Bi‐criteria optimal control of redundant robot manipulators using LVI‐based primal‐dual neural network

In this paper, a bi‐criteria weighting scheme is proposed for the optimal motion control of redundant robot manipulators. To diminish the discontinuity phenomenon of pure infinity‐norm velocity minimization (INVM) scheme, the proposed bi‐criteria redundancy‐resolution scheme combines the minimum kinetic energy scheme and the INVM scheme via a weighting factor. Joint physical limits such as joint limits and joint‐velocity limits could also be incorporated simultaneously into the scheme formulation. The optimal kinematic control scheme can be reformulated finally as a quadratic programming (QP) problem. As the real‐time QP solver, a primal‐dual neural network (PDNN) based on linear variational inequalities (LVI) is developed as well with a simple piecewise‐linear structure and global exponential convergence to optimal solutions. Since the LVI‐based PDNN is matrix‐inversion free, it has higher computational efficiency in comparison with dual neural networks. Computer simulations performed based on the PUMA560 manipulator illustrate the validity and advantages of such a bi‐criteria neural optimal motion‐control scheme for redundant robots. Copyright © 2009 John Wiley & Sons, Ltd.     

MPC‐based tracking for real‐time systems subject to time‐varying polytopic constraints

This paper presents a real‐time MPC‐based tracking strategy for linear systems subject to time‐varying constraints. The framework is quite general because the time‐varying constraints can apply both to the state and to the input. To handle the problem, a polytopic invariant set computed off‐line is homogeneously dilated or contracted on‐line to fit the polytopic time‐varying constraints. The invariant set is used as an admissible terminal constraint set so that it guarantees stability and convergence in the tracking task. The on‐line cost of the homothetic invariant set computation is low enough to cope with systems subject to stringent real‐time constraints. Copyright © 2015 John Wiley & Sons, Ltd.     

Delay‐dependent robust passive control for a class of nonlinear systems with time‐varying delays

In this paper, the problem of robust passive control for a class of nonlinear systems with time‐varying delays is considered. The uncertainties investigated in this paper are norm bounded and time varying, and they enter all system matrices. Based on the Lyapunov–Krasovskii functionals approach, a new robust passive control criterion is proposed in terms of linear matrix inequalities, which is dependent on the size of time delay. We also design a state feedback controller that guarantees a robust asymptotically stable and strictly passive closed‐loop system for all admissible uncertainties. Finally, two numerical examples are given to illustrate the effectiveness of the developed techniques. Copyright © 2007 John Wiley & Sons, Ltd.     

Constrained linear parameter‐varying control using approximate multiparametric programming

We develop an approximate multiparametric convex programming approach with its application to control constrained linear parameter‐varying systems. Recently, the application of the real‐time model predictive control (MPC) for various engineering systems has been significantly increased by using the multiparametric convex programming tool, known as explicit MPC approach. The main idea of explicit MPC is to move the major parts of the computations to offline phase and to provide an explicit piecewise affine solution of the constrained MPC problem, which is defined over a set of convex polyhedral partitions. In the proposed method, the idea of convex programming and partitioning is applied for linear parameter‐varying control systems. The feasible space of the time‐varying parameters is divided into simplices in which approximate solutions are calculated such that the approximation error is kept limited by solving sequences of linear programs. The approximate optimal solution within each simplex is obtained by linear interpolation of the optimal solutions in the simplex vertices, and then multiparametric programming tool is utilized to compute an explicit state feedback solution of linear quadratic optimal control problem for simplex vertices subject to state and input constraints. The proposed method is illustrated by a numerical example and the simulation results show the advantages of this approach.     

Stabilization of positive coupled differential‐difference equations with unbounded time‐varying delays

This paper researches the static output‐feedback stabilization of single‐input single‐output (SISO) positive coupled differential‐difference equations (CDDEs) with unbounded time‐varying delays. First, a necessary and sufficient condition is provided for the positivity and asymptotical stability of CDDEs with unbounded time‐varying delays. For this type of system, based on the constructed estimates of its solution, a necessary and sufficient condition on asymptotical stability is provided. Then, based on this criterion, for CDDEs with unbounded time‐varying delays, a kind of static output‐feedback controller is designed to ensure the positivity and asymptotical stability of the corresponding closed‐loop systems. It is also worth pointing out that the controller is designed by the linear programming method without parameterization technique. This design approach can also be applied to the static state feedback stabilization problem of CDDEs with unbounded time‐varying delays. Finally, two illustrative examples are given to show the effectiveness of our results.     

