Approximation-based decentralized output-feedback control for uncertain stochastic interconnected nonlinear time-delay systems with input delay and asymmetric input saturation

This paper proposes an adaptive observer-based neural controller for a class of uncertain large-scale stochastic nonlinear systems with actuator delay and time-delay nonlinear interactions, where drift and diffusion terms contain all state variables of their own subsystem. First, a state observer is established for estimating the unmeasured states, and a predictor-like term is utilized to transform the input delayed system into the delay-free system. Second, novel appropriate Lyapunov–Krasovskii functionals are used to compensate the time-delay terms, and neural networks are employed to approximate unknown nonlinear functions. At last, an output-feedback adaptive neural control scheme is constructed by using Lyapunov stability theory and backstepping technique. It is shown that the designed neural controller can ensure that all the signals in the closed-loop system are semi-globally uniformly ultimately bounded (SGUUB) and the tracking error is driven to a small neighborhood of the origin. The simulation results are presented to further show the effectiveness of the proposed approach.     

Distributed optimal output feedback consensus control for nonlinear Euler-Lagrange systems under input saturation

In this paper, the distributed optimal consensus control of a group of Euler-Lagrange systems under input saturation is considered. The objective function is only known by each agent itself. Meanwhile it is assumed that the velocities of the systems are unknown. To solve this problem, the filters and observers are designed for each agent. The magnitudes of the control input could be guaranteed within the bounds which are given in advance. It is shown that global optimal consensus control could be achieved under the proposed bounded controllers. The states of all agents will reach a consensus which minimizes the sum of the objective functions of all agents. Simulation results illustrate the effectiveness of the control schemes.     

Distributed control of time-delay interconnected nonlinear systems

This paper addresses the distributed control of delayed interconnected nonlinear systems with time-varying delays in both the local subsystems’ dynamics and the physical interconnections among the subsystems. The Takagi–Sugeno fuzzy model with nonlinear consequent parts (N-TS), which is capable to provide less complex representations than standard T–S fuzzy models, is considered to efficiently deal with this class of complex systems. Then, based on Lyapunov–Krasovskii stability arguments, a synthesis condition is proposed to design a distributed control law such that the origin of the closed-loop interconnected system is locally asymptotically stable together with a guaranteed set of admissible initial conditions for which the validity of the N-TS fuzzy model is ensured. Moreover, a quasi-convex optimization procedure is formulated to enlarge the set of admissible initial conditions. The effectiveness of the proposed synthesis condition is validated in two numerical examples, including an interconnected power network with seven generators.     

Fraction dynamic-surface-based adaptive neural finite-time control for stochastic nonlinear systems subject to unknown control directions,time-varying input delay and state delay

In this paper, an adaptive neural finite-time tracking control is studied for a category of stochastic nonlinearly parameterized systems with multiple unknown control directions, time-varying input delay, and time-varying state delay. To this end, a novel criterion of semi-globally finite-time stability in probability (SGFSP) is proposed, in the sense of Lyapunov, for stochastic nonlinear systems with multiple unknown control directions. Secondly, a novel auxiliary system with finite-time convergence is presented to cope with the time-varying input delay, the appropriate Lyapunov Krasovskii functionals are utilized to compensate for the time-varying state delay, Nussbaum functions are exploited to identify multiple unknown control directions, and the neural networks (NNs) are applied to approximate the unknown functions of nonlinear parameters. Thirdly, the fraction dynamic surface control (FDSC) technique is embedded in the process of designing the controller, which not only the “explosion of complexity” problems are successfully avoided in traditional backstepping methods but also the command filter convergence can be obtained within a finite time to lead greatly improved for the response speed of command filter. Meanwhile, the error compensation mechanism is established to eliminate the errors of the command filter. Then, based on the proposed novel criterion, all closed-loop signals of the considered systems are SGPFS under the designed controller, and the tracking error can drive to a small neighborhood of the origin in a finite time. In the end, three simulation examples are applied to demonstrate the validity of the control method.     

