Invariant Control Research Articles

Viable immersion and invariance control for a class of nonlinear systems and its application to aero-engines

This paper presents a novel approach to stabilize a class of nonlinear systems with state constraints. The motivation behind this study is the need to develop a stabilizing state feedback controller that does not require the knowledge of Lyapunov function and can regulate the states to the equilibrium while meeting the constraints. By using an integration of two relatively new tools: immersion and invariance (I&I) theory and viability theory, a sufficient condition for stability and stabilizability of a general nonlinear affine system with state constraints is derived; Then, the related results are exploited to stabilize a class of nonlinear system in feedback form and with state constraints represented by inequalities and the viable I&I stabilizing state feedback controller is obtained constructively. Further, an application to a nonlinear aero-engine model with the temperature constraint is given to illustrate the applicability and the effectiveness of the proposed method. Finally, a comparative simulation is presented, highlighting the advantages of the viable I&I controller.

On Avoiding the Effect of Non-Minimum Phase Zeros Over the Signal-to-Noise Ratio Limitation

Fundamental limitations in networked control systems have been researched for the last years with many stability results, from channel transmission minimal rate based on information theory, to minimal signal-to-noise (SNR). For the latter, it has been confirmed early on that the usual culprits increase the minimal SNR for stability, such as unstable plant poles, non-minimum phase (NMP) zeros, time delay, together with new ones such as communication channel bandwidth and colored transmission noise. In this letter we specifically propose two approaches to completely avoid the effect of NMP zeros on the minimal SNR for stability in discrete-time. The first approach stems from the observation that the controller that achieves the minimal SNR for a minimum phase plant in discretetime, has all its zeros located outside the unit circle (NMP zeros). Such observation allow then to characterize this set of NMP zeros as candidate NMP zeros of alternative plant models with the same unstable poles, which in turn will not increase the minimal SNR for stability above the expression imposed only by the plant unstable poles. Our second approach extends the set of possible NMP zeros that do not increase the SNR limitation to any location, by proposing the synthesis of a two-degree of freedom linear time invariant controller solution that achieves the minimal SNR for stability imposed only by the plant unstable poles.

Current development on using Rotary Inverted Pendulum as a benchmark for testing linear and nonlinear control algorithms

Abstract Rotary Inverted Pendulum (RIP) is an under-actuated mechanical system which is inherently nonlinear and unstable. For decades, it has been widely used as an experimental setup to explain and test different kinds of control algorithms. The main control objectives of RIP are: Swing-up control, stabilization control, switching control and trajectory tracking control. All these control objectives are described in this study. State-of-the art works proposed for each control objective have also been reviewed. These comprise the linear, nonlinear time invariant, self-learning and adaptive nonlinear controllers. Moreover, different kinds of nonlinear dynamic models of the RIP together with the developed linear models in the literature have been analyzed. This is because most of the proposed controllers applied on RIP are found to be model dependent since they are mainly based on integral and/or invariant motion. Other types of RIP are also reported along with their advantages. Future research opportunities and challenges of the previous approaches in this area of research are presented. We believe that expert researchers can use this paper as starting point for further advancement while graduate scholars can use it as an initial point.

Design of Loading System for Thrust Reverser Ground Simulation Test

Thrust reverser is a necessary device on large passenger plane and large culvert ratio turbofan engine, which has the advantages of shortening the landing distance, reducing the wear of wheel brake, prolonging the service life of braking parts and improving landing safety of aircraft. The thrust reverser ground test is one of the important contents in the design of aircraft nacelle, and generally, it is an effective way to carry out the research test work by semi-physical simulation, in which the analysis of the thrust reverser loading control system are the basis for the design of test loading device. In this paper, take the cascade thrust reverser as the object, firstly, the thrust reverser structure and working principle were specially explained. Then, according the characteristic of the hydraulic actuation system, the loading channel was designed and analyzed theoretically, especially the loading control system. Finally, the model of loading control system was established in Simulink, and the time domain and frequency characteristic were analyzed. For the redundant force in the passive loading system, PID and the principle of the structure invariance were chosen to correct the control system. The simulation results show that the principle of the structure invariance control strategy has a better effect on eliminating the redundant force to meet engineering requirements.

