Lower Triangular Structure Research Articles

Comments on "Robust stabilization of a class of time-delay nonlinear systems"

The purpose of the above paper by Nguang (ibid. vol.45 (2000)) is to construct a robust memoryless state feedback controller for a class of uncertain time-delay systems with lower triangular structure, namely, strict feedback structure. However, there are some mistakes in the paper. The purpose of this note is to point out the mistakes and propose some suggestions to correct the mistakes. For simplicity, all the symbols in this note are the same as those in original paper.

Output feedback stabilization for stochastic nonlinear systems in observer canonical form with stable zero-dynamics

We study the problem of output feedback stabilization for stochastic nonlinear systems. We consider a class of stochastic nonlinear systems in observer canonical form with stable zero-dynamics. We introduce a sequence of state transformations that transform the system into a lower triangular structure that is amenable for integrator backstepping design. Then we design the output feedback controller and prove that the closed-loop system is bounded in probability. Under an infinite-horizon risk-neutral cost criterion, the controller designed can guarantee an arbitrarily small long term average cost. Furthermore, when the disturbance vector field vanishes at the origin, the closed-loop system is asymptotically stable in the large, and the risk-neutral cost is guaranteed to be zero. With special care, the controller preserves the equilibrium of the nonlinear system.

Adaptive Regulation of High-Order Lower-Triangular Systems with an Unknown Virtual Control Coefficient

This paper deals with adaptive control of a class of linearly parametrized highorder nonlinear systems that are of a lower-triangular structure, but neither feedback Iinearizable nor affine in the control input. In Lin, et al. (2000a) it was shown that such a class of nonlinear systems can be adaptively regulated in a globally stable manner by using a new adaptive control technique called adding a power integrator recursively. In this paper adding a power integrator is extended to adding a power integrator with an unknown constant; called virtual control coefficient.

Adaptive regulation of high-order lower-triangular systems: an adding a power integrator technique

In this paper, a new adaptive control technique called adding a power integrator is proposed, for a class of linearly parametrized high-order nonlinear systems that are of a lower-triangular structure, but neither feedback linearizable nor affine in the control input. Using the adaptive adding a power integrator technique as a basic design tool, we show how to explicitly construct, in a recursive manner, a smooth adaptive controller that solves the problem of adaptive regulation with global stability. The development of the adding a power integrator technique leads to a significant relaxation on the system nonlinearities such as feedback linearizability and affineness, which are known to be two standard hypotheses made in the existing nonlinear adaptive control schemes.

Global H infinty control and almost disturbance decoupling for a class of interconnected non-linear systems

This paper is concerned with a global H infinity control problem for a class of interconnected non-linear systems. We first consider a fairly general clas of large-scale non-linear systems with strong non-linear interconnections. It is shown that the decentralized H infinity control problem for the system can be converted into the centralized control problems associated with a set of auxiliary systems. The solutions to the latter problems in general rely on solutions of their associated Hamilton-Jacobi-Isaacs (HJI) inequalities. Realizing that finding a global solution of the HJI inequality is usually impossible, we then consider a global decentralized almost disturbance decoupling problem (DADDP) and a global decentralized inverse H infinity control problem (DIHCP) for a class of interconnected systems with lower triangular structure. The DADDP is concerned with the design of decentralized control laws that achieve an arbitrarily small disturbance input to the controlled output. The DIHCP involves seeking not only control laws but also state-dependent weights of the control inputs such that the associated global decentralized control problem is solvable. It is shown that the solutions to both the DADDP and DIHCP can be obtained via a recursive design technique. L2-gain from the

Global H ∞ control for a class of interconnected nonlinear systems

Abstract This paper is concerned with a global H ∞ control problem for a class of interconnected nonlinear systems. We first consider a fairly general class of large-scale nonlinear systems with strong nonlinear interconnections. It is shown that the decentralized H ∞ control problem for the system can be converted into centralized H ∞ control problems associated with a set of auxiliary systems whose solutions are related to the Hamilton Jacobi Isaacs (HJI) inequalities. Realizing that finding a global solution of the HJI inequality is usually impossible, we then concentrate on a globally inverse H ∞ , control problem for a class of interconnected nonlinear systems which are transformable to interconnected systems with lower triangular structure. We show that the decentralized control laws and the weights can be constructed explicitly using a two-way (backward and forward) recursive design technique extended from (Isidori and Lin, 1998).

Parallel Strategies for Computing the Orthogonal Factorizations Used in the Estimation of Econometric Models

Parallel strategies based on compound disjoint Givens rotations are proposed for computing the main two factorizations that are used in the solution of seemingly unrelated regression and simultaneous equations models. The first factorization requires the triangularization of a set of upper-trapezoidals after deleting columns. The second factorization is equivalent to updating a lower-triangular matrix with a matrix having a block lower-triangular structure. Theoretical measures of complexity and examples are used for comparing and investigating the various parallel strategies.