H∞ output feedback control for large-scale nonlinear systems with time delay in both state and input

The H∞ output feedback control problem for a class of large-scale nonlinear systems with time delay in both state and input is considered in this paper. It is a...     

Quantized H ∞ fault-tolerant control for networked control systems

Quantized H_∞ fault-tolerant control for networked control systems (NCSs) with partial actuator fault with respect to actuators is concerned in this paper. Considering transmission delay, packet dropout and quantization, a synthesis model with partial actuator fault is established. The piecewise constant controller is adopted to model NCS with the transmission delay and packet dropout. Due to data transmitted in practical NCSs should be quantized before they are sent to the next network node, the logarithmic static and time-invariant quantizers at the sensor and controller sides are proposed in the paper. For the established model, an appropriate type of Lyapunov functions is provided to investigate the delay-dependent H_∞ control problem. According to an optimal problem, the controller that makes the system achieve the best performance is designed. Finally, an illustrative example is given to demonstrate the effectiveness of the proposed approach.     

Robust H ∞ filter design for time-delay systems with saturation

This paper investigates the H∞ filtering problem for a class of linear continuous-time systems with both time delay and saturation. Such systems have time delay in their state equations and saturation in their output equations, and their process and measurement noises have unknown statistical characteristics and bounded energies. Based on the Lyapunov-Krasovskii stability theorem and the linear matrix inequalities (LMIs) technique, a generalized dynamic filter architecture is proposed, and a filter design method is developed. The linear H∞ filter designed by the method can guarantee the H∞ performance. The parameters of the designed filter can be obtained by solving a kind of LMI. An illustrative example shows that the design method proposed in this paper is very effective.     

Delay-fractioning-dependent robust H ∞ control for linear systems with delay in state or input and its applications

A new delay fraction technique is proposed to investigate the H _∞ control of uncertain systems with time delay in state or input. First, the variation interval of the time-varying delay is divided into several subintervals with equal length. By checking the variation of derivative of the Lyapunov functional in every subinterval, some new criteria on H _∞ performance analysis of the systems are derived in terms of the convexity properties of a matrix inequality and some other new analysis techniques. Then, criteria for the H _∞ control design are presented, which are concluded from the H _∞ performance analysis results. As applications of the derived results, H _∞ performance analysis and H _∞ control design are carried out for some systems, including two numerical systems, linearised truck trailer system and traffic network system. Discussions show that, the proposed method is effective for these systems and much less conservativeness appears than those given in the existing references.     

Adaptive H_∞ Control for Nonlinear Hamiltonian Systems with Time Delay and Parametric Uncertainties

This paper addresses the adaptive H∞ control problem for a class of nonlinear Hamiltonian systems with time delay and parametric uncertainties. The uncertainties under consideration are some small parameter perturbations involved in the structure of the Hamiltonian system. Both delay-independent and delay-dependent criteria are established based on the dissipative structural properties of the Hamiltonian systems and the Lyapunov-Krasovskii functional approach. In order to construct the adaptive H∞controller, the situation that the parameter perturbation is inexistent in the system is also studied and the controller is designed.The adaptive H∞ control problem is solved under some sufficient conditions which ensure the asymptotic stability and the L2 gain performance of the resulted closed-loop system. Numerical example is given to illustrate the applicability of the theoretical results.     

Feedback control of nonlinear differential algebraic systems using Hamiltonian function method

Many complex dynamic systems, such as power systems, robotic systems, etc. can be modeled as the following nonlinear differential algebraic systems (NDAS) [1-4](1) where the vector 1 x1 ∈ X 1 ? Rn represents the state variable, and x2 ∈X2? Rn2 is the al…     

Robust H_∞ control for discrete-time polytopic uncertain systems with linear fractional vertices

The robust H∞ control problem for discrete-time uncertain systems is investigated in this paper. The uncertain systems are modelled as a polytopic type with linear fractional uncertainty in the vertices. A new linear matrix inequality (LMI) characterization of the H∞ performance for discrete systems is given by introducing a matrix slack variable which decouples the matrix of a Lyapunov function candidate and the parametric matrices of the system. This feature enables one to derive sufficient conditions for discrete uncertain systems by using parameter-dependent Lyapunov functions with less conservativeness. Based on the result, H∞ performance analysis and controller design are carried out. A numerical example is included to demonstrate the effectiveness of the proposed results.     