ADAPTIVE STABLE CONTROL OF MANIPULATOR SYSTEM BASED ON IMMERSION AND INVARIANCE

This work focused on the manipulator system containing uncertainties, and proposes an immersion and invariance (I&I) control strategy, in order to avoid the damage on the mechanical and the operation object caused by parameter uncertainty. A stable target system with lower dimension than the manipulator system was chosen to design the control law and estimation laws of uncertain parameters. Then finding an invariant and attractive manifold in state space with internal dynamics a copy of the desired closed-loop dynamics. Finally, design a control law that can steer the state of the system sufficiently close to the manifold. The immersion and invariance adaptive control does not rely on certainty equivalence. The whole uncertain parameter estimations are the sum of two terms. One is obtained by an iterative law like the traditional adaptive backstepping method. On the other hand, a nonlinear function is introduced. The role of this additional term makes the parameter estimations more exible and effective. Lyapunov function is not necessary for the process of designing adaptive controllers. So immersion and invariance can effectively avoid the 'computing expansion' of backstepping method. Compared with the traditional adaptive methods, simulation results show that the proposed immersion and invariance adaptive controller can improve the system performance, including dynamic response, stability and accuracy of parameter estimations.

Invariant sets and controllability of discrete‐time bilinear systems

In this study, the author investigates controllability of discrete-time bilinear systems by using invariant sets. An invariant set defined in this study is a set on which the system is invariant, namely for any initial state that belongs to the set, the system cannot be steered away from this set. If a system is controllable, then it has no invariant set in its state space other than the state space itself. Invariant sets are thus closely related to controllability. By studying the invariant sets of discrete-time bilinear systems, the author first presents a necessary and sufficient condition for controllability of the systems in dimension two, which covers a classical result under the same condition. Then the author considers the high-dimensional systems and improve the recent results on controllability by relaxing a condition concerning invariant sets, where more general controllability criteria are derived. Finally, examples are given to illustrate the obtained results.

Mobile Robot Control and Navigation: A Global Overview

The aim of this paper is to provide a global overview of mobile robot control and navigation methodologies developed over the last decades. Mobile robots have been a substantial contributor to the welfare of modern society over the years, including the industrial, service, medical, and socialization sectors. The paper starts with a list of books on autonomous mobile robots and an overview of survey papers that cover a wide range of decision, control and navigation areas. The organization of the material follows the structure of the author’s recent book on mobile robot control. Thus, the following aspects of wheeled mobile robots are considered: kinematic modeling, dynamic modeling, conventional control, affine model-based control, invariant manifold-based control, model reference adaptive control, sliding-mode control, fuzzy and neural control, vision-based control, path and motion planning, localization and mapping, and control and software architectures.

Stealth identification strategy for closed loop linear time invariant system

Many identification strategies for closed loop linear time invariant system assume that an open loop system is closed by a feedback mechanism, which contains a known, linear time invariant controller. This assumption means that these identification strategies are feasible under some prior knowledge of feedback controller. To relax this assumption in some complex systems with unknown controller, a new stealth identification strategy is proposed to tackle the identification problem for closed loop linear time invariant system with unknown controller. Stealth identification modifies the closed loop system, so that the new prediction error and inverse covariance matrix are all independent of the unknown controller. This independence can simplify the problems of estimating parameter vector and designing optimal input. By using this simplified prediction error to construct an objective function, a candidate domain of attraction for the objective function is introduced and one convergence condition is derived to guarantee a given set be a candidate domain of attraction. Finally a simulation example confirms our theoretical results.

A Robust Control Invariant Set Approach to Yaw Stability of Four-Wheel Drive Electric Vehicle

In this paper, a novel yaw stability control strategy for four-wheel drive electric vehicle under critical driving situations is presented. The motivation of this research is that oversteer occurs or yaw response performance is reduced when an inappropriate desired yaw rate is designed during the yaw rate tracking control. Although the bounded desired yaw rate is widely utilized to prevent oversteer in literatures, it is difficult to put forward the desired yaw rate which takes both yaw response and stability performance into account in practice. Considering that oversteer is caused by lateral forces saturation of rear wheels, this paper proposes a control strategy to constrain the lateral forces of rear wheels directly instead of bounding the desired yaw rate. The key of this work is that the state space consisting of yaw rate and side slip angle is firstly divided into two parts: saturated and unsaturated space of lateral forces of rear wheels. In the unsaturated space, the yaw rate tracking control is applied to enhance the yaw response performance. And in the saturated space, a robust invariant set yaw rate control is proposed to keep the tire slip angle of rear axle in a robust invariant set to constrain lateral forces of rear wheels. In this paper, the design approach of the robust invariant set control for yaw stability is discussed in detail. Simulation results show the effectiveness of the proposed method for enhancing yaw rate response performance and preventing lateral forces saturation of rear wheels.

