Output feedback control of switched nonlinear systems using multiple Lyapunov functions

In this paper, we propose an adaptive fuzzy output feedback control method for trajectory tracking control problem for robotic systems. Using Lyapunov method, we first develop a stable adaptive fuzzy state feedback control algorithm by assuming that the systems output and its derivatives are available for feedback control design. The algorithm combines fuzzy systems with robust adaptive controller. The fuzzy system approximates the certainty equivalent (CE)-based optimal controller while robustifying adaptive control term is used to cope with uncertainties that appeared from the effect of external disturbance, fuzzy approximation errors and other modeling errors. Then, an output feedback form of the position-velocity (state feedback) controller is proposed where unknown velocity signal is replaced by the output of model-free linear estimator. We show via asymptotic analysis that the tracking performance of the output feedback design can recover the performance achieved under the state feedback control design. Finally, the proposed method is implemented and evaluated on a 2-DOF robotic system to demonstrate the theoretical development for the real-time applications.

In this paper, a new continuous output feedback control mechanism is developed for output tracking for a class of high-order multi-input nonlinear systems with an input gain matrix that is positive definite but non-symmetric. The controller yields semiglobal uniformly ultimately bounded (SGUUB) tracking while compensating for unstructured uncertainty in both the drift vector and the input matrix. First, a fullstate feedback controller is designed based on limited assumptions on the structure of the system nonlinearities and the controller is proven to yield SGUUB tracking through a Lyapunov-based analysis. Then, an output feedback control design based on a high gain observer is proposed. A comprehensive stability analysis of the closed-loop system under output feedback is carried out and a recovery of the state feedback SGUUB result is demonstrated for the output feedback control system. Neural network estimation method is employed in both state and output feedback control design to feedforward compensate for the nonlinear system uncertainty.

We propose an algorithm for nonlinear receding-horizon output feedback control by combining a real-time nonlinear optimal state feedback control algorithm and a real-time nonlinear optimal state estimation algorithm. The algorithms of state feedback control and state estimation are obtained by minimizing receding-horizon performance indexes. Application of the stabilized continuation method results in algorithms that do not involve any successive approximation methods. Simulation results of a 2-wheeled car clarify characteristics of the output feedback control algorithm.

In this paper, a nonlinear robust output feedback control is proposed for a class of autonomous underwater vehicles. In specific, we consider the nonlinear mathematical model of a heavy-weight torpedo and design a sliding mode controller to achieve robust stabilization of the closed-loop system in the presence of environmental disturbances and parametric uncertainties. Lyapunovs method is used to present the closed-loop stability analysis of the system. Then, the state feedback sliding mode control law is extended to an output feedback control design using a fourth order observer. It is highlighted that the performance of the state feedback control is recovered arbitrarily fast by the proposed output feedback controller in the presence of parametric uncertainties and environmental disturbances. Finally, the performance of the proposed control design is shown using simulation.

This paper is concerned with the output feedback control problem for a class of nonlinear system with time delay. First, a state feedback controller is design and a sufficient condition with exponential stability is obtained. Second, we study the observer design problem. And we proved that the observer designed in this paper ensure the observation error exponential converge to zero. Furthermore, output feedback controller using state feedback control and observer design is studied.

This chapter presents a general adaptive inverse approach for control of plants with uncertain nonsmooth actuator nonlinearities such as dead-zone, backlash, hysteresis, and other piecewise-linear characteristics which are common in control systems and often limit system performance. This chapter gives an overview of various state feedback and output feedback control designs for linear, nonlinear, single-input and single-output, and multi-input and multi-output plants as well as open problems in this area of major theoretical and practical relevance. A key problem is to develop linearly parametrized error models suitable for developing adaptive laws to update the inverse and feedback controller parameters, which is solved for various considered cases. The chapter shows that control systems with commonly used linear or nonlinear feedback controllers such as a model reference, PID, pole placement, feedback linearization, or backstepping can be combined with an adaptive inverse to handle actuator nonlinearities.

To a non-minimum phase nonlinear system, it was supposed that, if there is an output feedback control that stabilizes the auxiliary system, then there is an output feedback that stabilizes the original system. The existing methods base designing output feedback for non-minimum phase nonlinear system on the hypothesis that there exists output feedback for auxiliary system. However, the auxiliary system could be unobservable. Alternatively, this study aims to create a way to design output feedback for auxiliary systems in unobservable situation. An output state is constructed in the last equation of auxiliary system, which artificially makes the internal dynamics of the auxiliary system observable. Then, a cascade high-gain observer is designed for the auxiliary system, consisting of an extended high-gain observer for external dynamics and a high-gain observer for internal dynamics of the auxiliary system. Therefore, the output feedback control for auxiliary system can be designed via the cascade high-gain observer and a state feedback. Finally, the proposed method is demonstrated by an academic example and an inverted pendulum on a cart in the simulation.

Permanent magnet synchronous motors (PMSM) are mainly used in high-performance and high-efficiency motor drives such as used in railways. PMSM has the performance required for traction motors and is more compact, light weighted and efficient than induction motors. This paper presents the detailed modeling of PMSM drive in Simulink environment and also presents the speed control of PMSM using vector control approach and by use of state feedback (SFB) controller. The observer is designed to eliminate the need of sensors. The observer is designed for estimating any one of the state variable if the other state variable is known thus eliminating the need to sense both speed and current. The state feedback (SFB) controller is designed such to provide zero steady state error. For observation purpose a PI controller is also designed and the results of control actions have been compared and observed that SFB controller are more robust than PI controllers bpth in case of normal and over loading. In this paper, we have designed and simulated the mathematical model of PM synchronous motor and designed the state feedback control system using pole placement method and PI controller using bode plot method, for speed control of PMSM. The controller hence designed is found to be satisfactory and robust over wide range of operating condition and parameter variations.

