Optimal control of linear delay systems via hybrid of block-pulse and Legendre polynomials

A method for finding the optimal control of a linear time varying delay system with quadratic performance index is discussed. The properties of the hybrid functions which consists of block-pulse functions plus Legendre polynomials are presented. The operational matrices of integration, delay and product are utilized to reduce the solution of optimal control to the solution of algebraic equations. Illustrative examples are included to demonstrate the validity and applicability of the technique.     

Routh-type table test for zero distribution of polynomials with commensurate fractional and integer degrees

This paper mainly presents Routh-type table test methods for zero distribution of polynomials with commensurate fractional degrees on the left-half plane, right-half plane and imaginary axis in the complex plane. The proposed tabular methods are derived for extension and generalization of the Routh test, which is widely used in controls for zero distribution of polynomials with integer degrees. Singular cases are discussed and handled efficiently and simply. Necessary and sufficient conditions for the second singular case are completely analyzed in terms of symmetric zeros. A particular property is revealed that a polynomial with commensurate fractional degrees without pure imaginary zero may still be stable in the presence of the second singular case, which is impossible for a real polynomial with integer degrees. Furthermore, we present a test to solve the zero distribution problem with respect to general sector region for polynomials with commensurate fractional degrees and real/complex coefficients. Finally, numerical examples are given to illustrate the correctness and effectiveness of the results. The proposed methods have broad application areas, including various systems, circuits and control.     

Finite-time stabilization of nonlinear time delay systems using LQR based sliding mode control

In this paper, we discussed the robust finite-time stability of conic type nonlinear systems with time varying delays. Some novel conditions are derived to design a linear quadratic regulator (LQR) based sliding mode control (SMC) by proposing an integral switching surface. The sufficient conditions are derived for the considered nonlinear system using Lyapunov–Krasovskii stability theory and linear matrix inequality (LMI) approach. The proposed conditions can be solved using some standard numerical packages. Finally, a practical example is provided to validate the advantages and effectiveness of the proposed results.     

Data-driven optimal tracking control for discrete-time systems with delays using adaptive dynamic programming

In this paper, the data-driven adaptive dynamic programming (ADP) algorithm is proposed to deal with the optimal tracking problem for the general discrete-time (DT) systems with delays for the first time. The model-free ADP algorithm is presented by using only the system’s input, output and the reference trajectory of the finite steps of historical data. First, the augmented state equation is constructed based on the time-delay system and the reference system. Second, a novel data-driven state equation is derived by virtue of the history data composed of input, output and reference trajectory, which is considered as a state estimator.Then, a novel data-driven Bellman equation for the linear quadratic tracking (LQT) problem with delays is deduced. Finally, the data-driven ADP algorithm is designed to solve the LQT problem with delays and does not require any system dynamics. The simulation result demonstrates the validity of the proposed data-driven ADP algorithm in this paper for the LQT problem with delays.     

New results on exact controllability of a class of fractional neutral integro-differential systems with state-dependent delay in Banach spaces

This article deals with the use of Krasnoselskii’s fixed point theorem and Leray–Schauder alternative theorem combined with resolvent operator and some analytical methods to investigate the exact controllability and continuous dependence of a class of neutral fractional integro-differential systems with state-dependent delay in Banach spaces. An application to exemplify the concept is provided at the end.     

Robust FOPID stabilization of retarded type fractional order plants with interval uncertainties and interval time delay

This study investigates the robust stability of the retarded type of interval fractional order plants with an interval time delay. To this end, the characteristic quasi-polynomial is divided into two terms. The first term is simply the denominator interval polynomial of the open loop system and the second term is the multiplication of the interval delay term in the numerator of the open loop system which is an interval polynomial. Each of these two terms of the characteristic quasi-polynomial makes their own value sets in the complex plane for a given frequency. In this paper, based on these two value sets and by using the zero exclusion principle, the robust stability of the closed loop system by applying a FOPID controller is analyzed. Finally, two numerical examples and an experimental verification are provided to demonstrate the effectiveness of the proposed method in the robust stabilization of fractional order plants with interval uncertainties and interval time delay.     

Output feedback control for a class of high-order nonholonomic systems with complicated nonlinearity and time-varying delay

This paper considers the output feedback control problem for high-order nonholonomic time-delay system. Remarkably, the studied system allows the polynomial time-delay growing conditions. Moreover, the applicable power ranges of nonlinear drift and diffusion terms are further relaxed to be a interval rather than a fix point. By choosing a new Lyapunov–Krasovskii (L–K) functional, and by modifying the adding a power integrator method, a delay-independent output feedback controller is designed such that the system is globally asymptotically stable. A simulation example is given to show the validity of the proposed theory.     

