Construction of Control Lyapunov Functions for a Class of Nonlinear Systems

The construction of control Lyapunov functions for a class of nonlinear systems is considered. We develop a method by which a control Lyapunov function for the feedback linearizable part can be constructed systematically via Lyapunov equation. Moreover, by a control Lyapunov function of the feedback linearizable part and a Lyapunov function of the zero dynamics, a control Lyapunov function for the overall nonlinear system is established.

Universal construction of control Lyapunov functions for a class of nonlinear systems

A method is developed by which control Lyapunov functions of a class of nonlinear systems can be constructed systematically. Based on the control Lyapunov function, a feedback control is obtained to stabilize the closed-loop system. In addition, this method is applied to stabilize the Benchmark system. A simulation shows the effectiveness of the method.

Stabilization of discrete nonlinear systems based on control Lyapunov functions

The stabilization of discrete nonlinear systems is studied. Based on control Lyapunov functions, a sufficient and necessary condition for a quadratic function to be a control Lyapunov function is given. From this condition, a continuous state feedback law is constructed explicitly. It can globally asymptotically stabilize the equilibrium of the closed-loop system. A simulation example shows the effectiveness of the proposed method.

Predictive Functional Controller with a Similar Proportional Integral Optimal Regulator Structure:Comparison with Traditional Predic-tive Functional Controller and Application to Heavy Oil Coking Equipment

By extending the system's state variables,a novel predictive functional controller has been developed.The structure of this controller is similar to that of classical proportional integral(PI)optimal controller and in-cludes a control block that can perform a feed-forward control of future P-step set points.It considers both the state variables and the output errors in its cost function,which results in enhanced control performance compared with traditional state space predictive functional control(TSSPFC)methods that consider only the predictive output er-rors.The predictive functional controller(PFC)has been compared with TSSPFC in terms of tracking ability,dis-turbance rejection,and also based on its application to heavy oil coking equipment.The results obtained show the effectiveness of the controller.

A Survey on the Control Lyapunov Function and Control Barrier Function for Nonlinear-Affine Control Systems

This survey provides a brief overview on the control Lyapunov function(CLF)and control barrier function(CBF)for general nonlinear-affine control systems.The problem of control is formulated as an optimization problem where the optimal control policy is derived by solving a constrained quadratic programming(QP)problem.The CLF and CBF respectively characterize the stability objective and the safety objective for the nonlinear control systems.These objectives imply important properties including controllability,convergence,and robustness of control problems.Under this framework,optimal control corresponds to the minimal solution to a constrained QP problem.When uncertainties are explicitly considered,the setting of the CLF and CBF is proposed to study the input-to-state stability and input-to-state safety and to analyze the effect of disturbances.The recent theoretic progress and novel applications of CLF and CBF are systematically reviewed and discussed in this paper.Finally,we provide research directions that are significant for the advance of knowledge in this area.

Constrained Moving Path Following Control for UAV With Robust Control Barrier Function

This paper studies the moving path following(MPF)problem for fixed-wing unmanned aerial vehicle(UAV)under output constraints and wind disturbances.The vehicle is required to converge to a reference path moving with respect to the inertial frame,while the path following error is not expected to violate the predefined boundaries.Differently from existing moving path following guidance laws,the proposed method removes complex geometric transformation by formulating the moving path following problem into a second-order time-varying control problem.A nominal moving path following guidance law is designed with disturbances and their derivatives estimated by high-order disturbance observers.To guarantee that the path following error will not exceed the prescribed bounds,a robust control barrier function is developed and incorporated into controller design with quadratic program based framework.The proposed method does not require the initial position of the UAV to be within predefined boundaries.And the safety margin concept makes error-constraint be respected even if in a noisy environment.The proposed guidance law is validated through numerical simulations of shipboard landing and hardware-in-theloop(HIL)experiments.

