State Time Delay Research Articles

Time-scaling transformation for optimal control problem with time-varying delay

This paper focuses on the solution to nonlinear time-delay optimal control problems with time-varying delay subject to canonical equality and inequality constraints. Traditional control parameterization in conjunction with time-scaling transformation could optimize control parameters and switching times at the same time when the time-delays in the dynamic system are taken as constants. The purpose of this paper is to extend this method to solve the dynamic systems with time-varying delay. We introduce a hybrid time-scaling transformation that converts the given time-delay system into an equivalent system defined on a new time horizon with fixed switching times. Meanwhile, we obtain the value of time-delay state utilizing the relationship between the new time scale and the original one. After computing the gradients of the cost and constraints with respect to the control heights and its durations, we could solve the equivalent optimal control problem using gradient based optimization method.

Robust backstepping‐based trajectory tracking control for quadrotors with time delays

In this brief, the robust trajectory tracking control problem is addressed for uncertain quadrotor systems with time delays. The quadrotor dynamical model is an under-actuated system subject to non-linearity, unmodelled uncertainties, parametric perturbations, external disturbances, and state and input time delays. A robust cascade trajectory tracking controller is developed by the backstepping method and the robust compensation theory. Theoretical analysis is given to prove that the tracking errors can converge into the given neighbourhood of the origin ultimately. An on-line unidirectional tuning method is given to determine the controller parameters. Experimental results are provided to verify the effectiveness of the proposed control approach and the parameter tuning method.

Photonic generation of triangular-shaped waveform signal with adjustable symmetrical coefficient

ABSTRACTA configuration for triangular-shaped microwave signal generator is proposed and analysed. In the proposed model, a single-drive Mach–Zehnder modulator operated under the push–pull mode is firstly driven by a sinusoid signal. The lightwave is then split into two branches and converted by a balanced photodetector. According to the analysis, the output photocurrent contains infinite sinusoidal harmonics of the driven frequency. By adjusting three variables (modulation index, bias state and optical time delay), the power of the first three harmonics can be arbitrarily controlled. Such a property can be used in triangular-shaped microwave generation with adjustable symmetrical coefficient δ. The theory and discussion are proposed in this work. A fitting error η is defined to evaluate the waveform quality. With a defined η < 6%, the symmetrical coefficient can be adjusted within a range of 20% ≤ δ ≤ 80%.

Fuzzy Approximation-Based Adaptive Control of Nonlinear Uncertain State Constrained Systems With Time-Varying Delays

In this paper, a novel adaptive fuzzy tracking control strategy is developed for nonlinear time-varying delayed systems with full state constraints. State constraints and time delays are normally found in various real-life plants, which are two important factors for degrading system performance significantly. In the framework of adaptive control, the effects of state constraints and time-varying delays are removed simultaneously. The integral Barrier Lyapunov functionals (IBLFs) are applied to achieve full-state-constraint satisfactions and remove the need of the transformed error constraints in previous BLFs. The unknown time-varying delays are completely compensated by introducing the separation technique and Lyapunov–Krasovskii functionals (LKFs). The unknown functions existing in systems are approximated by employing fuzzy logic systems (FLSs). With the help of less-adjustable parameters, only one parameter is needed to be adjusted online in each step of control design. The novel strategy can guarantee that a satisfactory tracking performance is achieved and the signals existing in the closed-loop system are bounded. Finally, by presenting simulation results, the efficiency of the proposed approach is revealed.

Discrete-Time Optimal Control of Electromagnetic Coil Systems for Generation of Dynamic Magnetic Fields With High Accuracy

Electromagnetic coil systems (ECSs) have been widely used for actuation and motion control of magnetic micro/nanorobots. In this paper, two typical ECSs with different system configurations are developed: One is computer-based and uses servoamplifiers for driving the coils and the other adopts an embedded control system with home-designed circuit boards for driving the coils. For dynamic control of the two types of ECSs, a unified control scheme is proposed with two objectives: 1) to make the output magnetic field converge to the reference without steady-state error; 2) to achieve optimal transient response under tunable requirement of control effort. In the scheme, dynamic models of the two systems are described by a unified state-space form with different dimensions, which are obtained by system identification. Then, a discrete-time optimal controller is designed based on the linear quadratic with integral action method to realize the control objectives. Finally, in order to make the controller applicable to the real ECSs, the time-delayed system states are estimated by utilizing a Kalman filter, and a Smith predictor inspired compensator is designed to compensate for time delay and modeling error. Simulations and experiments using the proposed control scheme are conducted for the two ECSs with three-axis Helmholtz coils, which show the easy adaption of the control approach to different coils. Experimental results validate the significantly improved dynamic performances of the two ECSs, and tracking a three-dimensional dynamic magnetic field with high accuracy is also demonstrated.