A hybrid partial feedback linearization and deadbeat control scheme for a nonlinear gantry crane

This paper presents the design of a hybrid partial feedback linearization and deadbeat control scheme for a nonlinear gantry crane with friction to control its position and sway angle. The partial feedback linearization is used to linearize the nonlinear model and to stabilize its internal dynamics. In many crane applications, it's necessary to accelerate the system response. As a result, this will cause oscillation in the position as well as the sway angle. So, the deadbeat controller is added to get the desirable accelerated response without any oscillation or adverse effects on the internal dynamics stability. By using Lyapunov stability method, the proposed scheme is proved to be globally stable, with converging tracking errors to the desired performance. The simulation results are accomplished to evaluate the effectiveness of the proposed scheme and to demonstrate its reliability to control crane systems with comparative results.     

Neural networks-based adaptive output feedback control for a class of uncertain nonlinear systems with input delay and disturbances

This paper focuses on the problem of adaptive output feedback control for a class of uncertain nonlinear systems with input delay and disturbances. Radial basis function neural networks (NNs) are employed to approximate the unknown functions and an NN observer is constructed to estimate the unmeasurable system states. Moreover, an auxiliary system is introduced to compensate for the effect of input delay. With the aid of the backstepping technique and Lyapunov stability theorem, an adaptive NN output feedback controller is designed which can guarantee the boundedness of all the signals in the closed-loop systems. Finally, a simulation example is given to illustrate the effectiveness of the proposed method.     

Robust simultaneous fault detection and control for a class of nonlinear stochastic switched delay systems under asynchronous switching

This paper concerns the simultaneous fault detection and control (SFDC) problem for a class of nonlinear stochastic switched systems with time-varying state delay and parameter uncertainties. The switching signal of detector/controller unit (DCU) is assumed to be with switching delay, which results in the asynchronous switching between the subsystems and DCU. By constructing a switching strategy depending on the state and switching delays, new sufficient conditions expressed by a set of linear matrix inequalities (LMIs) is derived to design DCU gains. This problem is formulated as an H_∞ optimization problem and both mean square exponential stability and fault detection of augmented system are considered. A numerical example is finally exploited to verify the effectiveness and potential of the achieved scheme.     

Iterative learning control for linear delay systems with deterministic and random impulses

This paper investigates convergence of iterative learning control for linear delay systems with deterministic and random impulses by virtute of the representation of solutions involving a concept of delayed exponential matrix. We address linear delay systems with deterministic impulses by designing a standard P-type learning law via rigorous mathematical analysis. Next, we extend to consider the tracking problem for delay systems with random impulses under randomly varying length circumstances by designing two modified learning laws. We present sufficient conditions for both deterministic and random impulse cases to guarantee the zero-error convergence of tracking error in the sense of Lebesgue-p norm and the expectation of Lebesgue-p norm of stochastic variable, respectively. Finally, numerical examples are given to verify the theoretical results.     

An optimal Fuzzy-logic based frequency control strategy in a high wind penetrated power system

This paper introduces a new load frequency control (LFC) model in the presence of high wind power penetration level. The main issue in a wind-penetrated power system is to maintain the system frequency in a normal operating band which is specified by the given system grid codes. Essentially, the power system equilibrium point changes following a contingency, and in this case, the high penetration of wind farms makes it harder to regain an acceptable system equilibrium points through conventional control applications. In order to overcome the aforesaid problem, a new Fuzzy-logic controller is designed optimally in this paper using the artificial bee colony (ABC) algorithm. In this approach, the ABC algorithm tunes the membership function parameters of the Fuzzy controller to acquire a good-enough performace of the proposed strategy. More importantly, the proposed Fuzzy-logic controller is blessed with robustness, simplicity, and reliability in order to ameliorate the frequency deviation. It is worth saying that the stability analysis is presented in this paper as well as the noise analysis of the proposed method. The research results indicates how effectively wind farm could participate in the system frequency control through inertial control, primary frequency control, and supplementary frequency control.     

