Yinyan Zhang

Modified ZNN for Time-Varying Quadratic Programming With Inherent Tolerance to Noises and Its Application to Kinematic Redundancy Resolution of Robot Manipulators

For quadratic programming (QP), it is usually assumed that the solving process is free of measurement noises or that the denoising has been conducted before the computation. However, time is precious for time-varying QP (TVQP) in practice. Preprocessing for denoising may consume extra time, and consequently violates real-time requirements. Therefore, a model with inherent noise tolerance is urgently needed to solve TVQP problems in real time. In this paper, we make progress along this direction by proposing a modified Zhang neural network (MZNN) model for the solution of TVQP. The original Zhang neural network model and the gradient neural network model are employed for comparisons with the MZNN model. In addition, theoretical analyses show that, without measurement noise, the proposed MZNN model globally converges to the exact real-time solution of the TVQP problem in an exponential manner and that, in the presence of measurement noises, the proposed MZNN model has a satisfactory performance. Finally, two illustrative simulation examples as well as a physical experiment are provided and analyzed to substantiate the efficacy and superiority of the proposed MZNN model for TVQP problem solving.

Noise-Tolerant ZNN Models for Solving Time-Varying Zero-Finding Problems: A Control-Theoretic Approach

This technical note proposes a noise-tolerant zeroing neural network (NTZNN) design formula, and shows how recurrent (and recursive) methods for solving time-varying problems can be designed from the viewpoint of control. The NTZNN design formula provides a control-theoretic framework to deal with the convergence, stability and robustness issues of continuous-time (and discrete-time) models. NTZNN models derived from the proposed design formula demonstrate their advantages when applied to solving time-varying zero-finding problems in the presence of noises.

Predictive Suboptimal Consensus of Multiagent Systems With Nonlinear Dynamics

In this paper, a unified framework is proposed for designing distributed control laws to achieve the consensus of linear and nonlinear multiagent systems. The consensus problem is formulated as a receding-horizon dynamic optimization problem with an integral-type performance index subject to the dynamics of the considered multiagent system. Different from conventional optimal control that solves Hamilton–Jacobian–Bellman equation numerically in high dimensions, we present a suboptimal solution with analytical expressions by utilizing Taylor expansion for prediction along time and give the corresponding distributed control law in an explicit form. Theoretical analysis shows that the proposed control laws can guarantee exponential and asymptotical stability of the multiagent systems. It is also proved that the proposed suboptimal control laws tend to be optimal with time. Illustrative examples are also presented to validate the efficacy of the proposed distributed control laws and the theoretical results.

Adaptive Near-Optimal Control of Uncertain Systems With Application to Underactuated Surface Vessels

In this paper, a unified online adaptive near-optimal control framework is proposed for linear and nonlinear systems with parameter uncertainty. Under this framework, auxiliary systems converging to the unknown dynamics are constructed to approximate and compensate the parameter uncertainty. With the aid of the auxiliary system, future outputs of the controlled system are predicted recursively. By utilizing a predictive time-scale approximation technique, the nonlinear dynamic programming problem for optimal control is significantly simplified and decoupled from the parameter learning dynamics: the finite-horizon integral-type objective function is simplified into a quadratic one relative to the control action and there is no need to solve time-consuming Hamilton equations. Theoretical analysis shows that closed-loop systems are asymptotically stable. It is also proved that the proposed adaptive near-optimal control law asymptotically converges to the optimal. The efficacy of the proposed framework and the theoretical results are validated by an application to underactuated surface vessels.

Time-Scale Expansion-Based Approximated Optimal Control for Underactuated Systems Using Projection Neural Networks

In this paper, a time-scale expansion-based scheme is proposed for approximately solving the optimal control problem of continuous-time underactuated nonlinear systems subject to input constraints and system dynamics. By time-scale Taylor approximation of the original performance index, the optimal control problem is relaxed into an approximated optimal control problem. Based on the system dynamics, the problem is further reformulated as a quadratic programming problem, which is solved by a projection neural network. Theoretical analysis on the closed-loop system synthesized by the controlled system and the projection neural network is conducted, which reveals that, under certain conditions, the closed-loop system possesses exponential stability and the original performance index converges to zero as time tends to infinity. In addition, two illustrative examples, which are based on a flexible joint manipulator and an underactuacted ship, are provided to validate the theoretical results and demonstrate the efficacy and superiority of the proposed control scheme.

GD-aided IOL (input–output linearisation) controller for handling affine-form nonlinear system with loose condition on relative degree

ABSTRACT Input–output linearisation (IOL) may encounter a singularity problem when applied to the tracking control of affine-form nonlinear system (AFNS), which may not have a well-defined relative degree. The singularity problem has occurred in the area of control for decades. In this paper, we incorporate the gradient dynamics (GD) into IOL, which leads to the GD-aided IOL method to solve the singularity problem, with the proposition of the loose condition on relative degree. Moreover, detailed theoretical analyses on tracking-error bound and convergence performance of the corresponding GD-aided IOL controller are presented. Simulations and comparisons substantiate that the proposed GD-aided IOL method is capable of completing the tracking-control task and conquering the singularity encountered in the AFNS.

From Davidenko Method to Zhang Dynamics for Nonlinear Equation Systems Solving

The solving of nonlinear equation systems (e.g., complex transcendental dispersion equation systems in waveguide systems) is a fundamental topic in science and engineering. Davidenko method has been used by electromagnetism researchers to solve time-invariant nonlinear equation systems (e.g., the aforementioned transcendental dispersion equation systems). Meanwhile, Zhang dynamics (ZD), which is a special class of neural dynamics, has been substantiated as an effective and accurate method for solving nonlinear equation systems, particularly time-varying nonlinear equation systems. In this paper, Davidenko method is compared with ZD in terms of efficiency and accuracy in solving time-invariant and time-varying nonlinear equation systems. Results reveal that ZD is a more competent approach than Davidenko method. Moreover, discrete-time ZD models, corresponding block diagrams, and circuit schematics are presented to facilitate the convenient implementation of ZD by researchers and engineers for solving time-invariant and time-varying nonlinear equation systems online. The theoretical analysis and results on Davidenko method, ZD, and discrete-time ZD models are also discussed in relation to solving time-varying nonlinear equation systems.

A dynamic neural controller for adaptive optimal control of permanent magnet DC motors

The speed control of permanent magnet brushed (PMB) DC motors at low speeds is difficult due to the nonlinearity caused by various types of frictions. Under parameter uncertainty, the speed control becomes more difficult. In this paper, to handle the parameter uncertainty, we propose a dynamic neural network to adaptively reconstruct or learn the dynamics of PMB DC motors. Then, based on the parameters of the neural dynamic model, a near-optimal dynamic neural controller is designed and proposed for the speed control of PMB DC motors with frictions considered under parameter uncertainty. Simulations substantiate the efficacy of the proposed dynamic neural model and adaptive near-optimal controller for PMB DC motors with fully unknown parameters.

Optimal parameter value of Zhang equivalence for MVN redundancy resolution at velocity and acceleration levels

The equivalent relationship of two general scheme formulations at joint velocity and joint acceleration levels is established in this paper for robotic redundancy resolution, i.e., the so-called Zhang equivalence (ZE). As one representative case, ZE of the minimum velocity norm (MVN) type (i.e., MVN-type ZE) is further investigated for redundancy resolution. Moreover, computer simulations together with illustrative numerical experiments based on the widely-used robot manipulator PUMA560 show the phenomenon that an optimal equivalence value of the equivalent parameter exists within effective range from two different perspectives of equivalence; and then reveal the optimal value of the equivalent parameter in two situations from such perspectives.