Reachable set estimation for neutral Markovian jump systems with mode‐dependent time‐varying delays

This study, under zero initial condition, aims to characterize the reachable set bound for a class of neutral Markovian jump systems (NMJSs) with interval time‐varying delays and bounded disturbances. To begin with, the time‐delays are considered to be mode‐dependent while delay mode and system mode are different. By utilizing free‐weighting matrix method and reciprocally convex combination technique, an ellipsoid‐like bound is characterized for the concerned NMJS with completely known transition probabilities. Based on the provided analytical framework, the case of same delay mode and system mode is also handled. Then, benefitting from a group of free‐connection weighting matrices, the reachable set estimation issue is tackled for the NMJS involving mode‐independent time‐varying delays and partially known transition probabilities. The theoretical analysis is confirmed by numerical simulations.     

A suboptimal learning control scheme for non‐linear systems with time‐varying parametric uncertainties

In this paper, learning control is integrated with non‐linear optimal control to enhance control performance of a class of non‐linear systems with time‐varying parametric uncertainties. A suboptimal control strategy based on a control Lyapunov function (CLF) and Sontag's formula provides suboptimal performance as well as stability along the time horizon for the nominal part of the non‐linear dynamic system. The proposed learning mechanism learns the unknown time‐varying parametric uncertainties so as to eliminate uncertain effects. System information both in time horizon and learning repetition horizon are incorporated in a composite energy function (CEF). The proposed control scheme achieves asymptotic convergence along the learning repetition horizon and boundedness and pointwise convergence of the tracking error (perfect tracking performance) along the time horizon. Copyright © 2001 John Wiley & Sons, Ltd.     

Stochastic faulty actuator‐based reliable control for a class of interval time‐varying delay systems with Markovian jumping parameters

The paper addresses the problem of a reliable control for interval time‐varying delay system with Markovian jumping parameters. A new practical actuator fault model, by assuming that the actuator fault obeys a certain probabilistic distribution, is considered. Delay‐dependent conditions for the solvability of these problems are obtained via new parameter‐dependent Lyapunov function. The closed‐loop systems are stochastically stable not only when all actuators are operational, but also in case of some actuator failures. Numerical examples are given to illustrate the effectiveness of the proposed design method. Copyright © 2010 John Wiley & Sons, Ltd.     

Robust H∞ performance analysis for uncertain discrete‐time singular systems with time‐varying delays

This paper considers the problem of robust H∞ performance analysis for uncertain discrete‐time singular systems with time‐varying delays. Firstly, a delay‐dependent stability criterion under the H∞ performance index for the systems is given based on constructing a generalized Lyapunov–Krasovskii function and introducing a new difference inequality. Then, a sufficient condition ensuing the system to be regular, causal as well as stable for all admissible uncertainties is proposed in terms of a set of strict linear matrix inequalities (LMIs). Finally, we provide examples to show the reduced conservatism and effectiveness of the proposed conditions. Copyright © 2014 John Wiley & Sons, Ltd.     

Stability criteria for continuous‐time systems with additive time‐varying delays

This paper studies the problem of stability analysis for continuous‐time systems with two additive time‐varying delay components. By taking the independence and the variation of the additive delay components into consideration, more general type of Lyapunov functionals are defined. Together with a tighter estimation of the upper bound of the cross‐product terms derived from the derivatives of the Lyapunov functionals, less conservative delay‐dependent stability criteria are established in terms of LMIs. Combining with a reciprocally convex combination technique, the newly obtained stability conditions are also less complex. Two numerical examples are given to illustrate the effectiveness and the significant improvement of the proposed method. Copyright © 2013 John Wiley & Sons, Ltd.     

Design of an optimal feedback linearizing‐based controller for an experimental flexible‐joint robot manipulator

This paper presents the design of an optimal non‐linear position tracking controller for a two‐link flexible joint robot manipulator. The controller is designed based on the concept of exact feedback linearization and LQG/LTR techniques. It is shown that the non‐linear robot model is feedback linearizable and a characterization of the set, over which the linearizing transformation is diffeomorphic, is provided. The proposed control approach reduces the number of required measurement sensors and takes into account the effects of measurement noises. A new method for computing the non‐linear state estimate is also presented. It takes advantage of the linear structure of the transformed system. Simulation results demonstrate the potential benefits of the proposed control approach in reaching the desired performance with minimum control effort. Copyright © 1999 John Wiley & Sons, Ltd.     

Manipulator‐driven selection of semi‐active MR‐visible markers

Background

A method for the identification of semi‐active fiducial magnetic resonance (MR) markers is presented based on selectively optically tuning and detuning them.

Methods

Four inductively coupled solenoid coils with photoresistors were connected to light sources. A microcontroller timed the optical tuning/detuning of coils and image collection. The markers were tested on an MR manipulator linking the microcontroller to the manipulator control to visibly select the marker subset according to the actuated joint.

Results

In closed‐loop control, the average and maximum were 0.76° ± 0.41° and 1.18° errors for a rotational joint, and 0.87 mm ± 0.26 mm and 1.13 mm for the prismatic joint.

Conclusions

This technique is suitable for MR‐compatible actuated devices that use semi‐active MR‐compatible markers.     