Adaptive neural network control for nonstrict-feedback uncertain nonlinear systems with input delay and asymmetric time-varying state constraints

This paper is devoted to adaptive neural network control issue for a class of nonstrict-feedback uncertain systems with input delay and asymmetric time-varying state constraints. State-related external disturbances are involved into the system, and the upper bounds of disturbances are assumed as functions of state variables instead of constants. Additionally, during the approximations of unknown functions by neural networks, the online computation burdens are declined sharply, since the norms of neural network weight vectors are only estimated. In the process of dealing with input delay, an auxiliary function is applied such that the conditions for time delay are more general than the ones in existing literature. A novel adaptive neural network controller is designed by constructing the asymmetric barrier Lyapunov function, which guarantees that the output of system has a good tracking performance and the state variables never violate the asymmetric time-varying constraints. Finally, numerical simulations are presented to verify the proposed adaptive control scheme.     

Event-triggered decentralized output-feedback control for interconnected nonlinear systems with input quantization

In this paper, the event-triggered decentralized control problem for interconnected nonlinear systems with input quantization is investigated. A state observer is constructed to estimate the unmeasurable states, and the state-dependent interconnections are accommodated by presenting some smooth functions. Then by employing backstepping technique and neural networks (NNs) approximation capability, a novel decentralized output feedback control strategy and an event-triggered mechanism are designed simultaneously. It is proved through Lyapunov theory that the closed-loop system is stable and the tracking property of all subsystems is guaranteed. Finally, the effectiveness of the proposed scheme is illustrated by an example.     

Optimal control for linear systems with time delay in control input

This paper presents the optimal regulator for a linear system with time delay in control input and a quadratic cost function. The optimal regulator equations are obtained using the duality principle, which is applied to the optimal filter for linear systems with time delay in observations, and then proved using the maximum principle. Performance of the obtained optimal regulator is verified in the illustrative example against the best linear regulator available for linear systems without delays. Simulation graphs and comparison tables demonstrating better performance of the obtained optimal regulator are included.     

An improved model predictive control for uncertain systems with input saturation

In this work, a new design method of model predictive control (MPC) is proposed for uncertain systems with input constraints. By using a new method to deal with actuator constraints, our method can reduce the conservativeness. For the design of the robust MPC controllers, a sequence of feedback control laws is used and a parameter-dependent Lyapunov function is chosen to further reduce the conservativeness. The effectiveness and performance of our MPC design method are demonstrated by an example.     

Event-triggered control of interconnected nonlinear systems subjected to cyber-attacks and time-varying coupling

This paper addresses the problem of efficient control of nonlinear distributed networked control systems in the presence of stochastic deception attacks and time-varying coupling strength. A strategy combining model-based and event-triggered control to reduce the number of transmissions over a network thereby, saving network resources is proposed. In this strategy, a plant model at the controller end is used to estimate the state of each subsystem. Further, the control law between the two adjacent triggering instants changes in accordance with dynamics of the plant model. The nonlinearities present in each subsystem are approximated via neural network. The neural network weights and feedback signal are updated only when the event-triggering condition at the sensor end is violated. Also, a lower bound on the inter-event time is computed to avoid the occurrence of Zeno phenomena. Finally, the efficacy of the proposed methodology are verified through simulation examples.     

Decentralized adaptive tracking quantized control for interconnected pure feedback time delay nonlinear systems

This paper focuses on the problem of adaptive tracking quantized control for a class of interconnected pure feedback time delay nonlinear systems. To satisfy the requirement of prescribed performance on the output tracking error, a novel asymmetric tangent barrier Lyapunov function is developed. The decentralized adaptive controller is designed via backstepping method. To deal with the uncertain interconnected nonlinear functions, we design a new virtual control input in the first step. Instead of estimating the bound of each unknown function, we use the adaptive method to estimate the bound of the composite function which is composed of the unknown functions. Thus the over parameterization problem is avoided. It is proved that the output of each subsystem satisfies the prescribed performance requirement and other state variables are bounded. Finally, the simulations are performed and the results verify the effectiveness of the proposed method.     