洋流干扰下无人船限制水域直线跟踪安全视距制导

The collision-free straight-line following of an unmanned surface vehicle(USV)moving in a constrained water region subject to stationary and moving obstacles is addressed in this paper.USV systems are normally subjected to surge velocity constraints,yaw rate constraints,and unknown ocean currents.Herein,a safety-certificated line-of-sight(LOS)guidance method is proposed to achieve a constrained straight-line following task.First,an antidisturbance LOS guidance law is designed based on the LOS guidance scheme and an extended state observer.Furthermore,collision avoidance with waterway boundaries and stationary/moving obstacles is encoded in control barrier functions,utilizing which the safety constraints are transformed into input constraints.Finally,safety-certificated guidance signals are obtained by solving a quadratic programming problem subject to input constraints.Using the proposed safety-certified LOS guidance method,the USV can accomplish a straight-line following task with guaranteed input-to-state safety.Simulation results substantiate the efficacy of the proposed safety-certificated LOS guidance method for the straight-line following of USVs moving in a constrained water region subject to unknown ocean currents.

Time-stamped predictive functional control for networked control systems with random delays

The random delays in a networked control system (NCS) degrade control performance and can even destabilize the control system.To deal with this problem,the time-stamped predictive functional control (PFC) algorithm is proposed,which generalizes the standard PFC algorithm to networked control systems with random delays.The algorithm uses the time-stamp method to estimate the control delay,predicts the future outputs based on a discrete time delay state space model,and drives the control law that applies to an NCS from the idea of a PFC algorithm.A networked control system was constructed based on TrueTime simulator,with which the time-stamped PFC algorithm was compared with the standard PFC algorithm.The response curves show that the proposed algorithm has better control performance.

Predictive functional control based on fuzzy T-S model for HVAC systems temperature control

In heating, ventilating and air-conditioning （HVAC） systems, there exist severe nonlinearity, time-varying nature, disturbances and uncertainties. A new predictive functional control based on Takagi-Sugeno （T-S） fuzzy model was proposed to control HVAC systems. The T-S fuzzy model of stabilized controlled process was obtained using the least squares method, then on the basis of global linear predictive model from T-S fuzzy model, the process was controlled by the predictive functional controller. Especially the feedback regulation part was developed to compensate uncertainties of fuzzy predictive model. Finally simulation test results in HVAC systems control applications showed that the proposed fuzzy model predictive functional control improves tracking effect and robustness. Compared with the conventional PID controller, this control strategy has the advantages of less overshoot and shorter setting time, etc.

On Generality of the Data Plane and Scalability of the Control Plane in Software-Defined Networking

The control and data planes are decoupled in software-defined networking(SDN),which enables both planes to evolve independently,and brings about many advantages such as high flexibility,programmability,and rapid implementation of new network protocols.However,in order to improve the scalability of the control plane at present,some control functionalities are added to the data plane,which is probably to impact on the generality of the data plane.The key challenge of adding control functionalities to the data plane is to strike a careful balance between the generality of the data plane and the scalability of the control plane.We propose some basic principles that both control and data planes should comply with,based on the evolutionary trend of SDN.Moreover,we take two approaches for reference according to the principles,viewed from the control messages in OpenFlow-based SDN.Our evaluations demonstrate that the approaches can maintain the generality of the data plane and improve the scalability of the control plane.

Adaptive predictive functional control based on Takagi-Sugeno model and its application to pH process

In order to obtain accurate prediction model and compensate for the influence of model mismatch on the control performance of the system and avoid solving nonlinear programming problem,an adaptive fuzzy predictive functional control(AFPFC) scheme for multivariable nonlinear systems was proposed.Firstly,multivariable nonlinear systems were described based on Takagi-Sugeno(T-S) fuzzy models;assuming that the antecedent parameters of T-S models were kept,the consequent parameters were identified on-line by using the weighted recursive least square(WRLS) method.Secondly,the identified T-S models were linearized to be time-varying state space model at each sampling instant.Finally,by using linear predictive control technique the analysis solution of the optimal control law of AFPFC was established.The application results for pH neutralization process show that the absolute error between the identified T-S model output and the process output is smaller than 0.015;the tracking ability of the proposed AFPFC is superior to that of non-AFPFC(NAFPFC) for pH process without disturbances,the overshoot of the effluent pH value of AFPFC with disturbances is decreased by 50% compared with that of NAFPFC;when the process parameters of AFPFC vary with time the integrated absolute error(IAE) performance index still retains to be less than 200 compared with that of NAFPFC.

