State feedback ℋ/sub ∞/-suboptimal control of a rigid spacecraft

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 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. >

A closed-form solution is presented to the H ∞ sub-optimal control problem via state or output feedback. The problem formulation is general and does not impose any restrictions on feedthrough terms between the control input and the controlled output or between the disturbance input and the measurement output variables. It is, however, required that both the transfer function from the disturbance input to the measurement output and the transfer function from the control input to the controlled output have no invariant zeros on the jw axis and that they satisfy certain geometric conditions. For the same class of systems, the conditions under which the H ∞ optimal control problem, via state feedback, has a solution are given. Moreover, explicit expressions for the optimal solutions are provided. Finally, the pole/zero cancellations in the closed-loop system resulting from the H ∞ optimal or sub-optimal state or output feedback are examined.

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.

In contrast with /spl Hscr//sub /spl infin// and /spl Hscr//sub 2/ control theories, the problem of persistent disturbance rejection (l/sup 1/ optimal control) leads to dynamic controllers, even when the states of the plant are available for feedback. Using viability theory, Shamma showed (1993), in a nonconstructive way, that in the state-feedback case the same performance achieved by any dynamic linear time-invariant controller can be achieved using memoryless nonlinear state feedback. In this paper we give an alternative, constructive proof of these results for discrete- and continuous-time systems. The main result of the paper shows that in both cases, the l/sup 1/ norm achieved by any stabilizing state-feedback linear dynamic controller can be also achieved using a memoryless variable structure controller.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

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.

The nonlinear /spl Hscr//sub /spl infin//-control problem is considered with an emphasis on developing machinery with promising computational properties. The solutions to /spl Hscr//sub /spl infin//-control problems for a class of nonlinear systems are characterized in terms of nonlinear matrix inequalities which result in convex problems. The computational implications for the characterization are discussed. >

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.

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.

This paper deals with the linear /spl Hscr//sub /spl infin// filtering problem for a class of regionally stable uncertain nonlinear systems subject to bounded disturbances and measurement noises. The nonlinear systems is represented by differential-algebraic equations where the system matrices are allowed to be rational functions of the state and uncertain parameters. For this class of systems, LMI conditions are proposed for ensuring a prescribed upper-bound on the /spl Lscr//sub 2/-gain of the input-to-estimation error operator for a given linear asymptotically stable filter. The result is based on polynomial Lyapunov functions. Then, using an appropriate parameterization of the Lyapunov function we extend the analysis result for designing linear filters in a /spl Hscr//sub /spl infin// sense via a convex optimization problem.

In this paper, a behavioral version of the /spl Hscr//sub /spl infin// problem for continuous time, linear time invariant systems is formulated and solved. This general formulation, of which standard /spl Hscr//sub /spl infin// is a special case, provides added freedom in the design of optimal controllers, and can in fact be viewed as a means of designing optimal systems. In particular, the formulation presented allows for singular interconnections, which naturally occur when interconnecting systems. >

A mixed norm performance measure is presented to design the synthesis filters of a multirate filterbank. The mixed norm performance measure is based on the energy as well as the peak value of the error signal. Mathematically, the performance measure minimizes the l/sub 2/-norm of the error signal subject to the l/sub /spl infin//-norm of the error being bounded by some positive value v (this imposes a bound on the peak value of the error signal). The design problem is shown to be that of a mixed /spl Hscr//sub 2///spl Hscr//sub /spl infin// optimization problem. The theory of linear matrix inequalities (LMIs) offers a tractable solution to such multiobjective synthesis problems. The synthesis filters designed with the new performance measure are compared with those obtained by similar induced norm minimization techniques in terms of degree of reconstruction, order of the synthesis filters, SNR, and aliasing distortion.