Stability analysis and control synthesis for linear systems with non-symmetrical input saturation

This paper studies the stability and control problem of linear systems with non-symmetrical input saturation. A system with non-symmetrical input saturation is transformed into a system with switching symmetrical input saturation. A switching controller is designed based on a parametric algebra Riccati equation, dwell time and the equivalent switched system. Exponential stability is guaranteed with the proposed switching controller. The main advantages of the proposed method lie in reducing the conservatism caused by directly using symmetrical input saturation control and increasing the state convergent speed. The designed controller can be computed easily by solving the Riccati equation. Numerical examples are provided to demonstrate the effectiveness of the proposed method.     

On stabilization for systems with two additive time-varying input delays arising from networked control systems

This paper is concerned with the stability and stabilization for systems with two additive time-varying input delays arising from networked control systems. A new Lyapunov functional is constructed and a tighter upper bound of the derivative of the Lyapunov functional is derived by applying a convex polyhedron method. The resulting stability criteria are of fewer matrix variables and less conservative than some existing ones. Based on the stability criteria, a state feedback controller is designed such that the closed-loop system is asymptotically stable. Numerical examples are given to show the less conservatism of the stability criteria and the effectiveness of the designed method.     

Distributed total-amount optimal coordinated control of multi-motors with input and output saturation

Specific to the double saturation constraints of input and output in multimotor network systems, an anti-windup control framework with distributed total-amount optimal coordination is constructed, and a new saturated super-twisting sliding mode control strategy is designed in this paper. First, a mathematical model of direct torque and flux control of a multipermanent magnet synchronous motor is established. Next, the consistency of the total amount and output saturation are taken as the constraint conditions. Considering the lowest total energy consumption, the optimal multi-axis total-amount coordinated allocation algorithm is designed on the basis of the Karush-Kuhn-Tucker (KKT) condition. Then, the input saturation is introduced into the dynamic integral part of the super-twisting algorithm. A new saturated super-twisting sliding mode tracking control algorithm is designed, and the barrier Lyapunov function is used to prove the input constraint. Finally, the Matlab/Simulink simulation and RT-LAB semi-physical experiments verify that the anti-windup control strategy of distributed total-amount optimal coordination can effectively solve the double saturation constraints of input and output.     

Command filtered robust adaptive NN control for a class of uncertain strict-feedback nonlinear systems under input saturation

This paper develops a robust adaptive neural network (NN) tracking control scheme for a class of strict-feedback nonlinear systems with unknown nonlinearities and unknown external disturbances under input saturation. The radial basis function NNs with minimal learning parameter (MLP) are employed to online approximate the uncertain system dynamics. The adaptive laws are designed to online update the upper bound of the norm of ideal NN weight vectors, and the sum of the bounds of NN approximation errors and external disturbances, respectively. An auxiliary dynamic system is constructed to generate the augmented error signals which are used to modify the adaptive laws for preventing the destructive action due to the input saturation. Moreover, the command filtering backstepping control method is utilized to overcome the shortcoming of dynamic surface control method, the tracking-differentiator-based control method, etc. Our proposed scheme is qualified for simultaneously dealing with the input saturation effect, the heavy computational burden and the “explosion of complexity” problems. Theoretical analysis illuminates that our scheme ensures the boundedness of all signals in the closed-loop systems. Simulation results on two examples verify the effectiveness of our developed control scheme.     