A neuro‑observer‑based optimal control for nonaffine nonlinear systems with control input saturations

In this study, an adaptive neuro-observer-based optimal control (ANOPC) policy is introduced for unknown nonaffinenonlinear systems with control input constraints. Hamilton–Jacobi–Bellman (HJB) framework is employed to minimize anon-quadratic cost function corresponding to the constrained control input. ANOPC consists of both analytical and algebraicparts. In the analytical part, first, an observer-based neural network (NN) approximates uncertain system dynamics,and then another NN structure solves the HJB equation. In the algebraic part, the optimal control input that does not exceedthe saturation bounds is generated. The weights of two NNs associated with observer and controller are simultaneouslyupdated in an online manner. The ultimately uniformly boundedness (UUB) of all signals of the whole closed-loop systemis ensured through Lyapunov’s direct method. Finally, two numerical examples are provided to confirm the effectiveness ofthe proposed control strategy.     

H2 /H∞ control of networked control system with random time delays

This paper investigates the H 2 /H ∞ control problem for a class of discrete-time networked control systems with random communication time delays. Both sensor-to-controller (S-C) and controller-to-actuator (C-A) random network-induced delays are considered. Two independent Markov chains are used to model the S-C and C-A random delays. The resulting closed-loop system is a jump linear time-delay system induced by two Markov chains. Sufficient conditions for existence of H 2 /H ∞ controller are established by free-weighting matrix and stochastic Lyapunov functions. A simulation example illustrates the effectiveness of the proposed method.     

Robust H∞ dynamic output feedback control for spacecraft rendezvous with poles and input constraint

This paper is concerned with the output feedback control problem for spacecraft rendezvous subject to target angular velocity uncertainty and controller uncertainty, external disturbance and input constraint. A general full-order dynamic output feedback (DOF) controller is proposed. As a stepping-stone, the H_∞ performance requirement, poles and input constraint are analysed separately via linear matrix inequalities (LMIs). Then, with the obtained results, the controller design problem is cast into a convex problem subject to a set of LMI constraints through a critical change of controller variables. Furthermore, when the system states are all available, a reduced sufficient condition of the non-fragile state feedback controller is given. Compared with existing results, the designed controller has overcome the disadvantage of strictly proper DOF controller, where the initial value of the control input is zero. Besides, the constraint on poles placement is relaxed. A numerical simulation is performed to verify the effectiveness of the proposed method.     

Neural network solution for finite-horizon H ∞ state feedback control of nonlinear systems

In this article, neural networks are used to approximately solve the finite-horizon optimal H _∞ state feedback control problem. The method is based on solving a related Hamilton–Jacobi–Isaacs equation of the corresponding finite-horizon zero-sum game. The neural network approximates the corresponding game value function on a certain domain of the state-space and results in a control computed as the output of a neural network. It is shown that the neural network approximation converges uniformly to the game-value function and the resulting controller provides closed-loop stability and bounded L ₂ gain. The result is a nearly exact H _∞ feedback controller with time-varying coefficients that is solved a priori offline. The results of this article are applied to the rotational/translational actuator benchmark nonlinear control problem.     

Event-triggered H∞ consensus control for input-constrained multi-agent systems via reinforcement learning

This article presents an event-triggered H∞ consensus control scheme using reinforcement learning (RL) for nonlinear second-order multi-agent systems (MASs) with control constraints. First, considering control constraints, the constrained H∞ consensus problem is transformed into a multi-player zero-sum game with non-quadratic performance functions. Then, an event-triggered control method is presented to conserve communication resources and a new triggering condition is developed for each agent to make the triggering threshold independent of the disturbance attenuation level. To derive the optimal controller that can minimize the cost function in the case of worst disturbance, a constrained Hamilton–Jacobi–Bellman (HJB) equation is defined. Since it is difficult to solve analytically due to its strongly non-linearity, reinforcement learning (RL) is implemented to obtain the optimal controller. In specific, the optimal performance function and the worst-case disturbance are approximated by a time-triggered critic network; meanwhile, the optimal controller is approximated by event-triggered actor network. After that, Lyapunov analysis is utilized to prove the uniformly ultimately bounded (UUB) stability of the system and that the network weight errors are UUB. Finally, a simulation example is utilized to demonstrate the effectiveness of the control strategy provided.     

