondly, a load parameter adaptive law (LPAL) based on the discrete-time Lyapunov theory is proposed for the voltage control loop. The LPAL estimates the DC load parameter in real time and subsequently adjusts it in the voltage controller, achieving DC load adaptability. Finally, simulation and experimental results show that the DDAC exhibits better steady and dynamic performances, less current harmonic content than the DDFLC and the dual-loop discrete-time PI control (DDPIC), and a stronger robustness to inductance parameters and DC load disturbances.

Discrete-time feedback control of highly nonlinear hybrid stochastic neural networks with non-differentiable delays

This paper investigates the stability of a class of highly nonlinear hybrid stochastic neural networks (HSNNs). Distinct from existing results, the system coefficients satisfy polynomial growth conditions instead of the usual linear growth conditions; the delays in the considered systems are time-varying delays with non-differentiable. In this paper, feedback control based on discrete-time state and mode observations is used to make the system stable. By applying the Lyapunov functional method, four results on the stabilisation of the controlled systems are established. Moreover, the upper bound on the duration τ between two consecutive state and mode observations is gained. At last, two examples are given to illustrate the validity of the theoretical results.

Combined Observer-Based State Feedback and Optimized P/PI Control for a Robust Operation of Quadrotors

This paper deals with a discrete-time observer-based state feedback control design by taking into consideration bounded parameter uncertainty, actuator faults, and stochastic noise in an inner control loop which is extended in a cascaded manner by outer PI- and P-control loops for velocity and position regulation. The aim of the corresponding subdivision of the quadrotor model is the treatment of the control design in a systematic manner. In the inner loop, linear matrix inequality techniques are employed for the placement of poles into a desired area within the complex z-plane. A robustification of the design towards noise is achieved by optimizing both control and observer gains simultaneously guaranteeing stability in a predefined bounded state domain. This procedure helps to reduce the sensitivity of the inner control loop towards changes induced by the outer one. Finally, a model-based optimization process is employed to tune the parameters of the outer P/PI controllers. To allow for the validation of accurate trajectory tracking, a comparison of the novel approach with the use of a standard extended Kalman filter-based linear-quadratic regulator synthesis is presented to demonstrate the superiority of the new design.

Razumikhin technique for stabilisation of highly nonlinear hybrid systems by bounded discrete-time state feedback control working intermittently

Razumikhin technique for stabilisation of highly nonlinear hybrid systems by bounded discrete-time state feedback control working intermittently

Stabilization of nonlinear hybrid stochastic time-delay neural networks with Lévy noise using discrete-time feedback control

<p>This paper aims to formulate a class of nonlinear hybrid stochastic time-delay neural networks (STDNNs) with Lévy noise. Specifically, the coefficients of networks grow polynomially instead of linearly, and the time delay of given neural networks is non-differentiable. In many practical situations, nonlinear hybrid STDNNs with Lévy noise are unstable. Hence, this paper uses feedback control based on discrete-time state and mode observations to stabilize the considered nonlinear hybrid STDNNs with Lévy noise. Then, we establish stabilization criteria of $ H_{\infty} $ stability, asymptotic stability, and exponential stability for the controlled nonlinear hybrid STDNNs with Lévy noise. Finally, a numerical example illustrating the usefulness of theoretical results is provided.</p>

Structured stabilisation of superlinear delay systems by bounded discrete-time state feedback control

Taking different system structures in different Markovian modes into consideration, this paper studies the structured stabilisation of a class of superlinear hybrid stochastic delay systems by feedback control based on discrete-time state observations. The controller is designed in a bounded state area, rather than every observable state, in order to reduce control cost. The time delay is more general in terms of the classical differentiability assumption being relaxed. Compared with the existing papers on discrete-state-feedback stabilisation problem, a new method to estimate the difference between current-time state and discrete-time state is presented, as a result of which the conditions imposed on the underlying system and the control function are less restrictive. Meanwhile, the Lyapunov functional used in this paper is modified to adapt to this change. Finally, an application to stochastic structured neural networks is given to demonstrate the practicability of the developed theory.

Data-Based Control of Feedback Linearizable Systems

We present an extension of Willems' Fundamental Lemma to the class of multi-input multi-output discrete-time feedback linearizable nonlinear systems, thus providing a data-based representation of their input-output trajectories. Two sources of uncertainty are considered. First, the unknown linearizing input is inexactly approximated by a set of basis functions. Second, the measured output data is contaminated by additive noise. Further, we propose an approach to approximate the solution of the data-based simulation and output matching problems, and show that the difference from the true solution is bounded. Finally, the results are illustrated on an example of a fully-actuated double inverted pendulum.

New Criteria for Analyzing the Permanence, Periodic Solution, and Global Attractiveness of the Competition and Cooperation Model of Two Enterprises with Feedback Controls and Delays

This paper studies a class of the non-autonomous competition and cooperation model of two enterprises involving discrete time delays and feedback controls. The paper proposes new criteria for analyzing the permanence, periodic solution, and global attractiveness of the model. The common mathematical techniques of the Lyapunov method, the continuation theorem, and the comparison principle are used in this paper. By means of the comparison principle and inequality techniques, the concept of permanence is investigated, which refers to the long-term survival of the enterprises within the competitive and cooperative framework. Meanwhile, using the continuation theorem, we establish conditions under which the system exhibits periodic behavior. Additionally, the global attractiveness of the system is derived by constructing multiple Lyapunov functionals. Finally, an example is presented to illustrate the applicability and validity of the proposed criteria in this paper. This example serves as a demonstration that showcases the main results derived from the analysis.