Fractional optimal control in transmission dynamics of West Nile virus model with state and control time delay: a numerical approach

In this paper, an optimal control for a novel fractional West Nile virus model with time delay is presented. The proposed model is governed by a system of fractional delay differential equations, where the fractional derivative is defined in the Grünwald–Letnikov sense. Stability analysis of fixed points is studied. Corresponding fractional optimal control problem, with time delays in both state and control variables, is formulated and studied. Two simple numerical methods are used to study the nonlinear fractional delay optimal control problem. The methods are standard finite difference method and nonstandard finite difference method. Comparative studies are implemented, it is found that the nonstandard finite difference method is better than the standard finite difference method.

Some generalized global stability criteria for delayed Cohen–Grossberg neural networks of neutral-type

This paper carries out a theoretical investigation into the stability problem for the class of neutral-type Cohen–Grossberg neural networks with discrete time delays in states and discrete neutral delays in time derivative of states. By employing a more general type of suitable Lyapunov functional, a set of new generalized sufficient criteria are derived for the global asymptotic stability of delayed neural networks of neutral-type. The proposed stability criteria are independently of the values of the time delays and neutral delays, and they completely rely on some algebraic mathematical relationships involving the values of the elements of the interconnection matrices and the other network parameters. Therefore, it is easy to verify the validity of the obtained results by simply using some algebraic equations representing the stability conditions. A detailed comparison between our proposed results and recently reported corresponding stability results is made, proving that the results given in this paper generalize previously published stability results. A constructive numerical example is also given to demonstrate the applicability of the results of the paper.

Design of L1 Adaptive Control for PMSG Wind Turbine System

This paper focuses on the design of an L1 adaptive controller for variable speed wind turbines on a permanent magnet synchronous generator (PMSG) to maximize the wind power exploited in the presence of parameters uncertainties and wind speed turbulences. This control method based on the class of state feedback state for multiinput multi-output (MIMO) system can be applied to the current control and speed control of the system. The proposed controller successfully deals with the essential nonlinear problems of wind turbines and the effect of unknown parameters. Moreover, the L1 adaptive controller with fast adaptation is not only beneficial for both performance and robustness but also effective for the appearance of the time-delay state variables of wind turbine. Finally, with comparison to the indirect model reference adaptive control (MRAC), the performances of the system are verified by mean of several simulation results.

Adaptive NN Control Without Feasibility Conditions for Nonlinear State Constrained Stochastic Systems With Unknown Time Delays.

In the novel, an adaptive neural network (NN) controller is developed for a category of nonlinear stochastic systems with full state constraints and unknown time delays. The control quality and system stability suffer from the problems of state time delays and constraints which frequently arises in most real plants. The considered systems are transformed into new constrained free systems based on nonlinear mappings, such that full state constraints are never violated and the feasibility conditions on virtual controllers (the values of virtual controllers and its derivative are assumed to be known) are removed. To compensate for unknown time delayed uncertainties, the exponential type Lyapunov-Krasovskii functionals (LKFs) are employed. NNs are utilized to approximate unknown nonlinear functions appearing in the design procedure. In addition, by employing dynamic surface control (DSC) technique and less adjustable parameters, the online computation burden is lightened. The control method presented can achieve the semiglobal uniform ultimate boundedness of all the closed-loop system signals and the satisfactions of full state constraints by rigorous proof. Finally, by presenting simulation examples, the efficiency of the presented approach is revealed.

ADP-Based Online Tracking Control of Partially Uncertain Time-Delayed Nonlinear System and Application to Wheeled Mobile Robots.

