Distributed Asymptotic Consensus in Directed Networks of Nonaffine Systems With Nonvanishing Disturbance

In this paper the distributed asymptotic consensus problem is addressed for a group of high-order nonaffine agents with uncertain dynamics,nonvanishing disturbances and unknown control directions under directed networks.A class of auxiliary variables are first introduced which forms second-order filters and induces all measurable signals of agents’states.In view of this property,a distributed robust integral of the sign of the error(DRISE)design combined with the Nussbaum-type function is presented that guarantees not only the desired asymptotic consensus,but also the uniform boundedness of all closed-loop variables.Compared with the traditional sliding mode control(SMC)technique,the main feature of our approach is that the integral operation in the proposed control algorithm is designed to be adopted in a continuous manner and ensures less chattering behavior.Simulation results for a group of Duffing-Holmes chaotic systems are employed to verify our theoretical analysis.

Adaptive fuzzy controller for a class of strict-feedback nonaffine nonlinear systems

A robust adaptive fuzzy control scheme is presented for a class of strict-feedback nonaffine nonlinear systems with modeling uncertainties and external disturbances by using a backstepping approach.Fuzzy logic systems are employed to approximate the unknown parts of the desired virtual controls,and the approximation errors of fuzzy systems are only required to be norm-bounded.The function tanh（·） is introduced to avoid problems associated with sgn（·）.The tracking error is guaranteed to be uniformly ultimately bounded with the aid of an additional adaptive compensation term.Chua＇s circuit system and R o¨ssler system are presented to illustrate the feasibility and effectiveness of the proposed control technique.

Output regulation of nonaffine nonlinear systems using singular perturbation theory

A control synthesis method for output regulation based on singular perturbation theory combined with inverting design is considered for a class of nonaffine nonlinear systems. The resulting control signal is defined as a solution to ＂fast＂ dynamics which inverts a series error model, whose state is exponentially stable. It is shown that, under sufficient conditions being consistent with the assumptions of singular perturbation theory, this problem is solvable with （ε） tracking error if and only if a set of first-order nonlinear partial differential equations are solvable. The control law can be easily constructed and the simulations show the feasibility and effectiveness of the controller.

Nonaffine Network Structural Model for Molten Low-Density Polyethylene and High-Density Polyethylene in Oscillatory Shear

We propose molten polymer's entanglement network deformation to be nonaffine and use transient network structural theory with the revised Liu's kinetics rate equation and the revised upper convected Maxwell constitutive equation to establish a nonaffine network structural constitutive model for studying the rheological behavior of molten Low Density Polyethylene (LDPE) and High Density Polyethylene (HDPE) in oscillatory shear. As a result, when the strain amplitude or frequency increases, the shear stress amplitude increases. At the same time, the accuracy of the nonaffine network model is higher than that of affine network model. It is clear that there is a small amount of nonaffine network deformation for LDPE melts which have long chain branches, and there is a larger amount of nonaffine network deformation in oscillatory shear for HDPE melts which has no long chain branches. So we had better consider the network deformation nonaffine when we establish the constitutive equations of polymer melts in oscillatory shear.

Direct adaptive control for a class of MIMO nonlinear discrete-time systems

This paper considers the problem of adaptive con-trol for a class of multiple input multiple output （MIMO） nonlinear discrete-time systems based on input-output model with unknown interconnections between subsystems. Based on the Taylor ex-pand technology, an equivalent model in affine-like form is derived for the original nonaffine nonlinear system. Then a direct adap-tive neural network （NN） control er is implemented based on the affine-like model. By finding an orthogonal matrix to tune the NN weights, the closed-loop system is proven to be semiglobal y uni-formly ultimately bounded. The σ-modification technique is used to remove the requirement of persistence excitation during the adaptation. The control performance of the closed-loop system is guaranteed by suitably choosing the design parameters.

On PID Control Theory for Nonaffine Uncertain Stochastic Systems

PID(proportional-integral-derivative)control is recognized to be the most widely and successfully employed control strategy by far.However,there are limited theoretical investigations explaining the rationale why PID can work so well when dealing with nonlinear uncertain systems.This paper continues the previous researches towards establishing a theoretical foundation of PID control,by studying the regulation problem of PID control for nonaffine uncertain nonlinear stochastic systems.To be specific,a three dimensional parameter set will be constructed explicitly based on some prior knowledge on bounds of partial derivatives of both the drift and diffusion terms.It will be shown that the closed-loop control system will achieve exponential stability in the mean square sense under PID control,whenever the controller parameters are chosen from the constructed parameter set.Moreover,similar results can also be obtained for PD(PI)control in some special cases.A numerical example will be provided to illustrate the theoretical results.

Advanced Policy Learning Near-Optimal Regulation

Designing advanced design techniques for feedback stabilization and optimization of complex systems is important to the modern control field. In this paper, a near-optimal regulation method for general nonaffine dynamics is developed with the help of policy learning. For addressing the nonaffine nonlinearity, a pre-compensator is constructed, so that the augmented system can be formulated as affine-like form. Different cost functions are defined for original and transformed controlled plants and then their relationship is analyzed in detail. Additionally, an adaptive critic algorithm involving stability guarantee is employed to solve the augmented optimal control problem. At last, several case studies are conducted for verifying the stability, robustness, and optimality of a torsional pendulum plant with suitable cost.

A neuro-observer-based optimal control for nonaffine nonlinear systems with control input saturations

In this study,an adaptive neuro-observer-based optimal control(ANOPC)policy is introduced for unknown nonaffine nonlinear systems with control input constraints.Hamilton–Jacobi–Bellman(HJB)framework is employed to minimize a non-quadratic cost function corresponding to the constrained control input.ANOPC consists of both analytical and algebraic parts.In the analytical part,first,an observer-based neural network(NN)approximates uncertain system dynamics,and then another NN structure solves the HJB equation.In the algebraic part,the optimal control input that does not exceed the saturation bounds is generated.The weights of two NNs associated with observer and controller are simultaneously updated in an online manner.The ultimately uniformly boundedness(UUB)of all signals of the whole closed-loop system is ensured through Lyapunov’s direct method.Finally,two numerical examples are provided to confirm the effectiveness of the proposed control strategy.

Adaptive NN Dynamic Surface Control for a Class of Uncertain Non-affine Pure-feedback Systems with Unknown Time-delay

Adaptive neural network （NN） dynamic surface control （DSC） is developed for a class of non-affine pure-feedback systems with unknown time-delay. The problems of ＂explosion of complexity＂ and circular construction of the practical controller in the traditional backstepping algorithm are avoided by using this controller design method. For removing the requirements on the sign of the derivative of function f~, Nussbaum control gain technique is used in control design procedure. The effects of unknown time-delays are eliminated by using appropriate Lyapunov-Krasovskii functionals. Proposed control scheme guarantees that all the signals in the closed-loop system are semi-globally uniformly ultimately bounded. Two simulation examples are presented to demonstrate the method.