Asymptotic tracking for linear systems with actuator saturation by output feedback control

This paper addresses the problem of designing an output error feedback control for single-input, single-output nonlinear systems with uncertain, smooth, output-dependent nonlinearities whose local Lipschitz constants are known. The considered systems are required to be observable, minimum phase with known relative degree and known high frequency gain sign: linear systems are included. The reference output signal is assumed to be smooth and periodic with known period. By developing in Fourier series expansion a suitable periodic input reference signal, an output error feedback adaptive learning control is designed which ldquolearnsrdquo the input reference signal by identifying its Fourier coefficients: bounded closed loop signals and exponential tracking of both input and output reference signals are obtained when the Fourier series expansion is finite, while arbitrary small tracking errors are exponentially achieved otherwise. The resulting control is not model based, is independent of the system order and depends only on the relative degree, the reference signal period and the high frequency gain sign.

Markovian jumping systems have arisen naturally in the mathematical modeling of phenomena spanning disciplines in the social sciences, natural sciences, and engineering. This kind of stochastic dynamical systems can be employed to model the dynamics when parameters are subject to random abrupt changes due to sudden environment changes, subsystem switching, system noises, executor faults, and so forth. Much attention has been given to modeling, optimization, and real applications of such stochastic dynamical systems in the literature in recent years. As the advanced control and optimization will provide a basis for the design and application of such stochastic systems, these advanced techniques would result in substantial and sustainable benefits. The accepted papers in this special issue include stochastic stability, stabilization, stochastic control optimization, system modeling and identification methods, predictive control, signal processing, robust filtering, multiagent systems, networked control systems, time-delayed systems, neural networks, the Takagi-Sugeno fuzzy systems, simulated annealing, and fault detection methods.

Magnetorheological fluid (MRF) dampers have been utilized in semi-active air suspension (SAAS) due to their attractive advantages. This paper investigates a novel robust fuzzy output feedback controller for semi-active air suspension with MRF damper (SAAS-MRFD), considering time delay and actuator saturation. An aero-thermodynamics theory is first utilized to describe the nonlinear air spring. The damping force of the MRF damper is represented by a hyperbolic tangent model. The interval type-2 (IT-2) Takagi–Sugeno (T-S) fuzzy method is second employed to capture those nonlinearities of the air spring and MRF damper. Considering the difficulty to measure all states, a novel dynamic output feedback (DOF) controller is developed by an appropriate Lyapunov–Krasovskii function and the reciprocally convex technique with consideration of time delay, actuator saturation, and output constraints. The effectiveness of the proposed controller is validated by both simulation and a quarter-car test rig (QCTR). The results indicate that the proposed controller has better performance in vibration reduction than the recent similar controllers in the literature.

This study employs the free-weighting matrix approach to investigate the output feedback control of a linear discrete-time system with an interval time-varying delay. First, the delay-dependent stability is analyzed using a new method of estimating the upper bound on the difference of a Lyapunov function without ignoring any terms; and based on the results, a design criterion for a static output feedback (SOF) controller is derived. Since the conditions thus obtained for the existence of admissible controllers are not expressed strictly in terms of linear matrix inequalities, a modified cone complementarity linearization algorithm is employed to solve the nonconvex feasibility SOF control problem. Furthermore, the problem of designing a dynamic output feedback controller is formulated as one of designing an SOF controller. Numerical examples demonstrate the effectiveness of the method and its advantage over existing methods.

The internal model principle of control theory

This paper considers linear systems subject to sensor and actuator saturations, for which a dynamic output feedback controller has been a priori designed. The effects of unmodeled dynamics appearing as additive uncertainties are studied with respect to the regional (local) stability of the closed-loop system. Constructive conditions based on matrix inequalities, or at least linear matrix inequalities (LMI) are proposed in order to minimize the influence of these unmodeled dynamics on both the estimate of the closed-loop system basin of attraction and on the performance.

Output-feedback control of uncertain nonlinear systems using a self-structuring adaptive fuzzy observer

Linear programming optimization is widely used in several application areas. One possible application of this optimization technique, which has not received sufficient attention, is process control. In particular, the standard structure of linear programming optimization problems allows formulating optimal predictive control schemes with the additional advantage of facilitating the handling of actuator saturation. Actuator saturation appears in many engineering applications and there are several control approaches dealing with this problem. In this article, a very simple predictive control scheme based on linear programming optimization for actuator saturation control is proposed. The main characteristics of the presented scheme are simplicity and practical robustness/performance tuning parameters. First, the simplest possible output-feedback linear programming predictive controller is proposed as a starting point. Next, through several practical observations inspired in classical control engineering, a series of modifications to the basic controller structure are proposed. These modifications aim at effectively increasing the performance and robustness of the control algorithm. The experimental results confirm that the proposed control algorithm can operate effectively under the presence of perturbations, something which is currently not widely reported in the literature for linear programming actuator saturation predictive control.

T–S fuzzy-model-based piecewise [formula omitted] output feedback controller design for networked nonlinear systems with medium access constraint

This paper proposes dynamic output-feedback networked control with actuator saturation and sensor failure for Markovian jump descriptor systems (MJDS). First, the mode-dependent dynamic output-feedback controller is described as a quasi-linear parameter varying system. Then, the stochastic admissibility criterion for the closed-loop system with sensor failure and actuator saturation is obtained as matrix inequalities. To obtain the feasible solution of the non-convex condition, this paper successfully obtains the equivalent condition in terms of strict linear matrix inequalities (LMIs) and the controller gains. A numerical example shows the validity of the proposed result.

In this paper, an extension of the passivity-based output feedback trajectory tracking controller is addressed and implemented on a SCARA robot IBM 7547 by using generalized saturation. Compared with the output feedback controllers, a radial basis function saturated observer-based controller has been introduced. The controller will reduce the risk of actuator saturation effectively via generalized saturation functions. Implementation results are provided to illustrate the efficiency of the proposed controller in dealing with the actuator saturation.

This note investigates the problem of output feedback H∞ control for linear discrete-time systems. Three types of H∞ controllers are considered, namely, static output feedback controllers, dynamic output feedback controllers, and observer-based output feedback controllers. New design conditions for the three type of output feedback controllers are introduced in terms of unified linear matrix inequality (LMI) representations, which guarantee the prescribed H∞ performances of the closed-loop systems. In contrast to the existing LMI conditions for designing the output feedback H∞ controllers, the improvement of the proposed results over the existing ones is shown by theoretical proof and numerical example.

For linear time-varying single-input single-output systems, the paper treats the problem of designing an output feedback controller resulting in an (internally) stable closed-loop system that tracks a given reference signal. The design is accomplished by augmenting the given system to include an internal model of the reference signal. The internal model reduces to the usual form when the given plant is time invariant. An explicit construction for the internal model is given in the case of a step reference.

Adaptive backstepping control of uncertain linear systems under unknown actuator delay

Data-based adaptive neural network optimal output feedback control for nonlinear systems with actuator saturation