Robust quantized consensus of discrete multi-agent systems under input saturation

In this paper, we consider the quantized consensus problem of multiple discrete-time integrator agents which suffer from input saturation. As agents transmit state information through communication networks with limited bandwidth, the states of agents have to be quantized into a finite number of bits before transmission. To handle this quantized consensus problem, we introduce an internal time-varying saturation function into the controllers of all agents and ensure that the range of the state of each agent can be known in advance by its neighboring agents. Based on such shared state range information, we construct a quantized consensus protocol which implements a finite-bit quantization strategy to all states of agents and can guarantee the achievement of the asymptotic consensus under any given input saturation threshold. Such desired consensus can be guaranteed at as low bit rate as 1 bit per time step for each agent. Moreover, we can place an upper bound on the convergence rate of the consensus error of agents. We further improve that quantized consensus protocol to a robust version whose parameters are determined with only an upper bound on the number of agents and does not require any more global information of the inter-agent network. Simulations are done to confirm the effectiveness of our quantized consensus protocols.     

Robust state-feedback control design for active suspension system with time-varying input delay and wheelbase preview information

This paper develops a robust state-feedback controller for active suspension system with time-varying input delay and wheelbase preview information in the presence of the parameter uncertainties. By employing system augmentation technique, a multi-objective control optimization model is first established and then this controller design is converted to a static full-state feedback controller design with robust H_∞ and generalized H₂ performance, wherein the model-dependent control gain is evaluated by transforming the related nonlinear matrix inequalities into their corresponding linear matrix inequality forms based on Lyapunov theory, and then LMI (Linear-Matrix-Inequality) technique is applied to solve and obtain the desired controller. A numerical simulation case is finally provided to reveal the effectiveness and advantages of the proposed controller.     

Event-triggered control for multi-agent systems with randomly occurring nonlinear dynamics and time-varying delay

The paper investigates the consensus problem for multi-agent systems with randomly occurring nonlinear dynamics and time-varying delay. A novel event-triggered scheme has been proposed, which can lead to a significant reduction in information communication in a network. By utilizing stochastic analysis and properties of the Kronecker product, consensus criteria are derived in the form of linear matrix inequalities, which can be readily solved using the standard numerical software. Finally, an illustrative example is used to show the effectiveness of the event-triggered scheme.     

Observer-based finite-time asynchronous sliding mode control for Markov jump systems with time-varying delay

The issue of finite-time sliding mode control (SMC) is studied for a class of Markov jump systems, in which parameter uncertainties, external disturbances and time-varying delay are considered. Firstly, a suitable observer-based SMC law is devised so that state trajectory of the system can reach the designed sliding mode surface in finite-time, the gain of the controller is asynchronous to the mode of original system. Meanwhile, the sufficient conditions of finite-time boundedness in the sliding phase and reaching phase are derived by the time partition strategy. Moreover, the gains of the observer and the observer-based controller will be acquired by using the linear matrix inequalities tool. In fine, emulation products are used to confirm the merits of the SMC strategy.     

Dynamic gain scheduling control design for linear multiagent systems subject to input saturation

This paper considers the finite-time bipartite consensus problem governed by linear multiagent systems subject to input saturation under directed interaction topology. Due to the existence of input saturation, the dynamic performance of linear multiagent systems degrades significantly. For the improvement of the dynamic performance of systems, a dynamic gain scheduling control approach is proposed to design a dynamic Laplacian-like feedback controller, which can be obtained from the analytical solution of a parametric Lyapunov equation. Suppose that each agent is asymptotically null controllable with bounded control, and that the corresponding interaction topology of the signed directed graph with a spanning tree is structurally balanced. Then the dynamic Laplacian-like feedback control can ensure that linear multiagent systems will achieve the finite time bipartite consensus. The dynamic gain scheduling control can better improve the bipartite consensus performance of the linear multiagent systems than the static gain scheduling control. Finally, two examples are provided to show the effectiveness of the proposed control design method.     

Robust exponential stability for uncertain time-varying delay systems with delay dependence

This paper investigates the exponential stability problem for uncertain time-varying delay systems. Based on the Lyapunov-Krasovskii functional method, delay-dependent stability criteria have been derived in terms of a matrix inequality (LMI) which can be easily solved using efficient convex optimization algorithms. These results are shown to be less conservative than those reported in the literature. Four numerical examples are proposed to illustrate the effectiveness of our results.