An adaptive robust controller for time delay maglev transportation systems

For engineering systems, uncertainties and time delays are two important issues that must be considered in control design. Uncertainties are often encountered in various dynamical systems due to modeling errors, measurement noises, linearization and approximations. Time delays have always been among the most difficult problems encountered in process control. In practical applications of feedback control, time delay arises frequently and can severely degrade closed-loop system performance and in some cases, drives the system to instability. Therefore, stability analysis and controller synthesis for uncertain nonlinear time-delay systems are important both in theory and in practice and many analytical techniques have been developed using delay-dependent Lyapunov function. In the past decade the magnetic and levitation (maglev) transportation system as a new system with high functionality has been the focus of numerous studies. However, maglev transportation systems are highly nonlinear and thus designing controller for those are challenging. The main topic of this paper is to design an adaptive robust controller for maglev transportation systems with time-delay, parametric uncertainties and external disturbances. In this paper, an adaptive robust control (ARC) is designed for this purpose. It should be noted that the adaptive gain is derived from Lyapunov–Krasovskii synthesis method, therefore asymptotic stability is guaranteed.     

A novel feedback controller design with robust fault isolation ability

This paper proposes a novel feedback controller design scheme which can achieve fault isolation based on the control signal or its embedded signal, i.e., with the self-fault-isolation ability. First of all, according to the well-known Youla parameterization, a controller structure consisting of state and residual joint feedback is developed. Then, the residual feedback gain and observer gain are designed to make the cooperative structured residual feedback signal have fault isolation ability. Some free design parameters in the two gains are further utilized for robust self-fault-isolation. Moreover, the state feedback gain is designed, in the framework of switched system, to realize the self-fault-diagnosis and isolation, based on the control signal directly. The proposed control structure also has the advantage of cooperative fault tolerance. Finally, the simulation of HVAC (Heating, Ventilation and Air Conditioning) system, composed of four rooms in one story building scenario, is carried out to demonstrate the effectiveness and superiority of the proposed feedback controller design approach.     

Synchronization dynamics in a small pacemaker neuronal ensemble via a robust adaptive controller

The synchronization dynamics of a pacemaker neuronal ensemble under the action of a control command is studied herein. The ensemble corresponds to the pyloric central pattern generator of the stomatogastric ganglion of lobster. The desired dynamics is provided by means of an external master neuron and it is induced via a nonlinear controller. Such a controller is composed of a linearizing-like controller and a high gain observer; the controller is able to counteract uncertainties and external perturbations in the controlled system. Numerical simulations of the robust synchronization dynamics of the master neuron and the pacemaker neuronal ensemble are displayed.     

A discrete-time reduced-order controller for robust stabilization of plant in the normalized coprime-factor description

Using the technique of singlar perturbation, a procedure fordesigning a discrete–time reduced–order controllerfor robust stabilization is proposed. The theoretical aspectsare derived directly from the results of the generalized Popov–Yakubovichtheory recently developed. ¹Vlad Ionescu, 3 Emile Zola, Bucharest, 71272, Romania. ²Cristian Oara, 34 Austrului, Bucharest, 73115, Romania.     

非线性时滞系统的L2增益鲁棒控制器设计方法

讨论了一类非线性时滞系统的鲁棒H∞控制问题.基于Lyapunov函数的递推设计方法构造了H∞控制器,使得在L2增益意义下从干扰输入到控制输出的影响任意小.通过巧妙的选取Lyapunov函数解决了时滞问题,实现了递推设计的推广.数值例子和仿真证明了结论的正确性.     

Design of a robust nonlinear controller for a synchronous generator connected to an infinite bus

This article presents a new design of robust finite‐time controller which replaces the traditional automatic voltage regulator for excitation control of the third‐order model synchronous generator connected to an infinite bus. The effects of system uncertainties and external noises are fully taken into account. Then a single input robust controller is proposed to regulate the system states to reach the origin in a given finite time. The designed robust finite‐time excitation controller can refine the system behaviors in convergence and robustness against model uncertainties and external disturbances. The robustness and finite‐time stability of the closed‐loop system are analytically proved using the finite‐time control idea and Lyapunov stability theorem. The suitability and robustness of the designed controller are shown in contrast with two other strong nonlinear control strategies. The main advantages of the proposed controller are as follows: a) robustness against system uncertainties and external noises; b) convergence to the equilibrium point in a given finite time; and c) the use of a single control input. © 2015 Wiley Periodicals, Inc. Complexity 21: 203–213, 2016     