Impulsive phenomenon and state jumps at switching instants are inevitable control difficulties in the study of stability for switched singular systems. Proportional-derivative (P-D) state feedback may be an effective way to eliminate impulsive behaviors and state jumps. In this work, the problem of stabilization is studied for switched singular systems in the continuous-time case and discrete-time case. A synchronous design method of P-D state feedback controllers is proposed by introducing some free-weighting matrices. Based on P-D state feedback, some sufficient conditions, which can guarantee that the closed-loop systems are normal and stable (NS), are obtained by using multiple Lyapunov functions. Compared with step-by-step design, synchronous design brings more freedom to the design of P-D state feedback controllers and can better improve the dynamic performance of the systems. Finally, simulation examples are given to demonstrate the effectiveness of the proposed methods.

Output feedback (OFB) controllers for switched systems have been typically developed for linear systems. Of the OFB controllers that have been designed for switched nonlinear systems, at least partial knowledge of the system parameters is required, or the system results in local stability. In this paper, an OFB, time-dependent, switched controller is developed for an Euler-Lagrange system with parametric uncertainty and exogenous disturbances. The time-dependent switching signal is designed using an average dwell-time scheme based on multiple Lyapunov functions such that the switched system achieves semi-global uniformly ultimately bounded (UUB) tracking with arbitrary switching sequences.

In this paper, the transient stabilization of power systems will be enhanced using optimal nonlinear feedback control. To this end, a partial differential equation called Hamilton-Jacobi-Belman (HJB), should be solved, which does not have a closed form solution in general. Nevertheless, there are some approximate solutions to solve HJB equations. In this paper, by using a Taylor Series expansion, a sub-optimal nonlinear control law is obtained. As a result, a transient controller for a single-machine infinite-bus power system is designed. Also, the superiority of the designed nonlinear controller in some grounds like increasing the region of asymptotic stability of the system or in other words, increasing the domain of validity is shown. Simulation results reveal the effectiveness of the proposed approach.

This paper presents a systematic approach to design observer-based output feedback controllers for hybrid dynamical systems arising from bipedal walking. We consider a class of parameterized observer-based output feedback controllers for local exponential stabilization of hybrid periodic orbits. The properties of the Poincare map are investigated to show that the Jacobian linearization of the Poincare map takes a triangular form. This demonstrates the nonlinear separation principle for periodic orbits. In particular, the exponential stabilization of hybrid periodic orbits under dynamic output feedback control can be achieved by solving separate eigenvalue placement problems for the nonlinear state feedback and the observer. The paper then solves the state feedback and observer design problems by employing an iterative algorithm based on a sequence of optimization problems involving bilinear and linear matrix inequalities. The theoretical results are confirmed by designing a nonlinear observer-based output feedback controller for underactuated walking of a 3D humanoid model with 18 state variables, 54 state feedback parameters, and 271 observer parameters.

This paper investigates the stabilization problem of a class of singular fractional order fuzzy systems with order $$0<\alpha <1$$ . Firstly, by the method of full rank decomposition of matrix, equality constraint of admissibility criterion in most existing literature is eliminated. Next, we present a stabilization criterion for singular fractional order Takagi–Sugeno (T–S) fuzzy systems by designing non-fragile state feedback controllers. Then, applying an equivalent form of original system in admissibility, the non-fragile output feedback controllers are designed to guarantee the closed-loop systems stable. And for fractional order $$1<\alpha <2$$ case, using similar designing approaches, strict linear matrix inequality (LMI) stabilization criteria based on non-fragile state and output feedback controller are obtained. Finally, two numerical simulation examples are given to illustrate the effectiveness of the proposed method.

Design of output feedback semiglobally practically input-to-state (SPIS) stabilizing controllers for nonlinear strict-feedback networked systems is considered. We first design continuous-time state feedback globally asymptotically (GA) stabilizing controllers and discrete-time reduced-order observers and combine the emulation of state feedback controllers and the designed observers to construct discrete-time output feedback controllers. Then we show that the designed controllers SPIS stabilize nonlinear strict-feedback networked control systems when transmission intervals are sufficiently small and communication networks satisfy suitable assumptions. A numerical example is also given to illustrate the efficiency of proposed design of controllers.

The inverted wedge is a planar robot with two degrees of freedom and a single control input (i.e., it is "underactuated"). The goal is to develop a digital controller that can balance the wedge in the inverted position by shifting a weight on the top of the wedge. Because it is underactuated and has complicated nonlinear dynamics, the inverted wedge is a good testbed for the development of nonconventional advanced control techniques and comparative analysis between control methods. We begin with the development of a nonlinear state feedback controller and direct and adaptive fuzzy controllers, that we will later use as a baseline comparison to show what type of performance is possible for this testbed. Then we develop an adaptive control routine based on the genetic algorithm (GA). In particular, we will show that a GA can be used online in real-time to produce a particularly effective adaptive control method and this is the main contribution of this work. Computational and real-time implementation issues will be discussed and the genetic adaptive strategy will be compared with the state feedback and fuzzy control methods.