Vibration-Attenuation Controller Design for Uncertain Mechanical Systems with Input Time Delay

In this paper, the problems of exponential stability and control design for switched systems with time-varying delay are investigated. Under a class of switching signals counting with average dwell time, a new less conservative stability condition is proposed for the systems. To facilitate controller design for the switched systems with time-varying input delay, a new state transformation method is developed, with which the non-linear term in matrix inequality is removed. The method is also applicable to the existing stability conditions for controller design, while the existing methods may be not able to obtain computational control procedures from the stability conditions. In this paper, the computational algorithms are established for the stability analysis and control synthesis. Finally, some numerical examples are provided to illustrate the effectiveness of the proposed techniques.

A robust controller is developed for uncertain, second-order nonlinear\nsystems subject to simultaneous unknown, time-varying state delays and known,\ntime-varying input delays in addition to additive, sufficiently smooth\ndisturbances. An integral term composed of previous control values facilitates\na delay-free open-loop error system and the development of the feedback control\nstructure. A stability analysis based on Lyapunov-Krasovskii (LK) functionals\nguarantees uniformly ultimately bounded tracking under the assumption that the\ndelays are bounded and slowly varying.\n

This paper addresses the problem of adaptive tracking control for a class of stochastic nonlinear systems with time-varying input delays, and the nonlinear functions of the systems are with not only the unknown parameters but also the unknown state time-varying delays, which is different from the previous work. In this paper, through a state transformation, the system can be easily transformed into a system without the time-varying input delay; the appropriate Lyapunov–Krasovskii functionals are used to compensate the unknown time-varying delay terms, and the quadratic functions instead of the quartic functions often utilized in the existing results are used as Lyapunov functions to analyze the stability of systems and the hyperbolic tangent functions are introduced to deal with the Hessian terms. Fuzzy logic systems (FLSs) in Mamdani type are used to approximate the unknown nonlinear functions. Then, based on the backstepping technique, the adaptive fuzzy controller is designed. The three main advantages of the developed scheme are that (i) unlike the existing results which deal with the nonlinearly parameterized functions by using the separation principle, the nonlinearly parameterized functions are lumped into the continuous functions which can be approximated by using the FLS; (ii) the number of the adjusted parameters only depend on the order of the investigated systems, which can reduce the computational burden greatly; and (iii) the existence of the time-varying input delay such that the controller design becomes much more difficult, and in this paper, it can be dealt with by using an appropriate state transformation. It is proven that all the signals of the closed-loop system are semi-globally uniformly ultimately bounded in probability, whereas the tracking error converges to a small neighborhood of the origin. Finally, simulation results are provided to show the effectiveness of the proposed approach.

In this paper, a novel online tube model predictive control (Tube-MPC) method is proposed for flexible hypersonic vehicle with time-varying input delay. The polytopic linear parameter varying (LPV) model with time-varying input delay is established and further transformed into a polytopic LPV delay-free model by input delay model transformation (IDMT). Since the flexible states cannot be measured accurately due to vehicle body deformation, the polytopic Luenberger observer is developed. To reduce control conservatism, substitute observations are used to replace the actually observed states such that the new reduced control error invariant set (CEI) is generated. On the basis, the Tube-MPC controller is designed, where the offline robust feedback control law and the online nominal control law are devised via linear matrix inequality (LMI) separately. For figuring out the invariant set of nominal control, an offline-online synthesized method is proposed by combining interpolation-based offline computation (IOFC) with substitute observation-based online computation (SOOC). In IOFC, the sequences of observation error invariant set (OEI) and CEI are computed offline iteratively and further interpolated so as to reduce online computation burden. The online judgement and update mechanism is proposed in SOOC. When the observed states enter the expanded invariant set constructed by the interpolated OEI and CEI, the substitute observation-based control error invariant set (SOCEI) will be calculated online and accordingly the nominal control law can also be updated. The simulation results verify the proposed control method’s effectiveness for flexible hypersonic vehicle with time-varying input delay.

In this paper, a dynamic decoupling approach is proposed to improve the robust Takagi-Sugeno (T-S) fuzzy model-based control to cope with system uncertainty, input actuator nonlinearity, and input time delay. First, the basic dynamic decoupling concept is introduced by involving virtual input dynamics, such that the system uncertainty and control input are decoupled in each fuzzy rule. This leads to simplified linear matrix inequality (LMI) conditions. Next, the dynamic decoupling approach is extended to controlling uncertain systems with input actuator nonlinearity (e.g., saturation, quantization, dead-zone, etc.) or time-varying input delay. Due to the decoupling between uncertainty, actuator nonlinearity, and input delay, more relaxed stability conditions are obtained for the asymptotic stability and H ∞ control performance. Furthermore, the limit on the initial condition is removed when considering input saturation. Larger and faster time-varying state and input delays are allowed under fewer LMIs. Finally, to show the advantages of the developed control method, numerical simulations are carried out on an inverted pendulum (subject to either the saturation, quantization, or delay input), a delay mass-spring-damper system, and a delay truck-trailer system.