High performance robust linear controller synthesis for an induction motor using a multi-objective hybrid control strategy

A robust induction motor control should provide the desired performance in the face of both plant model and controller model uncertainty. In a recent work, Bottura and co-workers, using the field orientation principle, introduced a representation of a nonlinear time-varying induction motor model that admits robust induction motor controller synthesis in the linear _H∞$H_{\infty }$ framework. The present work considers the use of the approach of Bottura et al. for attaining robust performance of the main operating modes–tracking and disturbance rejection–of an induction motor control system under implementation constraints on the control signal magnitude. This approach requires two distinct mode-specific controllers with gains that cannot be bridged without considerable performance degradation. To address this problem, a multi-objective hybrid control design methodology is developed that employs the corresponding mode-specific controller in each mode, and organizes a rapid and smooth steady-state switching, or transfer, between these controllers to permit sequencing of the operating modes, as necessary. Simulation shows that the technique proposed yields controllers with performance minimally affected by an imprecise modeling of an induction motor, as well as a reduced cost controller implementation throughout the entire induction motor operating sequence.     

Synchronization of two different uncertain chaotic systems with unknown parameters using a robust adaptive sliding mode controller

In this paper, a robust adaptive sliding mode controller (RASMC) is proposed to realize chaos synchronization between two different chaotic systems with uncertainties, external disturbances and fully unknown parameters. It is assumed that both master and slave chaotic systems are perturbed by uncertainties, external disturbances and unknown parameters. The bounds of the uncertainties and external disturbances are assumed to be unknown in advance. Suitable update laws are designed to tackle the uncertainties, external disturbances and unknown parameters. For constructing the RASMC a simple sliding surface is first designed. Then, the RASMC is derived to guarantee the occurrence of the sliding motion. The robustness and stability of the proposed RASMC is proved using Lyapunov stability theory. Finally, the introduced RASMC is applied to achieve chaos synchronization between three different pairs of the chaotic systems (Lorenz–Chen, Chen–Lorenz, and Liu–Lorenz) in the presence of the uncertainties, external disturbances and unknown parameters. Some numerical simulations are given to demonstrate the robustness and efficiency of the proposed RASMC.     

Simple robust technique using time delay estimation for the control and synchronization of Lorenz systems

This work presents two simple and robust techniques based on time delay estimation for the respective control and synchronization of chaos systems. First, one of these techniques is applied to the control of a chaotic Lorenz system with both matched and mismatched uncertainties. The nonlinearities in the Lorenz system is cancelled by time delay estimation and desired error dynamics is inserted. Second, the other technique is applied to the synchronization of the Lü system and the Lorenz system with uncertainties. The synchronization input consists of three elements that have transparent and clear meanings.Since time delay estimation enables a very effective and efficient cancellation of disturbances and nonlinearities, the techniques turn out to be simple and robust. Numerical simulation results show fast, accurate and robust performance of the proposed techniques, thereby demonstrating their effectiveness for the control and synchronization of Lorenz systems.     

A cone complementarity linearization approach to robust controller design for continuous-time piecewise linear systems with linear fractional uncertainties

This paper investigates the robust H_∞ control problem for uncertain continuous-time piecewise systems by using the piecewise continuous Lyapunov function. The uncertainties of the systems under consideration are expressed in a linear fractional form. A strict linear matrix inequality approach is developed to obtain stability condition and H_∞ performance. The H_∞ controller design problem is solved by exploiting the cone complementarity linearization (CCL) method, which can be cast into an iterative minimization problem subject to LMI constraints. Finally two examples are given to illustrate the application of the proposed approach.     

Synchronization of circular restricted three body problem with lorenz hyper chaotic system using a robust adaptive sliding mode controller

In this computational study, we synchronize the Circular Restricted Three Body Problem (CRTBP) with Lorenz Hyper Chaotic System (LHCS) using a Robust Adaptive Sliding Mode Controller (RASMC) together with uncertainties, external disturbances and fully unknown parameters. A simple suitable sliding surface, which includes synchronization errors, is constructed and appropriate update laws are used to tackle the uncertainties, external disturbances and unknown parameters. All simulations to achieve the synchronization for the implemented technique for the two non‐identical systems under consideration are being done using Mathematica. © 2013 Wiley Periodicals, Inc. Complexity 18: 58‐64, 2013     

A robust robust optimization result

We study the loss in objective value when an inaccurate objective is optimized instead of the true one, and show that “on average” this loss is very small, for an arbitrary compact feasible region.     

