一类不确定非线性系统的自适应鲁棒控制

针对一类由非线性微分方程描述的不确定单输入单输出(SISO)系统,提出了一种自适应鲁棒控制算法.设计了一动态滤波器并将其与原系统组成扩展系统,由滤波器求得控制律稳定扩展系统.算法绕开辨识模型参数而是直接估计函数值,加快了控制律的求解.设计了状态误差观测器,用观测器的值构造控制律逼近状态反馈时的控制效果.基于Lyapunov 稳定理论分析了扩展系统的渐近稳定性并给出了闭环稳定的充分条件.最后仿真结果验证了算法的有效性和鲁棒性.     

Stability overlay for adaptive control laws

This paper proposes an architecture referred to as Stability Overlay (SO) for adaptive control of a class of nonlinear time-varying plants. The SO can be implemented in parallel with a wide range of “performance-based” adaptive control laws, i.e., adaptive control laws that seek to improve closed-loop performance, but may be susceptible to instability in the presence of unaccounted model uncertainty. In this architecture, the performance-based adaptive control law designates candidate controllers based on performance considerations, while the SO supervises this selection based upon online robust stability considerations. A particular selection of a performance-based adaptive control law is not specified. Rather, this selection can be from a wide range of adaptive control schemes. This paper provides stability proofs for the SO architecture and presents a simulation that illustrates the applicability of the proposed method.     

Global robust stabilization of cascaded polynomial systems

Global robust stabilization of nonlinear cascaded systems is a challenging problem when the zero-dynamics is not exponentially stable. Recently, some recursive procedure has been developed for handling this problem utilizing the small gain theorem. However, the success of the procedure depends on the satisfaction of some conditions which arise at each step of the recursion. In this paper, we will show that, for the important class of cascaded polynomial systems, the solvability conditions can be made satisfied by appropriately implementing the recursive procedure. This result leads to an explicit construction of the control law.     

Small-gain theorem for ISS systems and applications

We introduce a concept of input-to-output practical stability (IOpS) which is a natural generalization of input-to-state stability proposed by Sontag. It allows us to establish two important results. The first one states that the general interconnection of two IOpS systems is again an IOpS system if an appropriate composition of the gain functions is smaller than the identity function. The second one shows an example of gain function assignment by feedback. As an illustration of the interest of these results, we address the problem of global asymptotic stabilization via partial-state feedback for linear systems with nonlinear, stable dynamic perturbations and for systems which have a particular disturbed recurrent structure.The final version of this work was finished when Z.-P. Jiang held a visiting position at I.N.R.I.A., Sophia Antipolis.     

Global output-feedback path tracking of unicycle-type mobile robots

We present an output-feedback controller that forces the output (position and orientation) of a unicycle-type mobile robot to track a predefined path. A coordinate transformation is first derived to cancel the velocity quadratic terms. An observer is then designed to globally exponentially/asymptotically estimate the unmeasured velocities. The controller synthesis is based on Lyapunov's direct method and the backstepping technique. Our proposed controller works for both internally damped and un-damped cases. Simulations illustrate the soundness of the proposed controller.     

一类不确定非线性系统的鲁棒自适应控制

针对一类输入带有一定的不确定性的非线性系统 ,设计了一种鲁棒自适应控制器。该控制器作用与系统 ,能保证闭环系统信号的全局有界性 ,又能使闭环系统输出任意小。     

State observer-based adaptive fuzzy output-feedback control for a class of uncertain nonlinear systems

This paper aims to develop state observer-based adaptive fuzzy control techniques for controlling a class of uncertain nonlinear systems with bounded external disturbances. An adaptive fuzzy observer is proposed to estimate the system state variables. It is shown that the observation errors obtained from the observer are uniformly ultimately bounded. Applying the estimated system state for design of an output-feedback controller, the uniformly ultimate boundedness of the tracking errors for the resulting closed-loop system can be guaranteed. A typical robot arm system is employed in our simulation studies, and the results demonstrate the usefulness and effectiveness of the proposed techniques for controlling nonlinear systems with bounded external disturbances.     

Global partial-state feedback and output-feedback tracking controllers for underactuated ships

New global partial-state feedback and output-feedback control schemes for tracking control of an underactuated surface ship without sway force available are presented. For the case of partial-state feedback, we do not require measurements of the ship sway and surge velocities, while, for the case of output-feedback, none of the ship velocities are required for feedback. The reference trajectory to be tracked can be a curve including a straight-line. Global nonlinear coordinate changes are introduced to transform the ship dynamics to a system affine in the ship velocities to design observers to globally exponentially estimate unmeasured velocities. The controllers’ development is based on Lyapunov's direct method and backstepping technique, and utilizes the passive property of ship dynamics and their interconnected structure. Numerical simulations are provided to illustrate the effectiveness of the proposed controllers.     