In this paper, an adaptive dynamic programming-based online adaptive tracking control algorithm is proposed to solve the tracking problem of the partial uncertain time-delayed nonlinear affine system with uncertain resistance. Using the discrete-time Hamilton-Jacobi-Bellman function, the input time-delay separation lemma, and the Lyapunov-Krasovskii functionals, the partial state and input time delay can be determined. With the approximation of the action and critic, and resistance neural networks, a near-optimal controller and appropriate adaptive laws are defined to guarantee the uniform ultimate boundedness of all signals in the target system, and the tracking error convergence to a small compact set to zero. A numerical simulation of the wheeled mobile robotic system is presented to verify the validity of the proposed method.

Stability analysis of Cohen–Grossberg neural networks of neutral-type: Multiple delays case

The essential purpose of this work is to conduct an investigation into stability problem for the class of neutral-type Cohen–Grossberg neural networks including multiple time delays in states and multiple neutral delays in time derivative of states. By proposing an appropriate Lyapunov functional, a new sufficient criterion is derived for global asymptotic stability of neutral-type neural networks. The obtained stability criterion is independent of time delay and neutral delay parameters, and it is completely stated in terms of the elements of interconnection matrices and other network parameters. Thus, this newly presented stability condition can be validated by simply examining some algebraic equations establishing some relationships among the system parameters and matrices of the neutral-type neural system. A constructive example is presented to indicate applicability of the obtained sufficient stability condition. Since stability analysis of the class of neutral-type neural networks considered in this work has not been given much attention due to the difficulty of developing efficient mathematical techniques and methods enabling to conduct a stability analysis of such neutral-type neural systems, the criterion proposed in this paper can be considered as a leading stability result for neutral-type Cohen–Grossberg neural systems including multiple time and multiple neutral delays.

Stationary, isotropic and homogeneous two-dimensional turbulence: a first non-perturbative renormalization group approach

We study the statistical properties of stationary, isotropic and homogeneous turbulence in two-dimensional (2D) flows, focusing on the direct cascade, that is on large wave-numbers compared to the integral scale, where both energy and enstrophy are provided to the fluid. Our starting point is the 2D Navier–Stokes equation in the presence of a stochastic forcing, or more precisely the associated field theory. We unveil two extended symmetries of the Navier–Stokes action which were not yet identified, one related to time-dependent (or time-gauged) shifts of the response fields and existing in both 2D and 3D, and the other to time-gauged rotations and specific to 2D flows. We derive the corresponding Ward identities, and exploit them within the non-perturbative renormalization group formalism, and the large wave-number expansion scheme developed in Tarpin et al (2018 Phys. Fluids 30 055102). We consider the flow equation for a generalized n-point correlation function, and calculate its leading order term in the large wave-number expansion. At this order, the resulting flow equation can be closed exactly. We solve the fixed point equation for the 2-point function, which yields its explicit time dependence, for both small and large time delays in the stationary turbulent state. On the other hand, at equal times, the leading order term vanishes, so we compute the next-to-leading order term. We find that the flow equations for equal-time n-point correlation functions are not fully constrained by the set of extended symmetries, and discuss the consequences.

Robust controller design for uncertain delayed systems and its applications to hypersonic vehicles

AbstractThe longitudinal dynamics of hypersonic flight vehicles involves strong nonlinearity and coupling, uncertainties including parametric uncertainties, unmodeled uncertainties, external disturbances, and time‐varying input and state time delays. In this paper, a robust controller design method is proposed for the longitudinal stabilization of these vehicles by the signal‐compensation‐based control idea. Theoretical analysis is given to prove the robustness properties of the designed closed‐loop control system subject to multiple time‐varying uncertainties and time‐varying input and state delays. Simulation results are performed to show the validness and advantages of the proposed robust control approach.

Consensus in first-order nonlinear multi-agent systems with state time delays using adaptive fuzzy wavelet networks

In this paper, a consensus problem is addressed for first-order multi-agent systems with unknown nonlinear dynamics under undirected graphs. Adaptive fuzzy wavelet networks are used to design two novel control algorithms for nonlinear systems without delays and nonlinear systems with state time delays. In these algorithms, adaptive fuzzy wavelet networks are employed to compensate for nonlinear dynamics of systems. Using proper Lyapunov functions, adaptive laws are obtained and the uniform ultimately bounded stability of closed-loop systems is proved. In addition, this paper uses Lyapunov–Krasovskii functions to handle unknown time delays. Three simulation examples are provided to illustrate the effectiveness of the proposed control schemes.