Algorithm of robust stability region for interval plant with time delay using fractional order PID controller

By using PI^λD^μ controller, we investigate the problem of computing the robust stability region for interval plant with time delay. The fractional order interval quasi-polynomial is decomposed into several vertex characteristic quasi-polynomials by the lower and upper bounds, in which the value set of the characteristic quasi-polynomial for vertex quasi-polynomials in the complex plane is a polygon. The D-decomposition technique is used to characterize the stability boundaries of each vertex characteristic quasi-polynomial in the space of controller parameters. We investigate how the fractional integrator order λ and the derivative order μ in the range (0, 2) affect the stabilizability of each vertex characteristic quasi-polynomial. The stability region of interval characteristic quasi-polynomial is determined by intersecting the stability region of each quasi-polynomial. The parameters of PI^λD^μ controller are obtained by selecting the control parameters from the stability region. Using the value set together with zero exclusion principle, the robust stability is tested and the algorithm of robust stability region is also proposed. The algorithm proposed here is useful in analyzing and designing the robust PI^λD^μ controller for interval plant. An example is given to show how the presented algorithm can be used to compute all the parameters of a PI^λD^μ controller which stabilize a interval plant family.     

A chattering-free robust adaptive sliding mode controller for synchronization of two different chaotic systems with unknown uncertainties and external disturbances

In this paper, a robust adaptive sliding mode controller (RASMC) is introduced to synchronize two different chaotic systems in the presence of unknown bounded uncertainties and external disturbances. The structure of the master and slave chaotic systems has no restrictive assumption. Appropriate adaptation laws are derived to tackle the uncertainties and external disturbances. Based on the adaptation laws and Lyapunov stability theory, an adaptive sliding control law is designed to ensure the occurrence of the sliding motion even when both master and slave systems are perturbed with unknown uncertainties and external disturbances. Since the conventional sliding mode controllers contain the sign function, the undesirable chattering is occurred. We propose a new simple adaptive scheme to eliminate the chattering. Finally, numerical simulations are presented to verify the usefulness and applicability of the proposed control strategy.     

Efficient robust optimization for robust control with constraints

This paper proposes an efficient computational technique for the optimal control of linear discrete-time systems subject to bounded disturbances with mixed linear constraints on the states and inputs. The problem of computing an optimal state feedback control policy, given the current state, is non-convex. A recent breakthrough has been the application of robust optimization techniques to reparameterize this problem as a convex program. While the reparameterized problem is theoretically tractable, the number of variables is quadratic in the number of stages or horizon length N and has no apparent exploitable structure, leading to computational time of per iteration of an interior-point method. We focus on the case when the disturbance set is ∞-norm bounded or the linear map of a hypercube, and the cost function involves the minimization of a quadratic cost. Here we make use of state variables to regain a sparse problem structure that is related to the structure of the original problem, that is, the policy optimization problem may be decomposed into a set of coupled finite horizon control problems. This decomposition can then be formulated as a highly structured quadratic program, solvable by primal-dual interior-point methods in which each iteration requires time. This cubic iteration time can be guaranteed using a Riccati-based block factorization technique, which is standard in discrete-time optimal control. Numerical results are presented, using a standard sparse primal-dual interior point solver, that illustrate the efficiency of this approach.     

Simple groups, permutation groups, and probability

We derive a new bound for the minimal degree of an almost simple primitive permutation group, and settle a conjecture of Cameron and Kantor concerning the base size of such a group. Additional results concern random generation of simple groups, and the so-called genus conjecture of Guralnick and Thompson. Our proofs are based on probabilistic arguments, together with a new result concerning the size of the intersection of a maximal subgroup of a classical group with a conjugacy class of elements.

     

A note on fundamental,non-fundamental,and robust cycle bases

In many biological systems, robustness is achieved by redundant wiring, and reflected by the presence of cycles in the graphs connecting the systems’ components. When analyzing such graphs, cyclically robust cycle bases of are of interest since they can be used to generate all cycles of a given 2-connected graph by iteratively adding basis cycles. It is known that strictly fundamental (or Kirchhoff) bases, i.e., those that can be derived from a spanning tree, are not necessarily cyclically robust. Here we note that, conversely, cyclically robust bases (even of planar graphs) are not necessarily fundamental. Furthermore, we present a class of cubic graphs for which cyclically robust bases can be explicitly constructed.