Robust control of nonlinear feedback passive systems

In this paper we consider a class of nonlinear systems with uncertain parameters which enter the system nonlinearly. We assume that the uncertain nonlinear system is minimum phase and the uncertain parameters are from a bounded compact set. The problem under consideration is the design of a nonlinear static state feedback controller such that the closed-loop system is passive for all admissible uncertainties.     

Approximate linearization of nonlinear control systems

The paper address the problem of approximate linearization of a nonlinear control system by state feedback or dynamic feedback. The main result proved is that if the fast k d-relative degrees are equal to each other, then the input-output response of a nonlinear control system can be linearized to degree k. Any system having linear d-relative degree can be linearized to any degree by dynamic feedbacks. One example of signal tracking using dynamic feedback linearization method to improve the performance is also given.     

非线性奇异系统非交互控制的反馈实现

研究非线性奇异系统的非交互控制的反馈实现问题．首先给出了非线性奇异系统的向量相对阶与其非交互控制实现的关系；然后对正则非线性奇异系统的反馈控制系统的非交互控制的实现问题，给出了一种可使系统实现非交互控制的反馈律的构造方法。     

Constrained tracking control of nonlinear systems

The problem of tracking control for nonlinear systems subject to bounded-control constraints is considered. A novel nonlinear, continuous-time, predictive control approach is taken. Control laws are obtained for both nonlinear systems that are affine in the control and general nonlinear systems. Efficient and reliable algorithms based on contraction mapping theorems are devised for on-line implementation. Illustrative examples are provided.     

Reduced-order control for a class of nonlinear similar interconnected systems with mismatched uncertainty

In this paper, a class of nonlinear interconnected systems with similar structure is considered. The interconnected system consists of matched and mismatched uncertainties. Based on constrained Lyapunov equations and by exploiting the structure of the interconnected system, a continuous output feedback reduced-order control scheme is presented to stabilize the system robustly. Our approach allows more general forms of known and uncertain interconnections than existing work. The effectiveness of the proposed reduced-order control scheme is illustrated through a numerical example.     

Feedback nonlinear discrete-time systems

In this paper, we design an adaptive iterative learning control method for a class of high-order nonlinear output feedback discrete-time systems with random initial conditions and iteration-varying desired trajectories. An n-step ahead predictor approach is employed to estimate future outputs. The discrete Nussbaum gain method is incorporated into the control design to deal with unknown control directions. The proposed control algorithm ensures that the tracking error converges to zero asymptotically along the iterative learning axis except for the beginning outputs affected by random initial conditions. A numerical simulation is carried out to demonstrate the efficacy of the presented control laws.     

Feedback control of nonlinear stochastic systems for targeting a specified stationary probability density

In the present paper, an innovative procedure for designing the feedback control of multi-degree-of-freedom (MDOF) nonlinear stochastic systems to target a specified stationary probability density function (SPDF) is proposed based on the technique for obtaining the exact stationary solutions of the dissipated Hamiltonian systems. First, the control problem is formulated as a controlled, dissipated Hamiltonian system together with a target SPDF. Then the controlled forces are split into a conservative part and a dissipative part. The conservative control forces are designed to make the controlled system and the target SPDF have the same Hamiltonian structure (mainly the integrability and resonance). The dissipative control forces are determined so that the target SPDF is the exact stationary solution of the controlled system. Five cases, i.e., non-integrable Hamiltonian systems, integrable and non-resonant Hamiltonian systems, integrable and resonant Hamiltonian systems, partially integrable and non-resonant Hamiltonian systems, and partially integrable and resonant Hamiltonian systems, are treated respectively. A method for proving that the transient solution of the controlled system approaches the target SPDF as t→∞ is introduced. Finally, an example is given to illustrate the efficacy of the proposed design procedure.     

Output feedback control for a class of nonlinear systems

This paper studies the global stabilization problem by an output controller for a family of uncertain nonlinear systems satisfying some relaxed triangular-type conditions and with dynamics which may not be exactly known. Using a feedback domination design method, we explicitly construct a dynamic output compensator which globally stabilizes such an uncertain nonlinear system. The usefulness of our result is illustrated with an example.     

Feedback stabilization of nonlinear systems by locally bounded controls

In this paper results are presented on output regulation and stabilization of nonlinear control systems using Lyapunov-based methods. Sufficient conditions for global output regulation and stabilization using locally bounded state feedback are obtained. The approach used here is motivated by the work of Artstein (1983), Sontag (1989) and Tsinias (1989) on the relationship between control Lyapunov functions and feedback stabilization.     

Feedback classification of nonlinear control systems on 3-manifolds

We consider nonlinear control-affine systems with two inputs evolving on three-dimensional manifolds. We study their local classification under static state feedback. Under the assumption that the control vector fields are independent we give complete classification of generic systems. We prove that out of a singular smooth curve a generic control system is either structurally stable and thus equivalent to one of six canonical forms (models) or finitely determined and thus equivalent to one of two canonical forms with real parameters. Moreover, we show that at points of the singular curve the system is not finitely determined and we give normal forms containing functional moduli. We also study geometry of singularities, i.e., we describe surfaces, curves, and isolated points where the system admits its canonical forms.     

Adaptive output-feedback control of nonlinear systems with unknown nonlinearities

In this paper, we consider global adaptive output-feedback control of nonlinear systems in output-feedback form, without a priori knowledge of system nonlinearities. Our proposed adaptive controller is a high-gain linear controller (since we have no knowledge on system nonlinearities), with the high-gain parameter tuned online via a switching logic. Global stability results of the closed-loop system have been proved.     