Delay-dependent Robust Dissipative Control for Singular LPV Systems with Multiple Input Delays

This paper addresses the robust dissipative control problem for the singular linear parameter-varying (LPV) systems with multiple input time-delays. First, by constructing the parameter-dependent Lyapunov functional, a delay-dependent robust dissipativity criterion for singular LPV systems with multiple state time-delays is proposed. Second, on the basis of linear matrix inequalities (LMIs) technique, a novel delay-dependent robust dissipativity-based controller for the singular LPV delay systems is designed. Furthermore, it is proved that the resultant closed-loop system via state feedback controller is admissible and strictly robustly (Q,S,R)-dissipative. Finally, the effectiveness of the proposed method is demonstrated by three numerical examples.

Tube-Based Active Robust MPC for Uncertain Constrained Linear Systems With Time Delays

The problem of robust tube-based model predictive control (MPC) is considered for a class of discrete-time constrained linear systems with time-delayed states and additional disturbances. This paper presents an active robust control scheme that can simultaneously cope with disturbances and time-delay states using active approaches, rather than inherent system robustness. The proposed robust controller design methodology is implemented by constructing a minimal robust control-invariant set of nominal linear systems with time-delayed states neglecting additional disturbances. Based on the time-delay-dependent robust MPC approach for the nominal time-delay system, a novel active robust tube-based MPC algorithm considering time-delayed states is proposed. Furthermore, a delay-dependent sufficient condition for the tube-based controller is derived. Based on the implementation of the delay-dependent robust tube-based controller, the novel active control method is much less conservative than previous approaches. Numerical simulation results demonstrate the effectiveness of the proposed method.

A sufficient optimality condition for delayed state-linear optimal control problems

We give answer to an open question by proving a sufficient optimality condition for state-linear optimal control problems with time delays in state and control variables. In the proof of our main result, we transform a delayed state-linear optimal control problem to an equivalent non-delayed problem. This allows us to use a well-known theorem that ensures a sufficient optimality condition for non-delayed state-linear optimal control problems. An example is given in order to illustrate the obtained result.

Synchronization of Fuzzy Control Design Based on Bessel–Legendre Inequality for Coronary Artery State Time-Delay System

This paper investigates the problem of fuzzy state feedback control for a category of fuzzy-model-based coronary artery system(FMBCAS) with state time-delay. T-S fuzzy model is employed to close in coronary artery system(CAS) which exists unknown nonlinear characteristics. Through the use of linear matrix inequality technique, the synchronization controller for CAS are obtained. By utilizing the delay-partitioning method, we can get a less conservative results. The Bessel-Legendre inequality and the Moon’s et al. inequality with convex analysis are used to further reduce the conservatism of the system. Finally, a simulation of CAS proves the effectiveness of our strategy.

Reconstructibility of Boolean control networks with time delays in states

This paper deals with the reconstructibility of Boolean control networks (BCNs) with time delays in states. First, a survey on the semi-tensor product, weighted pair graph, constructed forest and finite automata is given. Second, by using the weighted pair graph, constructed forest and finite automata, an algorithm is designed to judge whether a Boolean control network with time delays in states is reconstructable or not under a mild assumption. Third, an algorithm is proposed to determine the current state. Finally, an illustrative example is given to show the effectiveness of the proposed method.

Guaranteed cost control for exponential stability of a nonlinear system with mixed time-varying delays in states and controls

This paper presents a new guaranteed cost control for exponential stability of a nonlinear system with mixed time-delays in state and feedback control. The considered mixed time-delays are both discrete and distributed time-varying delays, but not necessarily differentiable. The proposed conditions allow us to design the state feedback controllers which stabilize the closed-loop system. By constructing an appropriate Lyapunov–Krasovskii functional, new delay-dependent sufficient conditions for the existence of guaranteed cost control are given in terms of linear matrix inequalities (LMIs). Moreover, we design new quadratic cost functions and minimize their upper bound. Finally, numerical examples are given to illustrate the effectiveness and improvement over some existing results in the literature.