Disturbance Attenuation For Nonlinear Systems Research Articles

Adaptive dynamic surface control for disturbance attenuation of nonlinear systems

This paper proposes an adaptive dynamic surface control (DSC) approach for disturbance attenuation of uncertain nonlinear systems in the parametric strict-feedback form. In the proposed control system, a smooth projection algorithm is employed to train uncertain parameters. The proposed DSC system can overcome the complexity of an actual controller caused by the recursive differentiation of virtual controllers and parameter adaptation laws in the backstepping design procedure. From Lyapunov stability analysis, it is shown that the proposed controller has H∞ tracking performance to attenuate external disturbances

Finite-time disturbance attenuation of nonlinear systems

This paper is devoted to the finite-time disturbance attenuation problem of affine nonlinear systems. Based on the finite time Lyapunov stability theory, some finite-time H ∞ performance criterions are derived. Then the state-feedback control law is designed and the structure of such a controller is investigated. Furthermore, it is shown that the H ∞ controller can also make the closed-loop system satisfy finite-time H ∞ performance for nonlinear homogeneous systems. An example is provided to demonstrate the effectiveness of the presented results.

Robust disturbance attenuation of nonlinear systems using output feedback and state-dependent scaling

This paper presents an approach to output feedback stabilization with L 2 disturbance attenuation for nonlinear systems in the presence of dynamic uncertainties. A new formulation of state-dependent scaling is introduced into the output feedback design, which unifies treatment of nonlinear and linear gains. The effect of disturbance on the controlled output, which is allowed to be any function of output measurements, can be always attenuated to an arbitrarily small level with global asymptotic stability if the plant belongs to a wide class of triangular systems whose uncertainties do not necessarily have finite linear-gains. The uncertain dynamics is not limited to input-to-state stable systems either. The approach is not only a natural extension of popular approaches in robust linear control, but also advantageous to numerical computation which is applicable to non-triangular systems as well as triangular systems.

Design method for an adaptive robust controller with L2-gain disturbance attenuation for nonlinear systems with uncertainty

A nonlinear feedback control design for the adaptive robust H/sub /spl infin// control problem for nonlinear systems with gain bounded uncertainty is presented. An existing control scheme developed for nonlinear systems with relative degree of one is extended to the case where nonlinear systems have general relative degree. A Lyapunov function is constructed that ensures not only the stability of the closed-loop system but also satisfies the dissipation inequality ensuring L/sub 2/-gain performance. Then the controller can be obtained by the recursive use of the existing control scheme. A closed-form solution for the nonlinear H/sub /spl infin// control problem is provided without using a Hamilton-Jacobi inequality in the general relative degree case. Sufficient conditions which nonlinear systems should satisfy for solvability of the problem are provided.

Discussion on: ‘Stabilization and Disturbance Attenuation of Nonlinear Systems Using Dissipativity Theory’ by A. Astolfi, R. Ortega and R. Sepulchre

Discussion on: ‘Stabilization and Disturbance Attenuation of Nonlinear Systems Using Dissipativity Theory’ by A. Astolfi, R. Ortega and R. Sepulchre

Stabilization and Disturbance Attenuation of Nonlinear Systems Using Dissipativity Theory

In this paper, we survey some recent results on stabilization and disturbance attenuation for nonlinear systems using a dissipativity approach. After reviewing the basic dissipativity concept, we stress the connections between Lyapunov designs and the problem of achieving passivity by feedback. Focusing on physical models, we then illustrate how the design of stabilizing feedback can take advantage of the natural energy balance equation of the system. Here stabilization is viewed as the task of shaping the energy of the system to enforce a minimum at the desired equilibrium. Finally, we show the implications of dissipativity theory as an appropriate framework to study the nonlinear H^ control problem.

Practical L2 disturbance attenuation for nonlinear systems

In this work, a notion of generalized L 2-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 L 2-gain property (i.e. the L 2-gain depends on the operating point). Moreover, a notion of practical L 2-gain attenuation, which extends the standard definition and parallels (mutatae mutandis) the concepts of practical stability, is also proposed.

Smooth Feedback, Global Stabilization, and Disturbance Attenuation of Nonlinear Systems with Uncontrollable Linearization

Problems of global asymptotic stabilization and disturbance attenuation are addressed for a class of highly nonlinear systems that are comprised of a lower dimensional zero-dynamics subsystem and a chain of power integrators perturbed by a nontriangular vector field. It is shown in this paper that global stabilization and disturbance attenuation are solvable by smooth state feedback if one takes full advantage of the characteristics of the system in the feedback design to dominate the nonlinearity rather than to cancel it. A systematic design procedure which is based upon, but generalizes, the recent technique of adding a power integrator is developed for the explicit construction of the smooth controllers. Several examples are presented to demonstrate the key features of the proposed nonlinear control schemes.

Recursive design of nonlinearH ∞ excitation controller

This work is concerned with the problem ofL2 gain disturbance attenuation for nonlinear systems and nonlinear robust control for power systems. In terms of the recurrence design approach proposed, the nonnegative solution of dissipative inequality and the storage function of nonlinearH∞ control for a generator excitation system are acquired. From this storage function, the excitation controller is constructed. Moreover, simulation results manifest the effectiveness of this design method.

Closed-Form Solutions of Stochastic and Deterministic Nonlinear Control Problems

We review our recent results on stabilization and optimal disturbance attenuation for nonlinear systems with uncertainties. The systems are affine in the control and the disturbance but otherwise general. We treat both deterministic and stochastic disturbances. In both cases the disturbance attenuation problem is posed as a differential game (in the stochastic case the player opposed to control is not the noise itself but its covariance). The results are based on control Lyapunov function techniques. The full account of the results is given in our new monograph(Stabilization of Nonlinear Uncertain Systems, Springer, 1998).

On the relation between state feedback and full information regulators in nonlinear singular H/sub ∞/ control

In this paper the relationship between state feedback control laws and full information control laws, i.e. control laws which make explicit use of the disturbance signals, is discussed in the framework of nonlinear singular H/sub /spl infin// control. In particular, it is shown that any (polynomial) full information control law can always be approximated by a state feedback control law, provided that a certain (arbitrarily small) amount of performance is sacrificed. Moreover, the obtained result is used to give alternative proofs and generalizations to some existing results in the area of global disturbance attenuation for nonlinear systems and to establish some new and interesting results regarding the problem of approximate model matching.

Adaptive Controller Design for Tracking and Disturbance Attenuation in Parametric-Strict-Feedback Nonlinear Systems

We develop a systematic procedure for obtaining robust adaptive controllers that achieve asymptotic tracking and disturbance attenuation for nonlinear systems in parametric-strict-feedback form and subject to additional exogenous disturbance inputs. Our approach is performance based, where the objective is to find not only an adaptive controller, but also an appropriate cost functional, compatible with desired asymptotic tracking and disturbance attenuation specifications, with respect to which the adaptive controller is "worst-case optimal." Using the backstepping methodology, worst-case identification schemes, and singular perturbations analysis, we obtain closed-form expressions for the solutions of associated Hamilton-Jacobi-Isaacs equations or inequalities, thereby guaranteeing satisfaction of dissipation inequalities for the adaptive controllers.