Systems In Feedforward Form Research Articles

Feedback Linearizable Feedforward Systems: A Special Class

The problem of feedback linearizability of systems in feedforward form is addressed and an algorithm providing explicit coordinates change and feedback given. At each step, the algorithm replaces the involutive conditions of feedback linearization by some, easily checkable. We also reconsider type II subclass of linearizable strict feedforward systems introduced by Krstic and we show that it constitutes the only linearizable among the class of <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">quasilinear</i> strict feedforward systems. Our results allow an easy computation of the linearizing coordinates and thus provide a stabilizing feedback controller for the original system among others. We illustrate by few examples including the VTOL.

Asymptotic stabilization of dynamically quantized nonlinear systems in feedforward form

This paper studies the stabilizability of an n-dimensional quantized feedforward nonlinear system. The state of that system is first quantized into a finite number of bits, and then sent through a digital network to the controller. We want to minimize the number of transmitted bits subject to maintaining asymptotic stability. In the prior literature, n bits are used to stabilize the n-dimensional system by assigning one bit to each state variable (dimension). Under the stronger assumption of global Lipschitz continuity, this paper extends that result by stabilizing the system with a single bit. Its key contribution is a dynamic quantization policy which dynamically assigns the single bit to the most “important” state variable. Under this policy, the quantization error exponentially converges to 0 and the stability of the system can, therefore, be guaranteed. Because 1 is the minimum number of quantization bits (per sampling step), the proposed dynamic quantization policy achieves the minimum stabilizable bit number for that n-dimensional feedforward nonlinear system.

Disturbance Attenuation of Feedforward Systems With Dynamic Uncertainty

This paper studies the disturbance attenuation problem of a class of nonlinear systems in feedforward form that is subject to both dynamic uncertainty and disturbance. When the disturbance vanishes, the equilibrium of the closed-loop system is globally asymptotically stable. Two versions of small gain theorem with restrictions are employed to establish the global attractiveness and local stability of the closed-loop system at the equilibrium respectively.

Output feedback stabilization and approximate and restricted tracking for a class of cascaded systems

In this note, we discuss the problems of output feedback stabilization for a class of cascaded systems and of (approximate and restricted) output regulation for general nonlinear systems. It is shown that (global) output feedback stabilization for a class of systems in feedforward form can be achieved with a dynamic feedback law, yielding bounded control, and relying on the introduction of a reduced-order observer. The above result, together with standard tools borrowed from the output regulator theory, is instrumental to construct dynamic control laws achieving (approximate) disturbance rejection and output tracking in the presence of (small) disturbance/reference signals generated by a known exosystem.

N-bit stabilization of n-dimensional nonlinear systems in feedforward form

A methodology is presented which allows to design encoder, decoder and controller for stabilizing a nonlinear system in feedforward form using saturated encoded state feedback basically under standard assumption, namely local Lipschitz property of the vector field defining the system. n (respectively, n + 1) bits are used to encode the state information needed to the purpose of semiglobally (globally) stabilizing an n-dimensional system. Minimality of the data rate is discussed.

Stochastic stabilization of nonlinear systems in feedforward form with noisy outputs

We study the problem of globally stabilizing through measurement feedback a class of uncertain stochastic nonlinear systems in feedforward (or upper triangular) form, with state equations affected by a Wiener process adapted to a given filtration of /spl sigma/-algebras and measurements affected by a sample continuous and strongly Markov stochastic process adapted to the same filtration of /spl sigma/-algebras. We propose a step-by step design, based on splitting the system /spl Sigma/ into one-dimensional interconnected systems /spl Sigma//sub j/, j=1,...,n. Moreover, we introduce the notion of practical stability in probability, which corresponds to having a large probability of being the state small in norm whenever the noise affecting the measurements has a "small" second order moment.

N-Bit stabilization of n-Dimensional nonlinear systems in feedforward form

A methodology is presented which allows to design encoder, decoder and controller for stabilizing a nonlinear system in feedforward form using saturated encoded state feedback basically under standard assumption, namely local Lipschitz property of the vector field defining the system. n bits are used to encode the state information needed to the purpose of semi-globally stabilizing an n-dimensional system.

Robust nonlinear motion control of a helicopter

We consider the problem of controlling the vertical motion of a nonlinear model of a helicopter, while stabilizing the lateral and horizontal position and maintaining a constant attitude. The reference to be tracked is given by a sum of a constant and a fixed number of sinusoidal signals, and it is assumed not to be available to the controller. This represents a possible situation in which the controller is required to synchronize the vehicle motion with that of an oscillating platform, such as the deck of a ship in high seas. We design a nonlinear controller which combines recent results on nonlinear adaptive output regulations and robust stabilization of systems in feedforward form by means of saturated controls. Simulation results show the effectiveness of the method and its ability to cope with uncertainties on the plant and actuator model.

Stochastic Stabilization of Nonlinear Systems in Feedforward Form with Noisy Outputs

We study the problem of globally stabilizing through measurement feedback a class of uncertain stochastic nonlinear systems in feedforward form. We propose a step-by step backstepping design, based on splitting the system into one-dimensional interconnected systems ∑j, j = 1, …, n, assuming that for each disconnected system ∑j there exists a measurement feedback stabilizing controller Cj.

Robust nonlinear control of feedforward systems with unmodeled dynamics

We consider nonlinear systems in feedforward form and redesign-nested saturation control laws to guarantee global asymptotic stability in the presence of unmodeled dynamics appearing at the system input. Unlike most previous results, this redesign is applicable to a large class of unmodeled dynamics, including actuators that change the relative degree of the system.

Forwarding in discrete-time nonlinear systems

We propose a family of bounded globally asymptotically stabilizing feedbacks for a class of discrete-time 'feedforward' systems. Our approach is inspired by similar work for continuous-time nonlinear systems in feedforward form. The proposed methodology is constructive and is based on a Lyapunov design and allows the construction of arbitrarily small stabilizing feedbacks.

L2performance induced by feedbacks with multiple saturations

Multi-level saturation feedbacks induce nonlinear disturbance-to-state L 2 stability for nonlinear systems in feedforward form. This class of systems includes linear systems with actuator constraints.