Improving the performance of networked control systems with time delay and data dropouts based on fuzzy model predictive control

This paper proposes a fuzzy model predictive control (FMPC) combined with the modified Smith predictor for networked control systems (NCSs). The network delays and data dropouts are problems, which greatly reduce the controller performance. For the proposed controller, the model of the controlled system is identified on-line using the Takagi – Sugeno (T-S) fuzzy models based on the Lyapunov function. There are two internal loops in the proposed structure. The first is the loop around the FMPC, which predicts the future outputs. The other is the loop around the plant to give the error between the system model and the actual plant. The proposed controller is designed for controlling a DC servo system through a wireless network to improve the system response. The practical results based on MATLAB/SIMULINK are established. The practical results are indicated that the proposed controller is able to respond the networked time delay and data dropouts compared to other controllers.     

Fault tolerant cooperative control for affine multi-agent systems: An optimal control approach

The goal of this paper is to propose an optimal fault tolerant control (FTC) approach for multi-agent systems (MASs). It is assumed that the agents have identical affine dynamics. The underlying communication topology is assumed to be a directed graph. The concepts of both inverse optimality and partial stability are further employed for designing the control law fully developed in the paper. Firstly, the optimal FTC problem for linear MASs is formulated and then it is extended to MASs with affine nonlinear dynamics. To solve the Hamilton-Jacobi-Bellman (HJB) equation, an Off-policy Reinforcement Learning is used to learn the optimal control law for each agent. Finally, a couple of numerical examples are provided to demonstrate the effectiveness of the proposed scheme.     

Vibration control of a membrane antenna structure using cable actuators

This paper presents a control strategy of using cable actuators to control the vibration of a membrane antenna structure. The tension cables of the membrane antenna structure are used as actuators, the vibration of the structure can be suppressed by controlling the tension force in the cable actuators. First, the antenna structure with cable actuators is discretized by the finite element method (FEM), and governing equation of the whole structure is established. Then, a controller is designed based on the Lyapunov's stability theory, and the mechanism of this controller is studied through a simple single-degree-of-freedom (SDOF) system. The optimal placement of the cable actuators is also studied numerically in this paper. Simulation results indicate that vibration of the membrane antenna structure can be suppressed effectively by the cable actuators, and optimally placed cable actuators can produce better control effect with smaller control input.     

Data-driven adaptive optimal control of linear uncertain systems with unknown jumping dynamics

This paper focuses on the optimal control of a DC torque motor servo system which represents a class of continuous-time linear uncertain systems with unknown jumping internal dynamics. A data-driven adaptive optimal control strategy based on the integration of adaptive dynamic programming (ADP) and switching control is presented to minimize a predefined cost function. This takes the first step to develop switching ADP methods and extend the application of ADP to time-varying systems. Moreover, an analytical method to give the initial stabilizing controller for policy iteration ADP is proposed. It is shown that under the proposed adaptive optimal control law, the closed-loop switched system is asymptotically stable at the origin. The effectiveness of the strategy is validated via simulations on the DC motor system model.     

Non-fragile exponential synchronization of delayed complex dynamical networks with transmission delay via sampled-data control

This paper is devoted to the non-fragile exponential synchronization problem of complex dynamical networks with time-varying coupling delays via sampled-data static output-feedback controller involving a constant signal transmission delay. The dynamics of the nodes contain s quadratically restricted nonlinearities, and the feedback gain is allowed to have norm-bounded time-varying uncertainty. The control design is based on a Lyapunov–Krasovskii functional, which consists of the sum of terms assigned to the individual nodes, i.e., it is constructed without merging the complex dynamical network’s nodes into a single large-scale system. In this way, the proposed design method has substantially reduced computational complexity and improved conservativeness, and guaranties non-fragile exponential stability of the error system. The sufficient stability condition is expressed in terms of linear matrix inequalities that are solvable by standard tools. The efficiency of the proposed method is illustrated by numerical examples.     

State feedback control for stochastic Markovian jump delay systems based on LaSalle-type theorem

This paper investigates the problem of stochastic stability and stabilization of stochastic Markovian jump delay systems (SMJDSs) based on LaSalle theorem. The time delays are assumed to be time-varying and numerous stochastic disturbances are considered. Attention is focused on the design of the mode-dependent state feedback controller for SMJDSs based on LaSalle theorem such that the closed-loop SMJDSs are almost surely asymptotically stable. The sufficient conditions for the solvability of the state feedback control problem are obtained in terms of linear matrix inequalities (LMIs). When the LMIs are feasible, the desired state feedback controller is also given. Two numerical examples including the vertical take-off and landing (VTOL) helicopter system are employed to demonstrate the effectiveness and usefulness of the method proposed in this paper