Dynamic output feedback H ∞ control for networked control systems with quantisation and random communication delays

This article is concerned with the dynamic output feedback H _∞ control problem for networked control systems with quantisation and random communication delays, where the random communication delays from the sensor to the controller and from the controller to the actuator are considered simultaneously. A novel quantised random delay model is proposed, and by using this model, the relationship of the quantisations, delays and the system performance is studied. The quantiser considered here is dynamic and composed of an adjustable zoom parameter and a static quantiser. With the condition on the quantisation range and the error bound satisfied, a quantised H _∞ control strategy is derived such that the closed-loop system is exponentially mean-square stable and with a prescribed H _∞ performance bound. An example is presented to illustrate the effectiveness of the proposed method.     

Non-fragile H∞ dynamic output feedback control for uncertain Takagi–Sugeno fuzzy systems with time-varying delay

This paper mainly focuses on the problem of non-fragile H_∞ dynamic output feedback control for a class of uncertain Takagi–Sugeno fuzzy systems with time-varying state delay. Based on a new type of Lyapunov–Krasovskii functional without ignoring any subtle integral terms in the derivatives, a less conservative dynamic output feedback controller with additive gain variations is designed, which guarantees that the closed-loop fuzzy system is asymptotically stable and satisfies a prescribed H_∞-performance level. Furthermore, the obtained parameter-dependent conditions are given in terms of solution to a set of linear matrix inequalities, which improve some existing relevant results. Finally, numerical examples are given to illustrate the effectiveness and merits of the proposed method.     

Adaptive H_∞ Synchronization of Master-slave Systems with Mixed Time-varying Delays and Nonlinear Perturbations: An LMI Approach

This paper proposes an adaptive synchronization problem for the master and slave structure of linear systems with nonlinear perturbations and mixed time-varying delays comprising different discrete and distributed time delays. Using an appropriate Lyapunov-Krasovskii functional, some delay-dependent sufficient conditions and an adaptation law including the master-slave parame- ters are established for designing a delayed synchronization law in terms of linear matrix inequalities(LMIs). The time-varying cont...     

Decentralised indirect adaptive output feedback fuzzy H ∞ tracking design for a class of large-scale nonlinear systems

A novel decentralised indirect adaptive output feedback fuzzy controller with a compensation controller and an H _∞ tracking controller is presented for a class of uncertain large-scale nonlinear systems in this article. The compensator adaptively compensates for interconnections between subsystems as well as mismatched errors, while the H _∞ controller suppresses the effect of external disturbances. Based upon the combination of fuzzy inference systems, a state observer, H _∞ tracking technique and the strictly positive real condition, the proposed overall observer-based decentralised algorithm guarantees not only asymptotical tracking of reference trajectories but also an arbitrary small attenuation level of the unmodelled error dynamics including the disturbances on the tracking control. Simulation results substantiate the effectiveness of the proposed scheme.     

Dual-terminal event-triggered dynamic output feedback H∞ control for aero engine networked control systems with quantization

This study deals with the problem of dual-terminal event-triggered dynamic output feedback (DOF) control for aero engine networked control systems (NCSs) subject to network-induced delay, external disturbance, and quantization effects. First, we established a generalized mathematical model of the aero engine. Second, a dual-terminal dynamic event-triggered mechanism (DETM) was designed to reduce the utilization of the network bandwidth. In addition, a DOF controller with a compensation function was proposed to stabilize the system. By utilizing the Lyapunov-Krasovskii (LK) method, the stability criteria were determined. Accordingly, the design conditions of the DOF controller and DETMs were presented. Furthermore, based on a genetic algorithm (GA), a parameter tuning method was proposed to obtain the allowable delay upper bound with less conservatism. Finally, some examples were presented to show the effectiveness and superiority of the presented scheme.