Invariance entropy, quasi-stationary measures and control sets

For control systems in discrete time, this paper discusses measure-theoretic invariance entropy for a subset Q of the state space with respect to a quasi-stationary measure obtained by endowing the control range with a probability measure. The main results show that this entropy is invariant under measurable transformations and that it is already determined by certain subsets of Q which are characterized by controllability properties.

Computation of terminal costs and sets for discrete–time nonlinear MPC

The terminal cost and terminal set method for guaranteeing stability of nonlinear model predictive control (MPC) closed–loop systems is theoretically appealing but often impractical. This is due to the difficulty of computing invariant sets and control Lyapunov functions for general nonlinear systems. In this paper we propose a novel method for computing time–varying terminal costs and sets by means of first order or second order Taylor approximations of the nonlinear system dynamics. The method first solves a set of linear matrix inequalities to compute the terminal ingredients for the approximated dynamics. Then, a small scale global nonlinear optimization problem is solved to check the validity of the terminal ingredients for the nonlinear dynamics. The proposed method also allows for time–varying linear or nonlinear terminal control laws. The developed method can result in significant enlargements of the domain of attraction of the nonlinear MPC closed–loop system, as demonstrated by a benchmark academic example.

Enhanced Nonlinear Robust Control for TCSC in Power System

This paper proposes an enhanced robust control method, which is for thyristor controlled series compensator (TCSC) in presences of time-delay nonlinearity, uncertain parameter, and external disturbances. Unlike conventional adaptive control methods, the uncertain parameter is estimated by using system immersion and manifold invariant (I&I) adaptive control. Thus, the oscillation of states caused by the coupling between parameter estimator and system states can be avoided. In addition, in order to overcome the influences of time-delay nonlinearity and external disturbances, backstepping sliding mode control is adopted to design control law recursively. Furthermore, robustness of TCSC control subsystem is achievable provided that dissipation inequality is satisfied in each step. Effectiveness and efficiencies of the proposed control method are verified by simulations. Compared with adaptive backstepping sliding mode control and adaptive backstepping control, the time of reaching steady state is shortened by at least 11% and the oscillation amplitudes of transient responses are reduced by at most 50%.

Controllability and minimum energy control of fractional neutral delay system

In this paper, we consider a class of time invariant control system governed by the neutral delay differential equation of fractional order 1 < α ≤ 2. Necessary and sufficient conditions for the controllability of linear fractional neutral system is derived. The existence of solution and controllability for the proposed nonlinear system is obtained by using the successive approximation technique. Also, the minimum energy control problem of corresponding linear positive system is stated and proved by using the Grammian matrix approach. Finally two numerical examples are substantiated to illustrate the proposed theory.

Synthesis of control algorithms for robotic platform with electro-hydraulic drive

The article deals with a robotic vibroprotection platform with electro-hydraulic drive. Built mathematical model systems from the account for characteristics of the drive. Synthesized invariant controller by system state that uses reverse ties coefficients. Controller synthesized at discrete area with a restriction in the magnitude of the relative displacement of the object relative to the base. To ensure the stability of the controller are selected in regulation law amendment providing the desired value of the relative displacement. The results of mathematical modeling are presented.

Invariance Control for Safe Human–Robot Interaction in Dynamic Environments

In human–robot interaction, it is essential to ensure that the robot poses no threat to the human. Especially in applications that require close or physical interaction, e.g., collaborative manufacturing or rehabilitation, the danger emanating from the robot has to be minimized. Control schemes introducing virtual constraints have proven valuable in this context since they allow us to define a safe zone to move in without endangering the human. Combining the different requirements on the control scheme, such as real-time capability, stability, and reliability, in the presence of external disturbances and dynamic limits, however, turns out to be challenging. In this paper, we present a novel control scheme for human–robot interaction, which enforces dynamic constraints even in the presence of external forces. Based on an analytic constraint description and a feedback linearization of the system dynamics, a safe set of states is determined, which is then rendered controlled positively invariant, thus keeping the system in a safe configuration. The controlled system is analyzed with respect to invariance and boundedness with the results being illustrated in a full-scale experiment.

