Robust output feedback control for a class of time-varying systems

A robust dynamic output feedback controller synthesis algorithm considering H∞/H2performance and regional pole placement is addressed for a nonlinear system with parameter uncertainties and external disturbance. First, the formulation of a gain‐scheduled mixed‐objective robust dynamic output feedback controller for continuous‐time polytopic linear parameter varying (LPV) systems is presented. To reduce conservativeness, some auxiliary slack variables and parameter‐dependent Lyapunov functions are employed in addition to well‐established performance conditions. Then, sufficient conditions for the desired gain‐scheduled mixed‐objective robust dynamic output feedback controllers are cast into an efficiently tractable finite‐dimensional convex optimization problem in terms of linear matrix inequalities (LMIs). Finally, numerical simulation shows the validity of the proposed controller, which has good stability, strong robustness, satisfied disturbance attenuation ability, and smooth dynamic properties.

Robust adaptive fuzzy filters output feedback control of strict-feedback nonlinear systemsIn this paper, an adaptive fuzzy robust output feedback control approach is proposed for a class of single input single output (SISO) strict-feedback nonlinear systems without measurements of states. The nonlinear systems addressed in this paper are assumed to possess unstructured uncertainties, unmodeled dynamics and dynamic disturbances, where the unstructured uncertainties are not linearly parameterized, and no prior knowledge of their bounds is available. In recursive design, fuzzy logic systems are used to approximate unstructured uncertainties, and K-filters are designed to estimate unmeasured states. By combining backstepping design and a small-gain theorem, a stable adaptive fuzzy output feedback control scheme is developed. It is proven that the proposed adaptive fuzzy control approach can guarantee the all the signals in the closed-loop system are uniformly ultimately bounded, and the output of the controlled system converges to a small neighborhood of the origin. The effectiveness of the proposed approach is illustrated by a simulation example and some comparisons.

The paper presents a robust nonlinear output feedback control system for the attitude control of satellites, with unstructured (unmodelled) dynamics in elliptic orbits, using solar radiation pressure. The nonaffine-in-control spacecraft model includes the gravity gradient torque, the control torque produced by two solar flaps, and external time-varying disturbance torque. The objective is to control the pitch angle of the spacecraft using the solar flaps. A robust feedback linearizing control law is derived for the trajectory control of the pitch angle. The controller includes a high-gain observer, which estimates the derivatives of the pitch angle as well as a lumped unstructured nonlinearity including the external disturbance moment in the pitch dynamics for synthesis. In the closed-loop system, the designed output feedback law accomplishes large angle rotational maneuvers. Simulation results are presented which show that in the closed-loop system, precise pitch angle control is accomplished, despite unmodelled nonlinearities and external disturbance torque in the model.KeywordsPitch AngleElliptic OrbitSolar Radiation PressureAttitude Control SystemSolar SailThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

In present work we consider a multidimensional linear system with additive inputs (controls) and noise governed by a Brownian motion. We allow parameters of system to change in time. In addition we assume that exact form of coefficients is not known, rather intervals within which these coefficients fluctuate are given. In addition, we do not know exact state of system, rather we observe output correlated with this state. The set of allowable controls are feedback controls based on observation of output and an ideal model dynamics. With each control we associate a performance functional characterizing the quality of tracking process and objective is to construct a robust feedback control which minimizes maximal performance functional within class of systems with nonstochastic coefficients fluctuating in same intervals as those of our problem.

This paper proposes guaranteed cost design of robust output feedback controller for continuous linear parametric uncertain systems. New necessary and sufficient conditions for static output feedback stabilizability of linear continuous time systems underly the design procedure. Proposed algorithms are computationally simple and tightly connected with the Lyapunov stability theory and the LQR optimal state feedback design. The proposed approach allows for prescribing the structure of the output feedback gain matrix (including the decentralized one) by the designer. New design method proposed in this paper, exploit genetic algorithm to design robust controller with guaranteed cost for polytopic linear continuous time systems. Numerical example is given to illustrate the performance of the proposed robust controller.

A robust adaptive NN-based output feedback control scheme is presented for a dynamic positioning ship with uncertainties and unknown external disturbances. We tackle the problem that velocity vector of a ship is not available by employing a high-gain observer, and develop the proposed control approach by combing vectorial backstepping with dynamic surface control approach, which is simpler and easier to implement in engineering practice. The neural network (NN) approximation technique is used to compensate for the uncertainties and unknown external disturbances, and it removes the requirement for the prior knowledge about the vessel parameters and external disturbances. Also, it is demonstrated that the proposed control strategy can force the position and yaw angle of a dynamic positioning ship to approach the desired point while guaranteeing all singles of the designed closed-loop dynamic positioning system semi-globally uniformly ultimately bounded by means of the Lyapunov function. Simulation results of a supply ship illustrate the effectiveness of the proposed scheme.