Barrier-Certified Learning-Enabled Safe Control Design for Systems Operating in Uncertain Environments

This paper presents learning-enabled barriercertified safe controllers for systems that operate in a shared environment for which multiple systems with uncertain dynamics and behaviors interact.That is,safety constraints are imposed by not only the ego system’s own physical limitations but also other systems operating nearby.Since the model of the external agent is required to impose control barrier functions(CBFs)as safety constraints,a safety-aware loss function is defined and minimized to learn the uncertain and unknown behavior of external agents.More specifically,the loss function is defined based on barrier function error,instead of the system model error,and is minimized for both current samples as well as past samples stored in the memory to assure a fast and generalizable learning algorithm for approximating the safe set.The proposed model learning and CBF are then integrated together to form a learning-enabled zeroing CBF(L-ZCBF),which employs the approximated trajectory information of the external agents provided by the learned model but shrinks the safety boundary in case of an imminent safety violation using instantaneous sensory observations.It is shown that the proposed L-ZCBF assures the safety guarantees during learning and even in the face of inaccurate or simplified approximation of external agents,which is crucial in safety-critical applications in highly interactive environments.The efficacy of the proposed method is examined in a simulation of safe maneuver control of a vehicle in an urban area.

Incremental multivariable predictive functional control and its application in a gas fractionation unit

The control of gas fractionation unit(GFU) in petroleum industry is very difficult due to multivariable characteristics and a large time delay.PID controllers are still applied in most industry processes.However,the traditional PID control has been proven not sufficient and capable for this particular petro-chemical process.In this work,an incremental multivariable predictive functional control(IMPFC) algorithm was proposed with less online computation,great precision and fast response.An incremental transfer function matrix model was set up through the step-response data,and predictive outputs were deduced with the theory of single-value optimization.The results show that the method can optimize the incremental control variable and reject the constraint of the incremental control variable with the positional predictive functional control algorithm,and thereby making the control variable smoother.The predictive output error and future set-point were approximated by a polynomial,which can overcome the problem under the model mismatch and make the predictive outputs track the reference trajectory.Then,the design of incremental multivariable predictive functional control was studied.Simulation and application results show that the proposed control strategy is effective and feasible to improve control performance and robustness of process.

Predictive functional control of integrating process based on impulse response

The predictive model is built according to the characteristics of the impulse response of integrating process. In order to eliminate the permanent offset between the setpoint and the process output in the presence of the load disturbance, a novel error compensation method is proposed. Then predictive functional control of integrating process is designed. The method given generates a simple control structure, which can significandy reduce online computation. Furthermore, the tuning of the controller is fairly straightforward. Simulation results indicate that the designed control system is relatively robust to the parameters variation of the process.

Active disturbance rejected predictive functional control for space vehicles with RCS

Reaction control system(RCS) is a powerful and efficient actuator for space vehicles attitude control, which is typically characterized as a pulsed unilateral effector only with two states(off/on). Along with inevitable internal uncertainties and external disturbances in practice, this inherent nonlinear character always hinders space vehicles autopilot from pursuing precise tracking performance. Compared to most of pre-existing methodologies that passively suppress the uncertainties and disturbances, a design based on predictive functional control(PFC) and generalized extended state observer(GESO) is firstly proposed for three-axis RCS control system to actively reject that with no requirement for additional fuel consumption. To obtain a high fidelity predictive model on which the performance of PFC greatly depends, the nonlinear coupling multiple-input multiple-output(MIMO) flight dynamics model is parameterized as a state-dependent coefficient form. And based on that, a MIMO PFC algorithm in state space domain for a plant of arbitrary orders is deduced in this paper.The internal uncertainties and external disturbances are lumped as a total disturbance, which is estimated and cancelled timely to further enhance the robustness. The continuous control command synthesised by above controller-rejector tandem is finally modulated by pulse width pulse frequency modulator(PWPF) to on-off signals to meet RCS requirement. The robustness and feasibility of the proposed design are validated by a series of performance comparison simulations with some prominent methods in the presence of significant perturbations and disturbances, as well as measurement noise.

