Persistent disturbance rejection via static-state feedback

A state feedback /spl Hscr//sub /spl infin//-suboptimal control problem on TSO(3) for a rigid spacecraft with three control torques and disturbances is addressed, the Hamilton-Jacobi inequality associated with a corresponding state feedback /spl Hscr//sub /spl infin//-suboptimal control problem on TS/sup 3/ is solved globally. The /spl Hscr//sub /spl infin//-suboptimal state feedback on TS/sup 3/ involves the Euler parameters and solves the original problem on TSO(3) when the initial values of the Euler parameters are appropriately chosen.

A fault detection filter is designed by minimising the response to confounding noises whilst keeping the fault response constant. A linear quadratic optimisation problem, related to /spl Hscr//sub 2/ and /spl Hscr//sub /spl infin// optimal control is used. The Q matrix of the associated Riccati equation is indefinite in contrast to the indefinite R matrix of /spl Hscr//sub /spl infin// control. We extend linear optimal control theory to solve the fault detection problem in this framework.

Multiobjective frequency domain design aims to find a controller that gives desirable properties to several closed loop frequency responses simultaneously. This problem may be cast as a problem of finding a controller such that the worst-case /spl Hscr//sub /spl infin// norm, i.e. the largest among several /spl Hscr//sub /spl infin// norms, satisfies a prespecified bound. The authors define an upper bound, the /spl rho/ measure, for the worst-case /spl Hscr//sub /spl infin//, norm in terms of a scaled /spl Hscr//sub /spl infin// cost function. The authors show that the problem of finding a controller that minimizes /spl rho/ can be reduced to a finite dimensional convex program for the unknown scales and a standard /spl Hscr//sub /spl infin// problem. The authors give affine matrix inequalities for controller synthesis when the scales are restricted to constant matrices. A numerical example is used to illustrate the advantages of the authors' formulation, over the single objective /spl Hscr//sub /spl infin//, formulation, for solving multiobjective /spl Hscr//sub /spl infin// problems.

Deals with the direct design of state feedback mixed /spl Hscr//sub 2///spl Hscr//sub /spl infin//, control for sampled-data systems. In particular, a state feedback control design method is proposed to achieve the performance tradeoff between /spl Hscr//sub 2/ and /spl Hscr//sub /spl infin// objectives characterized by the Nash game approach in a continuous time domain.

The dynamic linear state feedback control problem is addressed for a class of nonlinear systems subject to time-delay. First, using the dynamic change of coordinates, the problem of global state feedback stabilization is solved for a class of time-delay systems under a type of nonhomogeneous growth conditions. With the aid of an appropriate Lyapunov-Krasovskii functional and the adaptive strategy used in coordinates, the closed-loop system can be globally asymptotically stabilized by the dynamic linear state feedback controller. The growth condition in perturbations are more general than that in the existing results. The correctness of the theoretical results are illustrated with an academic simulation example.

The standard state space solutions to the /spl Hscr//sub /spl infin// control problem for linear time-invariant systems are generalized to nonlinear time-invariant systems. A class of local nonlinear (output feedback) /spl Hscr//sub /spl infin//-controllers are parameterized as nonlinear fractional transformations on contractive, stable nonlinear parameters. As in the linear case, the /spl Hscr//sub /spl infin// control problem is solved by its reduction to state feedback and output estimation problems, together with a separation argument. Sufficient conditions for /spl Hscr//sub /spl infin//-control problem to be locally solved are also derived with this machinery. >

Attempts to solve the state-feedback H/sub 2//H/sub /spl infin// control problem by a LMI technique that allows for uncommon LMI solutions. In order to obtain a common controller ensuring the two performance criteria while allowing uncommon LMI solutions, we figure out what portion of the LMI solution should be constrained. Then, utilizing the freedom of the unconstrained portion, we propose an iterative method to obtain an updated controller gain which further improves the H/sub 2/ performance under the /spl Hscr//sub /spl infin// constraint. An illustrated example is included.

