Adaptive Output Feedback Design Using Asymptotic Properties of LQG / LTR Controllers

This technical note introduces an observer-based adaptive output feedback tracking control design for multi-input-multi-output dynamical systems with matched uncertainties. The reported methodology exploits asymptotic behavior of LQG/LTR regulators. Sufficient conditions for closed-loop stability and uniform ultimate boundedness of the corresponding tracking error dynamics are formulated. This method is valid for systems whose nominal linearized dynamics are controllable and observable. We assume that the number of the system measured outputs (sensors) is greater than the number of the control inputs (actuators) and that the system output-to-input matrix product has full column rank. In this case, the system can be “squared-up” (i.e., augmented) using pseudo-control signals to yield relative degree one minimum-phase dynamics. Since it is known that the “squaring-up” problem is solvable for any controllable observable triplet (A, B, C), the proposed design is applicable to systems whose regulated output dynamics may be non-minimum phase or have a high relative degree. A simulation example is presented to demonstrate key design features.

This paper mainly focuses on output feedback practical tracking controller design for stochastic nonlinear systems with polynomial function growth conditions. Mostly, there are some studies on output feedback tracking control problem for general nonlinear systems with parametric certainty in existing achievements. Moreover, we extend it to stochastic nonlinear systems with parametric uncertainty and system nonlinear terms are assumed to satisfy polynomial function growth conditions which are more relaxed than linear growth conditions or power growth conditions. Due to the presence of unknown parametric uncertainty, an output feedback practical tracking controller with dynamically updated gains is constructed explicitly so that all the states of the closed-loop systems are globally bounded and the tracking error belongs to arbitrarily small interval after some positive finite time. An example illustrates the efficiency of the theoretical results.

Adaptive fuzzy tracking control for a class of uncertain nonaffine nonlinear systems with dead-zone inputs

This paper studies the observer-based secure adaptive output feedback orbit tracking control issue for spacecraft systems with false data injection (FDI) attacks. By means of the inertial-line-of-sight coordinate system using relative distance, line-of-sight inclination and deviation angles, the model of spacecraft orbit system is constructed. An observer is designed to estimate unknown system states, thus improving the accuracy of the control system. The mechanism of parameter adaptive law is utilised to estimate the upper bound of false data injection attacks. Based on the back-stepping technique, the recursive scheme is developed to establish virtual and actual control laws step by step. The proposed secure adaptive output feedback tracking control scheme can not only guarantee that the estimation error and the tracking error converge to a small neighbourhood of the origin, but also ensure that the spacecraft orbit closed-loop system is uniformly ultimately bounded via the Lyapunov function. Finally, the effectiveness of the proposed scheme is demonstrated by a numerical simulation example.

This paper investigates an adaptive fuzzy tracking control design problem for single-input and single-output uncertain nonstrict feedback nonlinear systems. For the cases of the states measurable and the states immeasurable, fuzzy logic systems are separately adopted to approximate the unknown nonlinear functions or model the uncertain nonlinear systems. In the unified framework of adaptive backstepping control design, both adaptive fuzzy state feedback and observer-based output feedback control design schemes are proposed. The stability of the closed-loop systems is proved by using Lyapunov function theory. The simulation examples are provided to confirm the effectiveness of the proposed control methods.

This correspondence addresses the problem of designing robust tracking control for a class of uncertain nonlinear MIMO second-order systems. An adaptive neural-network-based output feedback tracking controller is constructed such that all the states and signals involved are uniformly bounded and the tracking error is uniformly ultimately bounded. Only the output measurement is required for feedback. The implementation of the neural network basis functions depends only on the desired reference trajectory. Therefore, the intelligent adaptive output feedback controller developed here possesses the properties of computational simplicity and easy implementation. A simulation example of controlling mass-spring-damper mechanical systems is made to confirm the effectiveness and performance of the developed control scheme.

This paper deals with a design problem of an adaptive output feedback tracking control for systems with a parallel feedforward compensator (PFC) introduced in order to realize the output feedback exponential passive (OFEP) augmented control system. It is well known that one can easily design an adaptive output feedback control system for nonlinear systems satisfying the OFEP conditions. We adopt introduceing a PFC to make a non-OFEP nonlinear system OFEP and propose an adaptive control system design scheme which improves the control performance of the practical control system without the PFC. The effectiveness of the proposed method will be confirmed through experiments of a magnetic levitation system.

The study presents an adaptive neural network output feedback tracking control scheme for a class of complicated agricultural mechanical systems. The scheme includes a dynamic gain observer to estimate the un-measurable states of the system. The main advantages of the authors scheme are that by introducing non-separation principle design neural network controller and the observer gain are simultaneously tuned according to output tracking error, the semi-globally ultimately bounded of output tracking error and all the states in the closed-loop system can be achieved by Lyapunov approach. With the universal approximation property of NN and the simultaneous parametrisation, no Lipschitz assumption and SPR condition are employed which makes the system construct simple. Finally the simulation results are presented to demonstrate the efficiency of the control scheme.

In this paper, an adaptive tracking control approach is developed for a class of rössler chaotic systems with control input saturation by using dynamic surface control technique. Firstly, the nonlinear dynamical models of rössler chaotic systems with control input saturation are given. Then, an adaptive tracking controller is designed in the framework of dynamic surface control, which guaranteed that all the signals of the closed-loop control systems are ultimately uniformly bounded. A compensation control input term is introduced in the design of adaptive tracking controller in order to solve the control input saturation problem. Further, the stability of the closed-loop control systems is analyzed based on the Lyapunov stability theory. Finally, simulation results are given to illustrate the feasibility of the proposed approach.

Adaptive asymptotic tracking control design for high-order uncertain nonlinear systems

This paper provides a design of event-triggered feedback stabilisation scheme for a class of sampled-data singular systems, in which the input matrix corresponding to the algebraic equation is not full column rank. First, unlike the conventional piecewise-constant sampled-data feedback controller, a novel hybrid impulsive and sampled-data state feedback controller is designed, which can effectively match with the algebraic equation at sampling instants. An improved discrete event-triggering mechanism with checking period is proposed to achieve exponential stabilisation. Based on these, by applying the input delay approach and defining a new input-delay dependent Lyapunov functional, a sufficient stability condition is presented which ensures that the solution of the event-triggered control system exists and is unique, and the system is exponentially stable with definite decay rate. The estimate of decay coefficient is also given explicitly. Then, an optimisation-based method is developed to jointly design the hybrid controller gains and the event parameters. Finally, two simulation examples including a linearised 2-generator and 6-bus power network system are given to illustrate the validity of the new approach.

Optimal design of adaptive tracking controllers for non-linear systems

Neural adaptive output feedback tracking control of underactuated AUVs

This paper focuses on the problem of adaptive output feedback tracking control for a class of non-strict-feedback nonlinear systems with unknown control coefficients. By employing a linear state transformation, the original system is transformed to a new system for which control design becomes feasible. Then, after the introduction of a simple input-driven observer, an adaptive output feedback controller which contains only one parameter is developed for such systems by using backstepping technique and variable separation method. The designed controller ensures that all the signals in the closed-loop systems are Semi-globally Uniformly Ultimately Bounded (SGUUB).

In this paper, real-time experiments on adaptive output feedback tracking control of manipulators are presented. The experiments were carried out in a two degrees-of-freedom manipulator. More precisely, the performance of a controller already proposed in the literature is compared with respect to a new one.