A novel methodology is proposed for robust gain-scheduled PID controller design for uncertain LPV systems. The proposed design procedure is based on the parameter-dependent quadratic stability approach. A new uncertain LPV system model has been introduced in this paper. To access the performance quality the notion of a parameter varying guaranteed cost is used. Numerical examples show the benefit of the proposed method.

This paper presents a scheme to design a tracking controller for a class of uncertain nonlinear systems using a robust feedback linearization approach. The scheme is composed of two steps. In the first step, a linearized uncertainty model for the corresponding uncertain nonlinear system is developed using a robust feedback linearization approach. In this step, the standard feedback linearization approach is used to linearize the nominal nonlinear dynamics of the uncertain nonlinear system. The remaining nonlinear uncertainties are then linearized at an arbitrary point using the mean value theorem. This approach gives a multi-input multi-output (MIMO) linear uncertain system model with a structured uncertainty representation. In the second step, a minimax linear quadratic regulation (LQR) controller is designed for MIMO linearized uncertain system model. In order to demonstrate the effectiveness of the proposed method, it is applied to a velocity and altitude tracking control problem for an air-breathing hypersonic flight vehicle.

This paper considers the design problems of a delay-dependent robust and non-fragile guaranteed cost controller for singular systems with parameter uncertainties and time-varying delays in state and control input. The designed controller, under the possibility of feedback gain variations, can guarantee that a closed-loop system is regular, impulse-free, stable, an upper bound of guaranteed cost function, and non-fragility in spite of parameter uncertainties, time-varying delays, and controller fragility. The existence condition of the controller, the controller’s design method, the upper bound of guaranteed cost function, and the measure of non-fragility in the controller are proposed using the linear matrix inequality (LMI) technique. Finally, numerical examples are given to illustrate the effectiveness and less conservatism of the proposed design method.

Robust backstepping control of uncertain nonlinear systems with unknown time-varying input delay

In this paper, we consider the problem of composite state and output feedback fuzzy control design for fuzzy time-delay systems with uncertainties via descriptor system approach. We can solve all the state and output feedback controller gain matrices, and some common positive-definite matrices via the Lyapunov stability theorem and the tool of linear matrix inequalities (LMIs). Two sufficient conditions are derived to stabilize the uncertain fuzzy time-delay systems. A numerical example is given to examine the validity of the proposed scheme.

Using the bilinear and tuning bilinear approximation together with the interval arithmetic operation, the discrete-time uncertain model and robust digital redesign of sampled-data uncertain system with input time delay are presented. The system matrices characterizing the stale-space representation of the original uncertain system are assumed to be interval matrices. The developed discrete-time interval model tightly encloses the exactly discretized continuous-time input time-delay uncertain system, and it can be utilized for digital simulation. Based on bilinear approximation, a tuning bilinear approximation is presented to find the digitally redesign controller of the digitally controlled sampled-data uncertain system with input time delay. The digitally redesigned predictor controller is able to closely match the states of the digitally redesigned uncertain sampled-data system with those of the original continuous-time predictor controlled uncertain system.

The output feedback stabilization of polytopic-type uncertain discrete systems with interval-like time-varying state and input delays is studied. Based on a new bounding inequality technique, combining a parameter-dependent Lyapunov functional, a stability criterion is firstly presented in terms of a set of simple convex feasibility tests. Then, the output feedback stabilization conditions are formulated in the form of non-convex matrix inequalities, of which a feasible solution can be obtained by solving an LMI-based minimization problem. The newly proposed inequality lies in the partitioning idea of the varying interval and shows its more tightness over some existing bounding techniques. No free weighting matrix is involved. Two illustrative examples are finally given to verify the advantage and effectiveness of the proposed method.

The dissipative analysis and control synthesis for uncertain singular systems with interval time-varying state and input delays are investigated in this paper. The parametric uncertainty in this paper is assumed to be norm bounded. A sufficient condition, in the form of linear matrix inequality (LMI) with nonlinear constraints, on the existence of robust dissipative controller is established based on the Lyapunov stability theory. In order to solve the nonlinear problem, Cone Complementarity Linearization (CCL) is offered.

Robust linear controller design of uncertain discrete systems with time-varying delay

This paper is concerned with the problem of state-feedback guaranteed cost controller design for uncertain networked systems with both network-induces delay and data dropout taken into consideration. The sufficient condition for the existence of the networked guaranteed quadratic cost controller is obtained in terms of matrix inequalities, and the controller design method is deduced in terms of linear matrix inequalities. Furthermore, the suboptimal networked guaranteed cost controller design method is obtained with cone complementarity linearization algorithm. A numerical example is given to illustrate the proposed method.