Optimal control of a wind turbine with digital fluid power transmission

Digital fluid power (DFP) technology may lead to a paradigm shift in large-scale transmission systems in, e.g., wind and wave energy. Therefore, the development of applicable control algorithms is of major importance, but is complicated by the non-smooth behavior of the DFP displacement machines. The power throughput of a full stroke operated digital displacement machine is quantized by the number of pressure chambers. The dynamics of each pressure chamber may be described by highly nonlinear continuous differential equations, whereas the input is discretely updated and binary (active or inactive). This paper contributes with a feedback control strategy for a digital displacement machine, where the binary inputs are handled by a pulse density modulator. The paper presents a linearization method of handling the many nonlinearities and thereby enabling the use of Discrete Linear Time Invariant (DLTI) control theory. The control strategy is validated for control of a digital fluid power wind turbine transmission, where both a deterministic and a stochastic optimal controllers are synthesized. The study is based on the NREL 5-MW reference wind turbine, where its model is combined with a nonlinear model of the DFP transmission and full-field flow wind profiles are used for a realistic performance evaluation scenario. By simulation, it is found that the performance of the optimal controllers using the DFP transmission is similar to that of the NREL controller using a conventional transmission.

Algorithms for estimating the motion of a spacecraft from its state data

Control of processing processes on the state of the spacecraft (SC) is represented by schemes of the invariant control loop of a complex dynamic object. Based on the analysis of the algorithms for estimating the parameters of the translational motion of an aircraft (LA), based on the results of external trajectory measurements, an iterative Gauss-Newton procedure is formulated that implements the approach of directly finding the extremal point of the response surface described by a multidimensional function. Applied to the problem of estimating the initial conditions of motion of an aircraft. The features of the implementation of the algorithm for estimating the initial conditions of the orbital motion of the apparatus based on the method of least squares are investigated.

Trajectory tracking using robust gain-scheduling control with a new independent variable

To reduce the expenditure, a low-performance guidance and control system is usually employed in the design of guided artillery rockets, which however will induce great difficulties in trajectory tracking because the rocket's parameters vary fast over a large operation range. The traditional time invariant control approaches for trajectory tracking cannot guarantee the adaptability of controller. On the other hand, since time is routinely considered as the independent variable, the dynamic error system varies sharply, resulting in a weak anti-jamming capability. To address these issues, a new trajectory tracking approach for guided rockets is developed by using the robust gain-scheduling control technique based on the linear parameter varying system, in conjunction with a new coordinate transformation that considers the arc length of reference trajectory as the independent variable. Through comparative studies, it is observed that the proposed method outperforms the existing ones in trajectory tracking during the whole flight trajectory, which demonstrates its effectiveness and advantages.

An improved analysis methodology for translational profiling by microarray.

Translational regulation plays a central role in the global gene expression of a cell, and detection of such regulation has allowed deciphering of critical biological mechanisms. Genome-wide studies of the regulation of translation (translatome) performed on microarrays represent a substantial proportion of studies, alongside with recent advances in deep-sequencing methods. However, there has been a lack of development in specific processing methodologies that deal with the distinct nature of translatome array data. In this study, we confirm that polysome profiling yields skewed data and thus violates the conventional transcriptome analysis assumptions. Using a comprehensive simulation of translatome array data varying the percentage and symmetry of deregulation, we show that conventional analysis methods (Quantile and LOESS normalizations) and statistical tests failed, respectively, to correctly normalize the data and to identify correctly deregulated genes (DEGs). We thus propose a novel analysis methodology available as a CRAN package; Internal Control Analysis of Translatome (INCATome) based on a normalization tied to a group of invariant controls. We confirm that INCATome outperforms the other normalization methods and allows a stringent identification of DEGs. More importantly, INCATome implementation on a biological translatome data set (cells silenced for splicing factor PSF) resulted in the best normalization performance and an improved validation concordance for identification of true positive DEGs. Finally, we provide evidence that INCATome is able to infer novel biological pathways with superior discovery potential, thus confirming the benefits for researchers of implementing INCATome for future translatome studies as well as for existing data sets to generate novel avenues for research.

Supports of invariant measures for piecewise deterministic Markov processes

For a class of piecewise deterministic Markov processes, the supports of the invariant measures are characterized. This is based on the analysis of controllability properties of an associated deterministic control system. Its invariant control sets determine the supports.