Synchronously discrete-time feedback control of large-scale systems

This paper studies the synchronously discrete-time feedback control of large-scale systems. Given an unstable complex networks (the ith subsystem is ẋi(t)=Aixi(t)+∑j=1NaijΓxj(t) ), we will design a discrete time feedback control Biei(tττ) to stabilize it. These discrete times are 0,τ,2τ,…, where τ>0 is the duration between two consecutive observations. When τ is sufficiently small, these discrete times are all over 0,∞. Thus we design an auxiliary system which is exponentially stable (the ith subsystem is eˆ̇i(t)=Aieˆi(t)+Bieˆi(t)+∑j=1NaijΓeˆj(t)), and hope to find a range of τ by the error of two feedback control systems. By constructing Lyapunov functions and using a graph-theoretic technique, we obtain a synchronization criterion.

Stabilization of highly nonlinear hybrid neutral stochastic differential equations with multiple time-varying delays and different structures

In this paper, the stabilization of a class of hybrid differently structured neutral stochastic differential equations with multiple time-varying delays is taken into consideration. The coefficients of these hybrid neutral stochastic differential delay equations with Markov switching (hybrid NSDDEs) are highly nonlinear in some modes while satisfying linear growth criteria in others. To ensure the existence and uniqueness of the solution, mild conditions are first applied to the system coefficients. Second, design techniques for discrete-time feedback control for only some of the modes are offered in order to stabilize the above systems that are unstable. New M-matrix criteria that are simple to calculate and verify are also proposed for the control functions. Then, a new theory on asymptotic and exponential stabilization is developed by using the Lyapunov function technique. Finally, the results are demonstrated with an example.

Investigating the law of tendential fall in the rate of profit based on feedback control

The rate of profit is a key element for understanding the movement of capitalism such as technological progress and economic crisis. Even though capitalists seek larger profit rates, there exists a tendency of stagnating or falling profit rates. According to Marx, the rate of profit would tend to decline in the long run as a result of technological progress, termed the law of tendential fall in the profit rate. This article introduces a novel approach based on the discrete-time feedback control mechanism to elucidate Marx’s theory. Specifically, this study presents a mechanism and conditions to show how the effort to maximize the profit rate, implemented by designing an “appropriate” control law under the sampling of fiscal years, eventually leads to the gradual decrease in the rate of profit in the long run.

Discrete-time feedback control for highly nonlinear hybrid stochastic systems with non-differentiable delays

Discrete-time feedback control for highly nonlinear hybrid stochastic systems with non-differentiable delays

Stabilization of Stochastic Highly Nonlinear Delay Systems With Neutral Term

In this article, stochastic highly nonlinear delay systems with neutral term are studied, which does not satisfy the linear growth condition. Under the local Lipschtiz condition and the polynomial growth condition, we study the existence and uniqueness, as well as boundedness, of global solution for stochastic highly nonlinear delay systems with neutral term. By designing a discrete-time feedback control function, the stabilization of stochastic highly nonlinear delay systems with neutral term is presented. Different from the previous literature, our discrete-time feedback control function depends on Markov switching signals with a delay. An illustrative example is given to show the effectiveness of the obtained results.

Stabilization of hybrid stochastic systems with time-varying delay by discrete-time state feedback control

In this paper, we are concerned with the stabilization of hybrid stochastic systems with variable delay by discrete-time state feedback control. By using Lyapunov functionals, we obtain an upper bound tau ^{*} on the duration τ between two consecutive state observations. Meantime, we show that hybrid stochastic systems with variable delay can be stabilized by discrete-time state feedback control as long as tau <tau ^{*}. Finally, two examples are given to demonstrate the applicability of our work.

Hybrid output regulation for linear impulsive systems with aperiodic jumps: A discrete-time feedback controller design approach

This paper is concerned with the problem of hybrid output regulation for a class of linear impulsive systems with aperiodic jumps. Firstly, by leveraging time-dependent Lyapunov function technique and impulsive control theory, sufficient conditions for achieving output regulation are obtained in state feedback case. Then, the results are extended to error feedback case by constructing an impulsive observer. In this framework, two novel hybrid controllers are designed. Such controllers only need the discrete-time system state or error signal for feedback. The complete procedures for controller designs are also presented. Finally, two illustrative examples, including a numerical example and an LC circuit, are given to show the validity and applicability of the proposed control laws.

Multi-time scale control and optimization via averaging and singular perturbation theory: From ODEs to hybrid dynamical systems

Multi-time scale techniques based on singular perturbations and averaging theory are among the most powerful tools developed for the synthesis and analysis of feedback control algorithms. This paper introduces some of the recent advances in singular perturbation theory and averaging theory for continuous-time dynamical systems modeled as ordinary differential equations (ODEs), as well as for hybrid dynamical systems that combine continuous-time dynamics and discrete-time dynamics. Novel multi-time scale analytical tools based on higher-order averaging and singular perturbation theory are also discussed and illustrated via different examples. In the context of hybrid dynamical systems, a class of sufficient Lyapunov-based conditions for global stability results are also presented. The analytical tools are illustrated through various new architectures and algorithms within the context of adaptive and extremum-seeking systems. These tools are suitable for the study of model-free optimization and stabilization problems that require the synergistic use of continuous-time and discrete-time feedback. The paper aims to acquaint the reader with a range of modern tools for studying multi-time scale phenomena in optimization and control systems, providing some guidelines for future research in this field.