Further results on H ∞ control for discrete‐time uncertain singular systems with interval time‐varying delays in state and input

This paper investigates the state feedback robust H _∞ control problem of a class of discrete‐time singular systems with norm‐bounded uncertainties and interval time‐varying delays in state and input. A new bounded real lemma for discrete‐time singular systems with a pair of time‐varying interval state delays is first investigated. Mathematical comparisons of the new bounded real lemma and two existing ones are presented. Then, on the basis of the bounded real lemma proposed here, a sufficient condition in the form of nonlinear matrix inequality, such that the considered state feedback robust H _∞ control problem is solvable, is given. In order to solve the nonlinear matrix inequality, a cone complementarity linearization algorithm is offered. Several numerical examples are presented to show the applicability of the proposed approach. Copyright © 2012 John Wiley & Sons, Ltd.     

Less conservative results on stability for linear systems with a time‐varying delay

This paper is focused on the problem of stability for linear systems with a time‐varying delay. A novel Lyapunov–Krasovskii functional that decomposed the delay in all integral terms is proposed. As a result, some less conservative stability criteria are derived by considering the relationship between time‐varying delay and its intervals, which have wider application than the existing ones because independent upper bounds of the delay derivative in the various delay intervals are taken into account. Some numerical examples are finally given to show the effectiveness and the benefits of the proposed method. Copyright © 2012 John Wiley & Sons, Ltd.     

Mixed and passive filtering for a class of singular systems with interval time‐varying delays

This paper deals with the problem of mixed and passive filtering for a class of singular systems with interval time‐varying delays. First, by combining the Wirtinger‐based integral inequality with the reciprocally convex inequality, sufficient delay‐range‐dependent conditions are obtained in terms of strict linear matrix inequalities to ensure that the considered singular system is admissible with a mixed and passivity performance level. Then, based on a matrix transformation technique and employing several free scalars, more flexible strict linear matrix inequality–based conditions are proposed to get the desired filter. Finally, 2 numerical examples are given to show less conservatism and the effectiveness of the results.     

New results on dynamic output feedback control for Markovian jump systems with time‐varying delay and defective mode information

This paper investigates the problem of delay‐dependent dynamic output feedback control for a class of discrete‐time Markovian jump linear systems (MJLSs). The systems under consideration are subject to time‐varying delay and defective mode information. The defective transition probabilities comprise of three types: exactly known, uncertain, and unknown. By employing a two‐term approximation for the time‐varying delay, the original MJLSs can be equivalently converted into a feedback interconnection form, which contains a forward subsystem with constant time‐delays and a feedback one with norm‐bounded uncertainties. Then, based on the scaled small‐gain theorem, the problem is therefore recast as an control problem in the face of uncertainties via an input–output framework. It is shown that the explicit expressions of the desired controller gains can be characterized in terms of strict linear matrix inequalities via some linearization techniques. Simulation studies are performed to illustrate the effectiveness and less conservatism of the proposed methods. Copyright © 2013 John Wiley & Sons, Ltd.     

H∞ control for linear switched systems with time‐varying delay and dead‐zone inputs via an adaptive memory controller

This paper deals with the problem of robust H_∞ control for linear switched systems with time‐varying delay and dead‐zone inputs. First, a new state‐dependent switching law is proposed for the switched system with stable and unstable subsystems. Based on the proposed switching law and using the scaled small gain theorem, a more general stability criterion for the switched delay systems is established. Second, an adaptive memory controller is proposed for the switched system with dead‐zone inputs. With the help of a two‐term approximation of the time‐varying delay, the proposed memory controller only depends on the bounds of the time‐varying delay. Sufficient conditions on the existence of the desired controller are formulated in terms of linear matrix inequalities. Three examples are provided to illustrate the effectiveness of the proposed methods. Copyright © 2016 John Wiley & Sons, Ltd.     

Theoretical and experimental study of dynamic load‐carrying capacity for flexible robotic arms in point‐to‐point motion

This paper involves the study of a general formulation and numerical solution for the dynamic load‐carrying capacity of a mechanical manipulator with elastic links. The approach presented in this article is based on an open‐loop optimal control. This method results from the Pontryagin minimum principle, which yields a 2‐point boundary value problem. The indirect method has been exploited to extract the optimality conditions. The dynamic equations of motion for this system have been obtained by means of the Gibbs‐Appell formulation and by applying the assumed modes method. The elastic characteristics of the members have been modeled based on the Timoshenko beam theory and its associated mode shapes. The aim of this research is to calculate the maximum‐allowed load that a mechanical manipulator with flexible links can carry while traversing an optimal path. At the end, to evaluate the proposed method, we made a comparison between the simulation results obtained from the presented model and the experimental results obtained from a manipulator with 2 flexible links. The comparison between the simulation and empirical data confirms the credibility of the presented method in computing the dynamic load‐carrying capacity and controlling the point‐to‐point motion of the considered 2‐link flexible manipulator.