A class of adaptive control systems which are not only asymptotically stable but also optimal or sub-optimal to some meaningful cost functionals, are derived. By relating Lyapunov functions with solutions of Hamilton-Jacobi (-Isaacs) equations, three types of adaptive optimal control problems are solved (Type 1/spl sim/3), and the adaptive /spl Hscr//sup 2/ (Type 2) and /spl Hscr//sup /spl infin// (Type 1 and 3) optimal (sub-optimal) control systems are constructed for generalized adaptive control problems.

This paper presents a rational /spl Lscr//sub 1/ and mixed /spl Lscr//sub 1///spl Hscr//sub /spl infin// compensator design methodology for continuous time systems. The problem formulation involves finding a finite dimensional stabilizing feedback controller that minimizes the /spl Lscr/1 norm of a closed-loop transfer matrix subject to a frequency domain /spl Hscr//sub /spl infin// norm constraint on another closed-loop transfer matrix. It is shown that for a one-block problem the optimal solution can be approximated arbitrarily closely in terms of the closed-loop /spl Lscr//sub 1/ norm, by solving a sequence of convex optimization problems over linear matrix inequalities. Numerical example is provided to demonstrate the effectiveness of this approach.

This paper presents a variational approach to H/sup /spl infin// control with transients in the state feedback case. The problem was formulated in Khargonekar et al. (1991). The approach here provides a precise description with equality, instead of inequality, in the necessary and sufficient conditions for the existence of a linear controller. Furthermore, the solution existence and uniqueness are also proved in terms of certain properties of the indefinite Riccati equations derived in this paper. The linear time-variant plant (LTV) on a finite horizon is considered first, and then the results are extended to the linear time-invariant (LTIV) plant on an infinite horizon. By this approach, it can be directly concluded that only sub-optimal H/sup /spl infin// state feedback control can be achieved from an input/output point of view and that the performance measure /spl gamma/(/spl mu//sup 1/2/ used in this paper) is a strict upper bound.

A controller is designed for automotive active suspension whose purpose is to improve the ride comfort against road disturbances. This disturbance rejection problem is formulated as an l/sub 1/ control problem, i.e., minimization of the effects of disturbances in terms of the l/sub /spl infin//-induced norm. Since l/sub 1/ control theory minimizes the maximum possible amplification of signal magnitude, the l/sub 1/ controller can specify the maximum magnitude of outputs in the time domain, regardless of the frequency of road disturbances. To design a static full state feedback controller, Shamma's l/sub 1/ near-optimal control theory is applied. Although l/sub 1/ control with full state feedback usually can be dynamic and of arbitrarily high order, this theory with a certain approximation is able to construct a simple static state feedback with nonlinearity. Therefore, for a linear quarter vehicle model, a nonlinear controller is designed. Finally, satisfactory performances of the controller are confirmed by numerical analysis.

Nonlinear state feedback for ℓ 1 optimal control

The problem of /spl Hscr//sup /spl infin// stabilization of a class of nonlinear systems with time delay is addressed. We investigate the Lyapunov-Krasovskii approach to deduce general conditions for stabilizing the closed loop system and also enforcing a bound on /spl Hscr//sup /spl infin// performance.

This paper solves a class of optimally scaled /spl Hscr//sub /spl infin// control problems with constant scalings and output feedback. This class of problems is characterized by a special rank-one assumption on the transfer matrix of the nominal plant. It is shown that, under this special assumption, the optimally scaled /spl Hscr//sub /spl infin// problem can be reduced to a convex optimization problem involving linear matrix inequalities, which can be solved numerically. We illustrate the results with an engineering problem; we use our method to find a controller that meets flying quality requirements for an F-16 aircraft despite uncertainty in the location of the center of gravity.

Approaches to uncertainty modeling for robust control of large flexible space structures (LFSSs) such as additive or multiplicative perturbations in /spl Hscr//sub /spl infin// do not work very well because of the special properties of LFSS dynamics. We propose the use of a left-coprime factorization (LCF) of LFSS dynamics in modal coordinates in order to get improved stability margins and performance in robust control design. The plant uncertainty is then described as stable perturbations of the coprime factors accounting for modal parameter uncertainty and unmodeled dynamics. Two multivariable /spl Hscr//sub /spl infin// designs based on LCFs of 46th-order collocated and noncollocated models of an LFSS experimental testbed are presented together with simulation and experimental results to illustrate the technique.