In the previous work, Zhang et al. developed a special type of recurrent neural networks called network (ZNN) with continuous-time and discrete-time forms for time-varying matrix inversion. this paper, novel ZNN (DTZNN) model inversion is proposed investigated. Specifically, new numerical difference rule based on Taylor series expansion established in paper first-order derivative approximation. Then, by exploiting Taylor-type rule, DTZNN model, which five-step iteration algorithm, thus...

A typical recurrent neural network called zeroing (ZNN) was developed for time-varying problem-solving in a previous study. Many applications result linear equation and inequality systems that should be solved real time. This paper provides ZNN model determining the solution of systems. By introducing nonnegative slack variable, are transformed into mixed nonlinear system. The is established via definition an indefinite error function usage exponential decay formula. Theoretical results...

Recently, a new formula with noise-tolerant capability has been designed by Zhang et al., and the resultant dynamics (ZD) models have developed to solve different types of time-varying problems. Based on previous research, this paper presents investigates application such ZD design kinematic control redundant robot manipulators via nonlinear equations solving. Specifically, exploiting system involved in control, redundancy-resolution scheme is established. Such contains proportional,...

This paper proposes a design method for robust fractional-order PID (FOPID) controller time-delay systems. A new Bode's ideal transfer function is introduced to tolerance the in loop. Robust stability analyzed model terms of gain and phase margins help parameter tuning. To simplify FOPID from solving nonlinear equations, five unknown parameters are reduced one Bode shaping by data fitting between parametric real plant. Then, problem simply solved one-dimensional searching. Furthermore,...

Recently, the approach based on recurrent neural network (RNN) has been considered a powerful alternative to mathematical problem solving. In this study, new discrete-time RNN (DTRNN) is proposed and investigated determine an exact solution of dynamic nonlinear equations. Specifically, resultant DTRNN model established for solving equations by utilizing Taylor-type difference rule. This then theoretically proven have O(τ <sup xmlns:mml="http://www.w3.org/1998/Math/MathML"...

Recurrent neural network (RNN) has recently been viewed as a significant alternative to online mathematical problem solving. This paper offers important improvements by proposing the first RNN model solve time-dependent underdetermined linear system with bound constraint. In particular, introducing nonnegative vector, bound-constrained is initially transformed into that comprises and nonlinear equations. The newly constructed can thus zero in on Then, theoretically proven have convergence...

Abstract The landmark Ziegler–Nichols (ZN) tuning method from 1942 for proportional‐integral‐derivative (PID) controller has had significant impacts on the industrial control industry to this day, even though it is thought be an empirical with little theoretical justifications. situation not changed much despite fact that a large amount of research and applications been reported over decades. This paper shows first time ZN can incorporated into framework active disturbance rejection (ADR),...

Continuous-time and discrete-time forms of Zhang dynamics (ZD) for time-varying nonlinear optimization have been developed recently. In this paper, a novel ZD (DTZD) algorithm is proposed investigated based on the previous research. Specifically, DTZD by adopting new Taylor-type difference rule. This five-step iteration process, thus, referred to as in paper. Theoretical analysis results are presented highlight its excellent computational performance. The geometric representation also...

In this paper, a new model identification method is developed for class of delay fractional-order system based on the process step response. Four characteristic functions are defined to characterize features normalized model. Based time scaling technology, two schemes proposed parameters U+02BC estimation. The scheme one utilizes three exact points response calculate directly. other employs optimal searching adjust fractional order best identification. both applicable any stable complex...

Guaranteed-cost active disturbance rejection control (ADRC) for uncertain systems is investigated in this study. Firstly, an integral action introduced the framework of ADRC to measure and reduce tracking error. Then, a robust stability condition presented, quadratic cost function where error appearing explicitly used performance assessment. The bound formulated by linear matrix inequality optimised obtain controller parameters. Full-dimension extended state observer used, thus, proposed...

Avoiding obstacle(s) is a challenging issue in the research of redundant robot manipulators. In addition, noise from truncation, rounding, and model uncertainty an important factor that affects greatly obstacle avoidance scheme. this paper, based on neural dynamics design formula, new scheme with pseudoinverse-type formulation proposed for manipulators noisy environment. Such has capability suppressing constant bounded time-varying noises, it thus termed as noise-tolerant (NTOA) paper....

In this paper, the application of recurrent neural network (RNN) activated by Li function to acceleration-level robots' kinematic control via time-varying matrix inversion is presented and investigated. Specifically, exploiting activation computing inverse related nonsingular matrix, resultant RNN model applied redundant robot manipulators at joint-acceleration level. Note that such a Li-function (LFARNN) can achieve purpose finite-time convergence, thus feasible manipulators. Simulation...

Summary The active disturbance rejection control (ADRC) scheme requires a high bandwidth in the extended state observer (ESO), causing heavy noise pollution system. This article develops an effective and simple adaptive ADRC to realize performance when ESO is limited. adaptative law generated by tracking error such that all feedback loops feedforward channels are activated for rejection. An “attached” “quantified” adaptation developed guarantee easy usage of proposed scheme. uniformly...

This paper considers a lead/lag compensator design problem for class of unstable delay processes based on new set gain and phase margin specifications. Due to the nature system, both upper lower margins are required measure true stability robustness with regard change. In addition margin, such combined leads nonlinear coupled equations which have no analytical solution. Thus, an effective graphical method is developed that solution determined from intersections curves constructed by...

Abstract A generalized disturbance observer‐based (GDOB) control system and its robust stability are studied in this paper. One feature of new GDOB scheme is that an inverse the nominal plant standard DOB no longer required. Thus, it applicable to both minimum‐phase (MP) non‐minimum‐phase (NMP) plants. New conditions for derived two cases: plants with right half plane (RHP) zero RHP pole, which a perfect dual form. The duality reveals zeros met when Q ‐filter has sufficiently large constant....