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.

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.

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.

Adaptive Sliding Mode Control for Re-entry Attitude of Near Space Hypersonic Vehicle Based on Backstepping Design

Combining sliding mode control method with radial basis function neural network(RBFNN), this paper proposes a robust adaptive control scheme based on backstepping design for re-entry attitude tracking control of near space hypersonic vehicle(NSHV) in the presence of parameter variations and external disturbances. In the attitude angle loop, a robust adaptive virtual control law is designed by using the adaptive method to estimate the unknown upper bound of the compound uncertainties. In the angular velocity loop, an adaptive sliding mode control law is designed to suppress the effect of parameter variations and external disturbances. The main benefit of the sliding mode control is robustness to parameter variations and external disturbances. To further improve the control performance, RBFNNs are introduced to approximate the compound uncertainties in the attitude angle loop and angular velocity loop, respectively. Based on Lyapunov stability theory, the tracking errors are shown to be asymptotically stable. Simulation results show that the proposed control system attains a satisfied control performance and is robust against parameter variations and external disturbances.

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.

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.

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.

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.

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.

Shape control on probability density function in stochastic systems

A novel strategy of probability density function （PDF） shape control is proposed in stochastic systems. The control er is designed whose parameters are optimal y obtained through the improved particle swarm optimization algorithm. The parameters of the control er are viewed as the space position of a particle in particle swarm optimization algorithm and updated continual y until the control er makes the PDF of the state variable as close as possible to the expected PDF. The proposed PDF shape control technique is compared with the equivalent linearization technique through simulation experiments. The results show the superiority and the effectiveness of the proposed method. The control er is excellent in making the state PDF fol ow the expected PDF and has the very smal error between the state PDF and the expected PDF, solving the control problem of the PDF shape in stochastic systems effectively.

Asymptotic controllability of a class of discrete-time systems with disturbances

This article deals with the uniformly globally asymptotic controllability of discrete nonlinear systems with disturbances.It is shown that the system is uniformly globally asymptotic controllability with respect to a closed set if and only if there exists a smooth control Lyapunov function.Further, it is obtained that the control Lyapunov function may be used to construct a feedback law to stabilize the closed-loop system.In addition, it is proved that for periodic discrete systems, the resulted control Lyapunov functions are also time periodic.

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.

Improved forwarding control design method and its application

Integrator forwarding is a recursive nonlinear design technique for the stabilization of feed-forward systems. However, this method still has some limitation. An improved design method is proposed to extend the field of application of this technique. This method is used to design a stabilizer for the inertia wheel pendulum system. Moreover, it is shown that the control Lyapunov function which is obtained from this method can also be used to design a globally asymptotically stabilizing controller with optimality.

GENERALIZED TRANSFER FUNCTION OF CONTROL SYSTEM AND AN IMPROVEMENT ON THE DECISION METHOD OF MOVEMENT STABILITY

In this paper the definitions of generalized transfer functios of control system and itscontinuity are presented.Using generalized transfer function as a tool,a set of theorems fordeciding movement stability have been constructed.Thus basing understanding of thecharacteristics of a control dynamics system on its measured procedure will simplify thedecision method of movement stability problems.

The Control of Population Growth Is the Function of the Central Government

Mr.Jiang Zcmin,Gencral-Seerctary of the Cen-tral Committee of the Chincse Communist Party and.Chairman of the People's Republic of China,in a rC-ccnt spcech cm phasized that the family planning pro-gramme should be strictly and effectively im plemented in 1994,a year of crucial importance for promoting re-form and opening and thc drive lowards.modernization.To makc continucd contributions to the sociocconomic development in the country,we must fulfil the plan for controlling population growth..The spcech was delivcred at the anua!National Fo-rum on Family Planning Work convened jointly by the Party's Central Committcc and the Statc Council.

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.

CBF-Based Distributed Model Predictive Control for Safe Formation of Autonomous Mobile Robots

A distributed model predictive control(DMPC)method based on robust control barrier function(RCBF)is developed to achieve the safe formation target of multi-autonomous mobile robot systems in an uncertain disturbed environment.The first step is to analyze the safety requirements of the system during safe formation and categorize them into collision avoidance and distance connectivity maintenance.RCBF constraints are designed based on collision avoidance and connectivity maintenance requirements,and security constraints are achieved through a combination.Then,the specified safety constraints are integrated with the objective of forming a multi-autonomous mobile robot formation.To ensure safe control,the optimization problem is integrated with the DMPC method.Finally,the RCBF-DMPC algorithm is proposed to ensure iterative feasibility and stability while meeting the constraints and expected objectives.Simulation experiments illustrate that the designed algorithm can achieve cooperative formation and ensure system security.