Output feedback control of nonlinear systems subject to sensor data losses

In this work, we focus on output feedback control of nonlinear systems subject to sensor data losses. We initially construct an output feedback controller based on a combination of a Lyapunov-based controller with a high-gain observer. We then study the stability and robustness properties of the closed-loop system in the presence of sensor data losses for both the continuous and sampled-data systems. We state a set of sufficient conditions under which the closed-loop system is guaranteed to be practically stable. The theoretical results are demonstrated using a chemical process example.     

Bifurcation suppression of nonlinear systems via dynamic output feedback and its applications to rotating stall control

1IntroductionBifurcation control has attracted great attention in thepast two decades[1].The study of bifurcation control atpresent mostly concerns bifurcation stabilization,delay ofthe onset of aninherent bifurcation,changingthe parametervalue of an existing bifurcation point,and so on[1~4].Fromthe stability point of view,a bifurcation point of anonlinear systemis very disadvantageous.Asystemthat hasa bifurcation point may have more than one equilibriumpoint in a neighborhood of the bifurcati…     

Bifurcation suppression of nonlinear systems via dynamic output feedback and its applications to rotating stall control

This paper deals with the problems of bifurcation suppression and bifurcation suppression with stability of nonlinear systems. Necessary conditions and sufficient conditions for bifurcation suppression via dynamic output feedback are presented; Sufficient conditions for bifurcation suppression with stability via dynamic output feedback are obtained. As an application, a dynamic compensator, which guarantees that the bifurcation point of rotating stall in axial flow compressors is stably suppressed, is constructed.     

Robust nonlinear output feedback control for brake by wire control systems

This work proposes a nonlinear output feedback control law for active braking control systems. The control law guarantees bounded control action and can cope also with input constraints. Moreover, the closed-loop system properties are such that the control algorithm allows to detect—without the need of a friction estimator—if the closed-loop system is operating in the unstable region of the friction curve, thereby allowing to enhance both braking performance and safety. The design is performed via Lyapunov-based methods and its effectiveness is assessed via simulations on a multibody vehicle simulator.     

Global output feedback control for uncertain nonlinear feedforward systems

This paper considers a class of uncertain nonlinear feedforward systems with unknown constant growth rate, output polynomial function growth rate and system input function growth rate. Under the most general growth rate condition, only one dynamic gain is used to compensate simultaneously these three types of growth rates, an output feedback controller is constructed to guarantee the boundedness of closed-loop system states and the convergence of original system states.     

Stabilization of a class of nonlinear systems by a smooth feedback control

We consider the stabilizability problem for systems of the form in the neighborhood of an equilibrium point of f(x). First, by means of center manifold theory, a lower order system is introduced. If this system is stabilizable, then so is the original system. Results on the stabilization of the low order system are presented. No resort is taken to Liapunov theory. The relation between stabilizability and controllability is discussed.     

Adaptive output feedback control for nonlinear time-delay systems using neural network

This paper extends the adaptive neural network （NN） control approaches to a class of unknown output feedback nonlinear time-delay systems. An adaptive output feedback NN tracking controller is designed by backstepping technique. NNs are used to approximate unknown functions dependent on time delay, Delay-dependent filters are introduced for state estimation. The domination method is used to deal with the smooth time-delay basis functions. The adaptive bounding technique is employed to estimate the upper bound of the NN approximation errors. Based on Lyapunov- Krasovskii functional, the semi-global uniform ultimate boundedness of all the signals in the closed-loop system is proved, The feasibility is investigated by two illustrative simulation examples.     

Fuzzy adaptive high-gain-based observer backstepping control for SISO nonlinear systems

In this paper, a new fuzzy adaptive control approach is developed for a class of SISO strict-feedback nonlinear systems, in which the nonlinear functions are unknown and the states are not available for feedback. By fuzzy logic systems to approximate the unknown nonlinear functions, a fuzzy adaptive high-gain observer is designed to estimate the unmeasured states. Under the framework of the backstepping design, fuzzy adaptive output feedback control is constructed recursively. It is shown that the proposed fuzzy adaptive control approach guarantees the semi-global boundedness property for all the signals of the resulting closed-loop system. Simulation results are included to illustrate the effectiveness of the proposed techniques.     

Uncertainty modeling and robust minimax LQR control of multivariable nonlinear systems with application to hypersonic flight

For a class of multi‐input and multi‐output nonlinear uncertainty systems, a novel approach to design a nonlinear controller using minimax linear quadratic regulator (LQR) control is proposed. The proposed method combines a feedback linearization method with the robust minimax LQR approach in the presence of time‐varying uncertain parameters. The uncertainties, which are assumed to satisfy a certain integral quadratic constraint condition, do not necessarily satisfy a generalized matching condition. The procedure consists of feedback linearization of the nominal model and linearization of the remaining nonlinear uncertain terms with respect to each individual uncertainty at a local operating point. This two‐stage linearization process, followed by a robust minimax LQR control design, provides a robustly stable closed loop system. To demonstrate the effectiveness of the proposed approach, an application study is provided for a flight control problem of an air‐breathing hypersonic flight vehicle (AHFV), where the outputs to be controlled are the longitudinal velocity and altitude, and the control variables are the throttle setting and elevator deflection. The proposed method is used to derive a linearized uncertainty model for the longitudinal motion dynamics of the AHFV first, and then a robust minimax LQR controller is designed, which is based on this uncertainty model. The controller is synthesized considering seven uncertain aerodynamic and inertial parameters. The stability and performance of the synthesized controller is evaluated numerically via single scenario simulations for particular cruise conditions as well as a Monte‐Carlo type simulation based on numerous cases. It is observed that the control scheme proposed in this paper performs better, especially from the aspect of robustness to large ranges of uncertainties, than some controller design schemes previously published in the literature. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society