Output feedback robust stabilization of switched fuzzy systems with time-delay and actuator saturation

\(\mathrm{{H}}_{2}\) and \(\mathrm{{H}}_{\infty }\) optimal control are two important breakthroughs in modern robust control. In recent years, the \(\mathrm{{H}}_{2}\) and \(\mathrm{{H}}_{\infty }\) controller design techniques have gained a lot of research attention. Both have strong theoretical basis and are efficient algorithms for synthesizing optimal controllers. The performance of \(\mathrm{{H}}_{2}\) robust controller is useful to handle stochastic aspects such as measurement noise and capture the control cost. In the robust \(\mathrm{{H}}_{2}\) approach, the controller is designed to minimize an upper bound on the worst case \(\mathrm{{H}}_{2}\) norm for a range of admissible plant perturbations. When a model under analysis is applied with \(\mathrm{{H}}_{2}\) robust controller, the closed loop system will have a good dynamic system performance, but it has poor robustness for the external disturbances of the uncertain system model. The performance of \(\mathrm{{H}}_{\infty }\) is convenient to enforce robustness to model uncertainty, but it is based on compromising system performance. Their combination, the mixed \(\mathrm{{H}}_{2}/\mathrm{{H}}_{\infty }\) allows intuitive quadratic performance specifications of the \(\mathrm{{H}}_{2}\) synthesis with robust stability requirements specifications expressed by the \(\mathrm{{H}}_{\infty }\) synthesis. In time domain aspects, satisfactory time response and closed loop damping can often be achieved by enforcing the closed loop poles into a predetermined region of the left half plane. Combining these requirements to form so-called mixed \(\mathrm{{H}}_{2}/\mathrm{{H}}_{\infty }\) design with regional pole placement constraints allows for more flexible and accurate specification of closed-loop behavior. This chapter introduces the work of design of improved LMI-based robust output feedback controller and related simulations.

The deployment of Autonomous Underwater Vehicles (AUVs) for ocean observation is one of the important methods in marine scientific research. The stability of AUV attitude control determines the efficiency and safety of underwater operations. In practical systems, the actuators carried by AUVs have saturation, and the saturation of the actuators greatly affects the performance and stability of AUV attitude control. This article designs an anti-windup [Formula: see text] robust state feedback controller and an anti-windup [Formula: see text] robust dynamic output feedback controller for the pitch attitude control of AUVs to solve the pitch attitude control problem of AUVs subject to input constraints. Firstly, building a Linear-parameter varying (LPV) model for the AUV. Then, we design two anti-windup [Formula: see text] robust controllers based on LPV model. Simulation results verify the reasonable of LPV model and the effectiveness of proposed controllers. Proposed controllers can enable the system to quickly reach the desired attitude under input constraints.

A vector decomposition approach to F–M model realization and its application to robust observed-state feedback control

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 paper addresses the problem of robust output feedback controller design with guaranteed cost and multiple quadratic Lyapunov function for linear switched systems in the continuous-time domain. The approach followed in this paper looks at the existence of switched quadratic Lyapunov function to check asymptotic stability of the switched system under consideration. Two different linear matrix inequality based conditions allow checking the existence of a family of quadratic Lyapunov functions. Then, a switched robust output feedback design method is established. The proposed method is illustrated on numerical example.

In this paper, a robust output feedback stabilization for a class of Autonomous Underwater Vehicle (AUV) is investigated. Two cases for, nonlinear, decoupled equations of motion of AUV in steering plane are considered in this work. In the first scenario, where all states are measurable, semi-global asymptotic stability for a class of AUV is shown by proposing a state-feedback controller based on Sliding Mode Control (SMC). The stability analysis is evaluated under model uncertainties and parametric variations. Then for the second case, Extended High-Gain Observer (EHGO), augmented with Extended Kalman Filter (EKF) is used to estimate the immeasurable states. It is shown that the states of the closed-loop system with output feedback controller, approach the invariant manifold in finite time and stay there. Efficacy of the proposed controllers is demonstrated with the help of numerical simulations.

Novel direct adaptive robust state and output feedback controllers are presented for the output tracking control of a class of nonlinear systems with unknown system dynamics and disturbances. Both controllers employ a variable-structure radial basis function (RBF) network that can determine its structure dynamically to approximate unknown system dynamics. Radial basis functions are added or removed online in order to achieve the desired tracking accuracy and prevent to network redundancy. The raised-cosine RBF is employed to enable fast and efficient training and output evaluation of the RBF network. The direct adaptive robust output feedback controller is constructed by utilizing a high-gain observer to estimate the tracking error for the controller implementation. The closed-loop systems driven by the variable neural direct adaptive robust controllers are actually switched systems.

A robust output feedback control which globally stabilizes a class of SISO minimum-phase nonlinear systems with known and constant relative degree containing a vector of unknown parameters is developed. The constant parameter vector is not restricted to enter linearly in the state equations but it is assumed to belong to a known compact set and an imprecise knowledge of the nonlinearities (e.g., lookup tables) is allowed. The class of nonlinear systems is determined by geometric conditions; an additional assumption, which generalizes the knowledge of the sign of high-frequency gain for linear systems, is also required. The nonlinearities are restricted to depend, in suitable coordinates, on the output only: no growth conditions, such as sector or Lipschitz, are required. The robust output feedback control stabilizes the system for every value of the parameter vector in a known compact set. The order of the compensator is equal to the relative degree minus one. >