Itopride therapy for functional dyspepsia:A meta-analysis

AIM:To evaluate the therapeutic effects of itopride vs other drugs(placebo,domperidone,mosapride) for functional dyspepsia(FD).METHODS:Randomized controlled trials(RCTs) of itopride for FD were retrieved from databases.Relevant information was extracted and analyzed,using the relative risk(RR) and weighted mean deviation,as appropriate.A random or fixed effect model was used,based on the heterogeneity of the included articles,and visual inspection of funnel plots was used to evaluate publication bias.RESULTS:Nine RCTs enrolling 2620 FD cases were included;1372 cases received itopride treatment and 1248 cases received placebo or other drugs(control groups).Compared with control groups,itopride had superior RR values of 1.11 [95%CI:(1.03,1.19),P = 0.006],1.21 [95%CI:(1.03,1.44),P = 0.02],and1.24 [95%CI:(1.01,1.53),P = 0.04] for global patient assessment,postprandial fullness,and early satiety,respectively.For the Leeds Dyspepsia Questionnaire score,the weighted mean deviation was-1.38 [95%CI:(-1.75,-1.01),P < 0.01].The incidence of adverse effects was similar in the itopride and control groups.The funnel plots for all indicators showed no evidence of publication bias.CONCLUSION:Itopride has good efficacy in terms of global patients assessment,postprandial fullness,and early satiety in the treatment of patients with FD and shows a low rate of adverse reactions.Itopride can greatly improve FD syndromes-score.

V-BILIPSCHITZ DETERMINACY OF WEIGHTED HOMOGENEOUS ANALYTIC FUNCTION-GERMS ON WEIGHTED HOMOGENEOUS REAL ANALYTIC VARIETIES

In this article, we provide estimates for the degree of V bilipschitz determinacy of weighted homogeneous function germs defined on weighted homogeneous analytic variety V satisfying a convenient Lojasiewicz condition.The result gives an explicit order such that the geometrical structure of a weighted homogeneous polynomial function germs is preserved after higher order perturbations.

Adaptive stabilization for cascade nonlinear systems

An adaptive controller of full state feedback for certain cascade nonlinear systems achieving input-to-state stability with respect to unknown bounded disturbance is designed using backstepping and control Lyapunov function (CLF) techniques. We show that unknown bounded disturbance can be estimated by update laws, which requires less information on unknown disturbance, as a part of stabilizing control. The design method achieves the desired property: global robust stability. Our contribution is illustrated with the example of a disturbed pendulum.

Direct adaptive control for nonlinear uncertain system based on control Lyapunov function method

The problem of adaptive stabilization of a class of multi-input nonlinear systems with unknown parameters both in the state vector-field and the input vector-field has been considered. By employing the control Lyapunov function method, a direct adaptive controller is designed to complete the global adaptive stability of the uncertain system. At the same time, the controller is also verified to possess the optimality. Example and simulations are provided to illustrate the effectiveness of the proposed method.

CONTROLLED ANIONIC SYNTHESIS OF FUNCTIONALIZED AND STAR-BRANCHED POLYMERS

The use of living, alkyllithium-initiated anionic polymerization to prepare chain-end functionalized polymers and heteroarm, star-branched polymers is discussed. The scope and limitations of specific termination reactions with a variety of electrophilic species are illustrated for carbonation, hydroxyethylation, amination, and sulfonation. The methodology of using substituted 1,1-diphenylethylenes to provide a general, quantitative functionalization procedure is outlined and illustrated with examples of amine and phenol end-functionalization. A methodology is described for the synthesis of functionalized, star-branched copolymers with compositionally heterogeneous arms of controlled molecular weight and narrow molecular weight distribution using 1, 3-bis(1-pbenylethenyl) benzene.