Fuzzy adaptive backstepping robust control for SISO nonlinear system with dynamic uncertainties

In this paper, a fuzzy adaptive backstepping design procedure is proposed for a class of nonlinear systems with three types of uncertainties: (i) nonlinear uncertainties; (ii) unmodeled dynamics and (iii) dynamic disturbances. The fuzzy logic systems are used to approximate the nonlinear uncertainties, nonlinear damping terms are used to counteract the dynamic disturbances and fuzzy approximation errors, and a dynamic signal is introduced to dominate the unmodeled dynamics. The derived fuzzy adaptive control approach guarantees the global boundedness property for all the signals and states, and at the same time, steers the output to a small neighborhood of the origin. Simulation studies are included to illustrate the effectiveness of the proposed approach.     

Robust MPC of constrained discrete-time nonlinear systems based on approximated reachable sets

A robust MPC for constrained nonlinear systems with uncertainties is presented. Outer bounds of the reachable sets of the system are used to predict the evolution of the system under uncertainty. A method that uses zonotopes to represent the approximated reachable sets is proposed. The closed-loop system is ultimately bounded thanks to a contractive constraint that drives the system to a robust invariant set.     

Robust adaptive fuzzy tracking control for a class of strict-feedback nonlinear systems based on backstepping technique

In this paper, the robust adaptive fuzzy tracking control problem is discussed for a class of perturbed strict-feedback nonlinear systems. The fuzzy logic systems in Mamdani type are used to approximate unknown nonlinear functions. A design scheme of the robust adaptive fuzzy controller is proposed by use of the backstepping technique. The proposed controller guarantees semi-global uniform ultimate boundedness of all the signals in the derived closed-loop system and achieves the good tracking performance. The possible controller singularity problem which may occur in some existing adaptive control schemes with feedback linearization techniques can be avoided. In addition, the number of the on-line adaptive parameters is not more than the order of the designed system. Finally, two simulation examples are used to demonstrate the effectiveness of the proposed control scheme.     

Intrinsic robustness of global asymptotic stability

Equivalence is shown for discrete time systems between global asymptotic stability and the so-called integral Input-to-State Stability. The latter is a notion of robust stability with respect to exogenous disturbances which informally translates into the statement “no matter what is the initial condition, if the energy of the inputs is small, then the state must eventually be small”.     

A global output-feedback controller for stabilization and tracking of underactuated ODIN: A spherical underwater vehicle

This paper presents a method to design an output-feedback controller that simultaneously solves global asymptotic stabilization and tracking of an underactuated omni-directional intelligent navigator—a spherical underwater vehicle moving in a horizontal plane (i.e. at a constant depth). The vehicle does not have a sway actuator and has only position and orientation measurements available. The control development is based on Lyapunov's direct method, backstepping technique and use of interconnected structure of the vehicle dynamics. Numerical simulations demonstrate the results.     

Practical L2 disturbance attenuation for nonlinear systems

In this work, a notion of generalized L₂-gain for nonlinear systems, where the gain is considered as a function of the state instead of a (global) constant, is presented. This new notion seems to be adequate to characterize the gain properties of several nonlinear systems which do not possess a uniform L₂-gain property (i.e. the L₂-gain depends on the operating point). Moreover, a notion of practical L₂-gain attenuation, which extends the standard definition and parallels (mutatae mutandis) the concepts of practical stability, is also proposed.     

一类Markov跳跃非线性系统的鲁棒自适应镇定

研究一类具有Markov 跳跃参数的随机非线性系统的鲁棒自适应镇定问题.利用随机控制的Lyapunov 设计方法,对受Wiener 噪声干扰的参数严格反馈形式的跳跃系统,利用backstepping 方法设计参数自适应律和控制律,使得闭环系统状态在4 阶矩意义下全局一致有界,并能收敛到平衡点的任意小邻域内.仿真结果表明了该设计方法的有效性.     

Global stability analysis scheme for a class of nonlinear time delay systems

We consider a class of nonlinear time delay systems created by generalizing the model for FAST TCP, an Internet congestion control algorithm. We achieve a time delay independent sufficient condition for the global asymptotic stability of the class of systems. The sufficient condition is verified by constructing two sequences that represent the lower and upper bound variations of the system trajectory in time, and showing that the two sequences converge to the equilibrium point of the system. The simulation results exemplify that the sufficient condition is valid for global asymptotic stability, and that the sufficient condition is a close approximation to the unknown necessary and sufficient condition for global asymptotic stability.