Kameshwar Poolla

Uniformly optimal control of linear time-invariant plants: Nonlinear time-varying controllers

Abstract It is shown that in the problems of uniformly (or H ∞ −) optimal control of linear time-invariant plants, arbitrary nonlinear, time-varying controllers offer no advantage over linear, time-invariant controllers.

Nonlinear time-varying controllers for robust stabilization

In this paper we consider the problem of robust stabilizallon for a certain class of plants with unstructured, infinite-dimensional uncertainty. We demonstrate that for the problem of robustly stabilizing this class of plants, linear time-invariant controllers perform as well as nonlinear time-varying (NLTV) ones. Ihis, in particular, implies that adaptive control laws offer no advantage as far as the problem of robust stabilization of this class of plants is concerned. As a corollary we demonstrate that the small-gain theorem is both necessary and sufficient for a certain class of NLTV operators.

Robust stabilization of distributed systems

Abstract This paper is devoted to the problem of robust stabilization for a class of distributed plants. We consider the gain margin optimization problem and the robust stabilization problem for multiplicative perturbations. Using techniques from interpolation theory and complex variables, we obtain explicit necessary and sufficient conditions for robust stabilizability. A few examples are included to illustrate the results.

Stabilizability and stable-proper factorizations for linear time-varying systems

The objective of this paper is to study in detail stabilizability and stable-proper factorizations for linear time-varying discrete-time systems. Our main results are: (i) If a linear-time-varying system can be stabilized by dynamic state feedback, then it can also be stabilized by memoryless state feedback. (ii) A complete characterization of the existence of stable-proper factorizations for linear time-varying input/output operators. This characterization is nontrivial; there exist input/output operators that do not admit stable-proper factorizations.

Heuristic approaches to the solution of very large sparse Lyapunov and algebraic Riccati equations

The authors present several algorithms that compute approximate solutions to the Lyapunov equation AX+XA/sup T/+BB/sup T/=0 and the algebraic Riccati equation A/sup T/X+XA-XBR/sup -1/ B/sup T/X+C/sup T/C=0, where A is large and sparse and B and C are low rank. In particular, they test the Krylov subspace approximation and reduced rank integration for the Riccati equation. Although the algorithms are heuristically good, no convergence proofs are as yet available.<<ETX>>

Upper bounds and approximate solutions for multidisk problems

Approximate solutions of multiobjective H/sup infinity /-optimization problems, also referred to as multidisk problems, are considered. The main result is an algorithm that makes it possible to compute an upper bound for linear two-disk problems and also a (suboptimal) controller that achieves this bound. The algorithm involves some graphical techniques which can also be used to demonstrate explicitly the design tradeoffs inherent in problems involving competing objectives. The results can be generalized to multidisk problems. >

On robust stabilization synthesis for plants with block structured modeling uncertainty

In this paper we consider the problem of robust stabilization of plants with additive block-structured uncertainty. This problem reduces to an optimization problem of the form ¿-1,¿,Q in H¿ ||¿(A + BQC) ¿-1||¿, where ¿ is constrained to be block-diagonal. Existing methods addressing this problem require complete knowledge of the scaling functions ¿. In this paper we provide an alternative algorithm which requires only the values of ¿ at the unstable poles of the nominal plant. Determining the corresponding robust controller involves outer function interpolation and we provide here a new procedure for this problem. This procedure yields far lower order interpolants than previous methods. Also, we derive sufficient conditions for infinite stability margins for these problems.

On the stabilizability of linear time-varying systems

This paper deals with problems related to the stabilizability of linear time-varying systems. One of the central results of the paper is that if a system can be stabilized by dynamic state feedback, it can also be stabilized by memoryless (static) state feed-back. A stable-proper factorization theory for linear time-varying systems is also introduced.

Asymptotic performance through adaptive robust control

A novel measure of asymptotic disturbance rejection for a physical system is introduced. A switching-type adaptive controller is presented that provides optimal asymptotic disturbance rejection properties. Bounds that quantify the transient response behavior of this adaptive control scheme are provided. A simulation is presented to illustrate the switching algorithms.<<ETX>>

Nonlinear feedback vs. linear feedback for robust stabilization

The relative merits of nonlinear feedback over linear feedback are investigated in the context of certain robust stabilization problems. In particular an absolute tight computable bound on the radius of unmodeled dynamics against which robust stabilization is possible using nonlinear (adaptive) feedback is presented. This is used to compare nonlinear and linear feedback for robust stabilization. A nonlinear/linear tradeoff ratio is developed to quantify this comparison. The results support the view that nonlinear feedback is of significant advantage in situations where the plant exhibits significantly more parametric modeling uncertainty than dynamic modeling uncertainty.<<ETX>>